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Classification of Variable Stars
A Compilation of Information
Contributions/reviews
Donn Starkey, Auburn, IN
Classification of Variable Stars, A Compilation of Information
John W Shepherd
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History
16-Feb-2006
19-Feb-2006
18-May-2006
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22-May-2006
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31-May-2006
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06-Jun-2006
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09-Jun-2006
22-Aug-2006
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Initial release
Addition of definitions, T Tauri information and correction to Stellar class table.
Incorporated omitted AM Her lecture notes
Addition of additional reading on the accretion discs around T Tauri stars.
(Sargent, Forrest et al. 2006)
Incorporated information obtained from an electronic pre-print on FU Ori and
references information on HAe/Be stars. (Quanz, Henning et al. 2006)
Addition of information for T Tauri stars per reading from (Herbig 1962; Bastian,
Finkenzeller et al. 1983; Bertout 1989)
Incorporated the comments of Donn Starkey on original release of T Tauri
information and embellishments on AM CVn based on his own research.
Embellishments to AM CVn section per (Iben, Sitemap et al.; Iben and Livio
1993; Hellier 2001; Nelemans, Portegies Zwart et al. 2001; Solheim and
Yungelson 2005; Sion, Solheim et al. 2006)
Rebuilt the TOC and index after incorporating key terms in the concordance file
used to generate the index. Corrected an improperly formatted reference (Iben
and Livio 1993)
Updated the index
Added additional information on the Oosterhoff effect as pertains to RR Lyrae
stars that I happened to find in my literature stack of scanned but not digested
info.
Added historical info on Be stars from (Slettebak 1979) but realize there is a
whole lot more information I can’t categorize due to literary controversy.
Added old lecture notes on Super Novae and pulled information from wikipedia
on SN I and II for definitions.
Added additional terms in the Abbreviations/Definitions table.
Rebuilt index
Classification of Variable Stars, A Compilation of Information
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Table of Contents
Introduction ................................................................................................................................................... 5
Definitions...................................................................................................................................................... 6
Spectral Classification .............................................................................................................................. 6
Nomenclature of Variable Stars................................................................................................................ 6
Abbreviations/Definitions .......................................................................................................................... 7
Greek Alphabet ....................................................................................................................................... 19
Constellations ......................................................................................................................................... 20
The Families................................................................................................................................................ 21
Intrinsic.................................................................................................................................................... 21
Eruptive Variables .............................................................................................................................. 21
Luminous Blue Variables (LBVs)/ S Dor Stars .............................................................................. 21
R Coronae Borealis Variables (RCB)............................................................................................. 22
Wolf-Rayet Stars (WR)................................................................................................................... 22
Pre-main Sequence Stars (PMS)................................................................................................... 23
T Tauri stars...............................................................................................................................24
Herbig Ae/Be stars..................................................................................................................... 27
Flare Stars...................................................................................................................................... 27
Pulsating Variables............................................................................................................................. 29
Cepheid Variables.......................................................................................................................... 29
RR Lyrae Variables ........................................................................................................................ 30
AH Leo ....................................................................................................................................... 32
RV Tauri Variables ......................................................................................................................... 32
α Cygni Variables........................................................................................................................... 34
β Cephei Variables......................................................................................................................... 34
Be Stars ......................................................................................................................................... 35
53 Per / mid-B / Slowly-Pulsating B Variables ............................................................................... 36
δ Scuti Variables ............................................................................................................................ 36
Type II Cepheids ............................................................................................................................ 36
Semi-regular and Slow Irregular Variables .................................................................................... 37
Mira Variables (Long Period Variables (LPVs)) ............................................................................. 38
ZZ Ceti Variables ........................................................................................................................... 39
Cataclysmic Variables ........................................................................................................................ 40
Supernovae.................................................................................................................................... 41
SN I ............................................................................................................................................ 41
SN II ........................................................................................................................................... 42
Novae ............................................................................................................................................. 44
NA – Fast Novae ....................................................................................................................... 44
NB – Slow Novae....................................................................................................................... 44
NC – Very Slow Novae .............................................................................................................. 45
NR – Recurrent Novae .............................................................................................................. 45
Nova-like Stars...............................................................................................................................45
AC – AM CVn systems .............................................................................................................. 45
AM – AM Her systems (polars).................................................................................................. 46
DQ – DQ Her systems (intermediate polars, IP) ....................................................................... 50
XY Ari .................................................................................................................................... 51
EX Hya .................................................................................................................................. 52
AO Psc .................................................................................................................................. 52
AE Aqr ................................................................................................................................... 52
WZ Sge.................................................................................................................................. 53
UX – UX UMa systems .............................................................................................................. 53
VY – VY Scl stars (anti-dwarf novae) ........................................................................................ 53
Dwarf Novae .................................................................................................................................. 53
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SS Cygni (UGSS) ...................................................................................................................... 54
U Geminorum (U Gem) ......................................................................................................... 54
SS Cygni (SS Cyg) ................................................................................................................ 55
BV Centauri (BV Cen) ........................................................................................................... 55
Z Camelopardis (UGZ) .............................................................................................................. 55
SU Ursae Majoris (UGSU)......................................................................................................... 55
VW Hyi................................................................................................................................... 56
ER UMa ................................................................................................................................. 56
Z Cha..................................................................................................................................... 56
WZ Sge.................................................................................................................................. 56
Symbiotic Stars .............................................................................................................................. 56
Very Slow Novae ....................................................................................................................... 58
Mira or D-type ............................................................................................................................ 58
S-type......................................................................................................................................... 58
CI Cyg ........................................................................................................................................ 58
AR Pav....................................................................................................................................... 58
AG Peg ...................................................................................................................................... 58
RR Tel........................................................................................................................................ 59
Extrinsic .................................................................................................................................................. 60
Rotating Variables .............................................................................................................................. 60
Ap and roAp Stars.......................................................................................................................... 60
Oblique Pulsator Model ............................................................................................................. 60
Spotted Pulsator Model ............................................................................................................. 60
Ellipsoidal Variables ....................................................................................................................... 61
BY Draconis Variables ................................................................................................................... 61
FK Comae Variables ...................................................................................................................... 62
Pulsars ........................................................................................................................................... 63
Eclipsing Binary Systems ................................................................................................................... 64
Algol Type Eclipsing Binaries (EA) ................................................................................................ 64
β Lyrae Type Eclipsing Binaries (EB) ............................................................................................ 66
RS Canum Venaticorum Eclipsing Binaries (RS) .......................................................................... 67
W UMa Type Variables (EW)......................................................................................................... 68
X-ray Binaries ..................................................................................................................................... 69
Bibliography ................................................................................................................................................ 71
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Introduction
There is ambiguity in classification of some variable stars due to the historical nature of how the various
classes were determined. Classification was and is often based on predominate characteristics of the
light or color curves as the available technology allows. As more sophisticated technological capability
avails itself, the more blurred the classification lines have become. Even as newly published catalogs or
review papers introduce new classes or subclasses of variable stars, the classification in itself becomes
less consistent or the same object appears in multiple classifications.
This discussion, or better yet, exercise of classification follows that of the General Catalog of Variable
Stars (GCVS) and its supplements as a base of understanding with the assistance of American
Association of Variable Star Observers (AAVSO) publications and website and the publication of Sterken
and Jaschek (Sterken and Jaschek 1996). As more classification schemes are proposed, each will be
considered and integrated based on their merit.
Two families of variable stars exist traditionally: intrinsic and extrinsic variable stars regardless of
available classification scheme examined. The intrinsic family is characterized by those stars that vary
due to physical processes in the star itself. The extrinsic family on the other hand is characterized as
stars which vary due to processes external to the star such as if it eclipses with a binary partner or its
rotation coupled with physical processes in the star such as “spots” or orbital motion.
A list of known or accepted (published) attributes is presented as a base understanding of each class of
variable. There are no claims of discovery but only a compilation of the accepted characteristics from the
listed sources or citations to assist in the delineation and the understanding of the differences between
classes. This should not be considered a static document but a living document as better understanding
or refined classification occurs.
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Definitions
Spectral Classification
Class
W
O
B
A
F
G
K
M
L
T
C
S
Spectrum
(Wolf-Rayet stars)
Ionized Helium and metals; weak Hydrogen
Neutral Helium, ionized metals, stronger Hydrogen
Balmer Hydrogen lines dominant, singly-ionized metals
Hydrogen weaker, neutral and singly-ionized metals
Singly-ionized Calcium most prominent, Hydrogen weaker, neutral metals
Neutral metals, molecular lines begin to appear
Titanium Oxide molecular lines dominant, neutral metals
No hydrogen, metallic anhydrides, alkali metals
Methane
Neutral metals, carbon
Zirconium Oxide, neutral metal lines, Yttrium, Barium
Color
Bluish
Blue-white
White
Yellow-white
Yellowish
Orange
Reddish
Red-infrared
infrared
infrared
infrared
Temp (K)
30000 – 70000
31000 – 49000
10000 – 31000
7400 – 10000
6000 – 7400
5300 – 6000
3900 – 5300
2200 – 3900
1500 – 2000
750 – 1000
~ 2500
~ 2000
Nomenclature of Variable Stars
The name of a variable star generally consists of one or two capital letters or a Greek letter, followed by a
three letter constellation abbreviation. There are also variables with names such as V746 Oph and
V1668 Cyg. These are stars in constellations for which all of the letter combinations have been
exhausted. (i.e. V746 Oph is the 746th variable to be discovered in Ophiuchus.)
Variable star names are determined by a committee appointed by the International Astronomical Union
(I.A.U.). The assignments are made in the order in which the variable stars were discovered in a
constellation. If one of the stars has a Greek letter name is found to be variable, the star will still be
referred to by that name. Otherwise, the first variable in a constellation would be given the letter R, the
next S, and so on to the letter Z. The next star is named RR, then RS, and so on to RZ; SS to SZ, and so
on to ZZ. Then, the naming starts over at the beginning of the alphabet: AA, AB, and continuing on to
QZ. This system (the letter J is omitted) can accommodate 334 names. There are so many variables in
some constellations in the Milky Way, however, that additional nomenclature is necessary. After QZ,
variables are named V335, V336, and so on. The letters representing stars are then combined with the
genitive Latin form of the constellation name.
This system of nomenclature was initiated in the mid-1800s by Friedrich Argelander. He started with an
uppercase R for two reasons: the lowercase letters and the first part of the alphabet had already been
allocated for other objects, leaving capitals towards the end of the alphabet mostly unused. Argelander
also believed that stellar variability was a rare phenomenon and that no more than 9 variables would be
discovered in any constellation.
There are also some special kinds of star names. For instance, sometimes stars are given temporary
names until such time as the editors of the General Catalogue of Variable Stars assign the star a
permanent name. An example of this would be N Cyg 1998 – a nova in the constellation of Cygnus which
was discovered in 1998. Another case is of a star that is suspected but not confirmed to be variable.
These stars are given names such as NSV 251 or CSV 3335. The first part of this name indicates the
catalogue in which the star is published, while the second part is the catalogue entry number for that star.
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Abbreviations/Definitions
Term
AAVSO
Accretion disc
AGB
Balmer lines
Blackbody
Blazhko effect
Blue Giant
Bolometric
Bremsstrahlung
Definition
American Association of Variable Star Observers
The thin disc of circling material, destined to settle onto the compact
star lurking at its center
Asymptotic giant branch: A region of the Hertzsprung-Russell diagram
that lies above and parallel to the red giant region. It is occupied by
evolved stars of intermediate to low mass (less than an initial mass of 8
Msun) that have a dormant, helium-filled core surrounded by a heliumfusing shell, on top of which lies a hydrogen-fusing shell. Initially, the
hydrogen-fusing shell produces most of the star’s energy output.
However, the hydrogen shell eventually dumps enough helium “ash”
onto the helium shell that the latter undergoes an explosive event called
a thermal pulse. Although this pulse is barely noticed at the surface of
the star, it serves to increase the mass of the carbon/oxygen core, so
that the size and luminosity of the star gradually increases with time.
As the star climbs the AGB, a wind develops in the star’s envelope that
blows the outer layers into space at a rate of 10-8 to 10-4 Msun per year.
Within this wind, dust particles (crucial to the development of interstellar
clouds and, eventually, protoplanetary systems) are formed from carbon
material dredged up from the core by convection currents. Also through
this mass loss, AGB stars avoid ending as supernovae. When the
envelope of the star is nearly gone, a time of enhanced loss with a rapid
velocity produces a planetary nebula and eventually leaves behind a
white dwarf of 0.6 to 0.7 Msun.
Lines arising from n = 2 transitions of the hydrogen atom;
Line
Angstroms
Color
Hα
6562.5
red
4861.33
aqua
Hβ
Hγ
4340.47
blue
4101.74
blue
Hδ
Strongest absorption when T = 10000 K
A blackbody is a theoretical object that absorbs 100% of the radiation
that hits it. Therefore it reflects no radiation and appears perfectly black.
A secondary variation of the amplitude and period of some RR Lyrae
stars and related pulsating variables, named for its discoverer, the
Russian astronomer Sergei Blazko (1870-1956). The effect is
displayed, for example, by the RR Lyrae star XZ Cygni, which has a
primary pulsation period of about 0.466 days but displays a further
modulation with a 57-day cycle. Although the Blazhko effect is not
properly understood, it is thought to involve double-mode pulsation or,
in some cases, an oblique rotator.
A massive, giant star of spectral type O or B. Blue giants typically have
a luminosity of 10,000 Lsun and a surface temperature of 30,000 K. They
have exhausted their core supply of hydrogen and are evolving to the
stage at which they will expand further and cool to become red giants.
Total energy radiated by an object at all wavelengths usually given in
joules sec-1 (watts)
Electromagnetic radiation that occurs when charged particles with
energies large compared to their rest energies are decelerated over a
very short distance. Since electrons are much lighter than protons,
electron bremsstrahlung is the most common. In bremsstrahlung, a
continuous spectrum with a characteristic profile and energy cutoff (i.e.,
wavelength minimum) is produced. In addition, lines can appear super
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Chandrasekhar limit
imposed, corresponding to the ejection of K and L shell electrons
knocked out of atoms in collisions with the high-energy electrons.
The theoretical upper limit to the mass of a white dwarf star –
approximately 1.4 Msolar; it is named after Subrahmanyan
Chandrasekhar. Above this mass, degenerate electron pressure is
insufficient to prevent gravity from collapsing the star further to become
either a neutron star or, if the Oppenheimer-Volkoff Limit is also
exceeded, a black hole.
CNO cycle
Carbon-Nitrogen-Oxygen or CNO cycle converts hydrogen to helium
according to the following sequence of reactions:
1.
2.
3.
4.
5.
6.
CP
Degenerate object
ELL
GCVS
Giant Star
GWR
HAeBe
Herbig-Haro Object
12
C captures a proton and emits a gamma-ray, producing the
N.
13
N is unstable and beta decays to 13C with a half-life of
approximately 10 minutes.
13
C captures a proton and emits a gamma-ray to become 14N.
14
N captures another proton and emits a gamma-ray to become
15
O.
15
O undergoes a beta decay to become 15N.
15
N captures a proton and emits an alpha-particle (that is, a
nucleus of helium) to close the cycle and return to 12C.
13
Chemically peculiar
White dwarf, neutron star, or black hole
GCVS designation of an ‘ellipsoidal’ type variable stemming from its
elliptical orbit around its companion star.
General Catalogue of Variable Stars; A list of all known variable stars,
first published by the Russian Academy of Sciences in 1948. The
fourth edition, identifying 28,435 stars, came out in three volumes in
1985-87. A companion catalogue of suspected variables is also
produced, the most recent edition being the New Catalogue of
Suspected Variable Stars, with 14,810 objects, in 1982.
A star whose surface layers have expanded and cooled following the
exhaustion of its core hydrogen reserves. In this post main sequence
state the star has a diameter of 5 to 25 times that of the Sun and a
luminosity of a few tens to a few hundreds of times that of the Sun.
Nearby giants include Aldebaran, Arcturus, and Capella. See also red
giant, blue giant, and supergiants.
Gravitational Wave Radiation
Referring to the Pre-main sequence subclass of the Herbig Ae/Be stars
Small patches of nebulosity associated with newly-born stars, and are
formed when gas ejected by young stars collides with clouds of gas and
dust nearby at speeds of several hundred kilometers per second.
Herbig-Haro objects are ubiquitous in star-forming regions, and several
are often seen around a single star, aligned along its rotational axis.
HH objects are transient phenomena, lasting only a few thousand years
at most. They can evolve visibly over quite short timescales as they
move rapidly away from their parent star into the gas clouds in
interstellar space (the interstellar medium or ISM). Hubble Space
Telescope observations reveal complex evolution of HH objects over a
few years, as parts of them fade while others brighten as they collide
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with clumpy material in the interstellar medium.
The objects were first observed in the late 19th century by Sherburne
Wesley Burnham, but were not recognized as being a distinct type of
emission nebula until the 1940s. The first astronomers to study them in
detail were George Herbig and Guillermo Haro, after whom they have
been named. Herbig and Haro were working independently on studies
of star formation when they first analyzed Herbig-Haro objects, and
recognized that they were a by-product of the star formation process.
H-R
Hypergiants
IRAS
Keplerian orbit
Kukarkin-Parengo relation
LBV
Light curve
LMC
Hertzsprung-Russell (diagram); A graph of stellar color, temperature, or
spectral type against stellar luminosity or absolute magnitude. It was
first plotted by Henry Norris Russell in 1913, but was discussed
independently by Ejnar Hertzsprung at about the same time. The
Hertzsprung-Russell diagram is dominated by the main sequence,
which forms a curved, diagonal band from bright blue stars to faint red
ones, and contains stars in their core hydrogen-burning stage, and the
giant branch, occupied by red giants. Other conspicuous regions are
represented by the supergiants (above the giant branch) and the white
dwarfs (below the main sequence). The HR diagram can be seen as
both a snapshot of the state of a large collection of stars, or a
generalization of the evolutionary pathways of stars.
Extremely bright and extremely hot, burning their fuel extremely quickly,
and only last a very short while. At the end of their lives they explode
catastrophically, leaving a black hole. This is the biggest, hottest,
brightest category of stars – supergiants are somewhat smaller.
Hypergiant stars can be as much as 100 times as heavy as our sun,
and they generally live only about 2 million years (approx. 1/8000 of our
sun’s lifespan).
Because they are so big, bright, and short-lived, hypergiant stars are
also quite rare compared to other kinds of stars.
Infrared Astronomical Satellite
An orbit involving two spherical objects and governed by gravitational
forces only. Also known as a Keplerian ellipse or Keplerian trajectory, it
is the path followed by an object in accordance with the first of Kepler’s
laws of celestial motion.
Relationship between outburst amplitude and the mean time interval
between two subsequent outbursts (cycle length)
Luminous Blue Variable; massive, luminous blue star often with
expanding envelope
A graph showing the way in which the brightness of an object, such as
a variable star, changes with time. The light variations may be due to
intrinsic changes in the source, as in the case of Cepheid variables, or
eclipses, when one member of a binary star system passes in front of
the other. Modern techniques in photometry enable even the tiny
fluctuations in the light received from a star by the transit of an orbiting
planet to be detected.
Large Magellanic Cloud; One of the two Magellanic Clouds — dwarf
irregular galaxies — visible in the southern hemisphere, that orbit the
Milky Way Galaxy; it spans 8° of the sky in Dorado and Mensa. The
LMC is about 20,000 light-years in diameter, has a visible mass of
about one-tenth that of our own galaxy, and, at a distance of some
180,000 light-years, was long considered to be the nearest external
galaxy before losing that distinction to the Sagittarius Dwarf Elliptical. It
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Main-sequence
Nebula
NRP
PNNV
Population I stars
Population II stars
displays a noticeable bar of stars, some of which, including S Doradus,
are extremely luminous; from the ends of the bar project a weak spiral
structure. The LMC is rich in a variety of diffuse nebulae, including the
spectacular Tarantula Nebula, planetary nebulae, open clusters,
globular clusters, and so-called blue populous clusters, which resemble
compact, young globulars and are of a type unseen in our own galaxy.
An absence of intermediate-age clusters suggests that the LMC has
experienced early and late bursts of star formation. The LMC was also
the site of supernova 1987A — the nearest observed supernova since
that recorded by Kepler.
The curving track on the Hertzsprung-Russell diagram, from top left
(high temperature, high luminosity) to lower right (low temperature, low
luminosity), along which 90% of visible stars lie. A star on the main
sequence is one that is generating light and heat by the conversion of
hydrogen to helium by nuclear fusion in its core. The Sun, along with
the bulk of the stars visible to the naked eye, are main sequence stars.
A star arrives on the main sequence after it starts hydrogen burning in
its core and remains there throughout its core-hydrogen-fusion phase.
A star’s position and length of stay on the main sequence depend
critically on mass. The most massive stars – the hot, blue-white O stars
and B stars – occur to the upper left and have main-sequence lifetimes
of only a few million or tens of millions if years. The least massive,
hydrogen-burning stars, the red dwarfs, sit to the lower right and may
remain on the main sequence for hundreds of billions of years.
A cloud of gas and dust in space. There are three general types:
emission nebulae, which shine by their own light, reflection nebulae,
which reflect light from nearby stars, and dark nebulae, which absorb
and appear dark against a brighter background. When cloudlike
material in space is patchy, or of a form that is difficult to categorize as
a particular type of nebula, is referred to as nebulosity.
Non-radial pulsations as in the Be stars.
variable planetary nebula nuclei
A term used to describe stars and other objects, such as star clusters,
that tend to be found in, or near to, the plane of a spiral galaxy and
follow roughly circular orbits around the center. They are younger than
Population II objects, have relatively high heavy element content, and
have probably been formed continuously throughout the lifetime of the
disc. Extreme Population I are found in spiral arms and consist of
young objects, such as T Tauri stars, O stars, B stars, and stars newly
arrived on the zero-age main sequence. It is, in fact, the brilliant light —
particular, the intense ultraviolet radiation – from extreme Pop I stars —
that causes the spiral arms to glow to brightly. Older Population I
objects include stars like the Sun. All Population I stars are relatively
rich in elements heavier than hydrogen and helium since they formed
from clouds of gas and dust which contained the products of
nucleosynthesis from previous generations of stars. The presence of
heavy elements in protoplanetary discs is believed to be a key factor in
the formation of planets, so that only Population I objects are expected
to harbor planetary systems, and possibly life, similar to our own.
A term used to describe old, red stars and other objects found in the
galactic halo and galactic bulge of a spiral galaxy, such as our own,
near the galactic center, and in parts of the disc of the galaxy which are
well away from the galactic plane. The halo contains individual old
stars and large groupings known as globular clusters. Population II
stars make up the overwhelming bulk of the stellar population in
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Population III stars
elliptical galaxies. Pop II stars follow highly elliptical orbits around the
galactic center and are relatively deficient in heavy elements (i.e. those
heavier than hydrogen or helium) because they formed when their
parent galaxy was young, before much stellar nucleosynthesis had
taken place. The importance of heavy elements in planet formation
suggests that few, if any, Population II stars have worlds in orbit around
them.
Population III stars are a hypothetical population of extremely massive
stars that are believed to have been formed in the early universe. They
have not been observed directly, but are thought to be components of
faint blue galaxies. Their existence is necessary to account for the fact
that heavy elements, which could not have been created in the Big
Bang, are observed in quasar emission spectra as well as the existence
of faint blue galaxies. It is believed that these stars triggered a period of
reionization.
Current theory is divided on whether the first stars were very massive or
not. One theory, which seems to be borne out by computer models of
star formation, is that with no heavy elements from the Big Bang, it was
easy to form stars much more massive than the ones visible today.
Typical masses for population III stars would be expected to be about
several hundred solar masses, which is much larger than current stars.
Analysis of data on low-metallicity Population II stars, which are
thought to contain the metals produced by Population III stars, suggests
that these metal-free stars had masses of 10 to 100 solar masses
instead. This also explains why there have been no low-mass stars
with zero metallicity observed. Confirmation of these theories awaits the
launch of NASA's James Webb Space Telescope.
The highest-mass star which may form today is about 110 solar
masses. Any attempt to form a star greater than this results in the
protostar blowing itself apart during the initial ignition of nuclear
reactions. Without enough carbon, oxygen and nitrogen in the core,
however, the CNO cycle could not begin and the star would not go
nuclear with such enthusiasm. Direct fusion through the proton-proton
chain does not proceed quickly enough to produce the copious amounts
of energy such a star would need to support its immense bulk. The end
result would be the star collapsing into a black hole without ever
actually shining properly. This is why astronomers consider population
III to be somewhat of a mystery--by all rights they should not exist, yet
they're needed to explain the quasar observations.
Protoplanetary disc
If these stars were able to form properly, their lifespan would be
extremely short, certainly less than one million years. As they can no
longer form today, viewing one would require us to look to the very
edges of the observable universe. (Since the time it takes light to reach
Earth from great distances is extremely long, it is possible to see "back
in time" by looking farther away.) Seeing this distance while still being
able to resolve a star could prove difficult even for the James Webb
Space Telescope.
A circumstellar disc of matter, including gas and dust, from which
planets may eventually form or be in the process of forming. The
existence of such discs was long suspected but was confirmed by direct
imaging in 1994 when the Hubble Space Telescope (HST) was used to
examine newborn stars in the Orion Nebula. About half of those were
found to be surrounded by discs of gas and dust. Prior to this, in the
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1980s, dust discs had been discovered around a number of more
mature stars using the Infrared Astronomy Satellite. Additionally,
infrared studies of nearby star-forming regions had revealed that at
least 50 percent of all 1-million-year-old stars have excess infrared
emission, suggests that they are surrounded by warm dust. In 1994,
John Stauffer and associates of the Harvard-Smithsonian Center for
Astrophysics reported that 70 to 80 percent of infant stars at the center
of the Orion Nebula showed signs of having discs. This high fraction
has since been confirmed by more sensitive observations by the
Infrared Space Observatory.
Conventional theory suggests that about 10 million years are required
for a planetary system to form completely from a protoplanetary disc, so
that, on this basis, the discs mentioned above might not yet be old
enough to contain planets. They should, however, be at the stage
where dust grains are accreting to give larger particles. This was
confirmed in 1998 by observations carried out with the HST which
showed that the discs around three stars in the Orion Nebula contain
dust at least 10 microns across, or nearly 100 times larger than dust
grains in interstellar space.
Some young protoplanetary discs are thought to have a mass of 0.01 to
0.1 solar masses, or more than 10 times that needed to make a
planetary system like our own. Much of this material will eventually be
blown away by the strong stellar wind from the central star. Dust
accounts for about 1 percent of the disc’s initial mass, the rest being
made up of gas, mainly hydrogen and helium. Young discs imaged by
the HST, in Orion and Taurus, are seen at many different angles, from
edge-on to nearly face-on, and are typically a few hundred astronomical
units in diameter.
Rayleigh-Taylor instability
As accretion continues within a protoplanetary disc, sizable objects
known as planetesimals form which, after several million years, give
rise to small, rocky planets close to the host star. Further out, where it
is cold enough for ice to form in the disc, more solid material is available
for world-building. Gas giants, like Jupiter and Saturn, may start with
cores of rock and ice of about 10 Earth-masses and then sweep up
large quantities of light gases to form thick atmospheres. This should
result in the creation of a central cavity within the circumstellar disc,
similar in size to the solar system, and a drastic depletion of the disc’s
gas content.
The Rayleigh-Taylor instability, or RT instability, occurs any time a
dense, heavy fluid is being accelerated by light fluid. This is the case
with a cloud and shock system, or when a fluid of a certain density
floats above a fluid of lesser density, such as dense oil floating above
water.
Two completely plane-parallel layers of immiscible fluid are stable, but
the slightest perturbation leads to release of potential energy, as the
heavier material moves down under the (effective) gravitational field,
and the lighter material is displaced upwards. As the instability
develops, downward-moving Dimples are quickly magnified into sets of
inter-penetrating RT fingers. The upward-moving, lighter material
behaves like 'Spherical Cap Bubbles'.
This process is evident not only in many terrestrial examples, from salt
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domes to weather inversions, but also in astrophysics and astronomy.
RT fingers are especially obvious in the Crab Nebula, in which hot gas
from the explosion is ramming into the surrounding interstellar medium,
and they give rise to the familiar clumpy appearance of material in these
and several other astronomical objects.
Red Giant
Roche lobe
RRab
RRc
RRd stars
Sandage Effect
SED
SMC
SN Ia
Note that the RT instability is not to be confused with the Rayleigh
instability of a liquid jet. This latter instability, sometime called the
hosepipe (or firehose) instability, occurs due to surface tension, which
acts to break a cylindrical jet into a stream of droplets having the same
volume but lower surface area.
A giant star with a surface temperature of 2,500 to 3,500°C, a spectral
type of M or K, and a diameter between 10 and 100 times that of the
Sun. Red giants represent a late stage in the evolution of stars with a
range of masses, from just under the mass of the Sun to tens of solar
masses (see stars, evolution of). The largest red giants, which form
from the most massive of stars, are known as red supergiants. A red
giant has exhausted its core supply of hydrogen and is now fusing
hydrogen to helium in a shell outside the core.
The volume around a star in a binary system in which, if you were to
release a particle, it would fall back onto the surface of that star. A
particle released above the Roche lobe of either star will, in general,
occupy the circumbinary region that surrounds both stars. The point at
which the Roche lobes of the two stars touch is called the inner
Lagrangian point. If a star in a close binary system evolves to the point
at which it fills its Roche lobe, calculations predict that material from this
star will overflow both onto the companion star (via the L1 point) and
into the environment around the binary system.
RR Lyrae type stars which pulsate in the fundamental mode
RR Lyrae type stars which pulsate in the first overtone mode
RR Lyrae type stars which pulsate in both fundamental and firstovertone modes simultaneously.
Pertains to RR Lyrae type stars, more specifically RRab, and their
associated Galactic Globular Clusters (GGC) with reference to the
Oosterhoff dichotomy. The mean period (Pab) in Oosterhoff class II
clusters is larger, just because all variables have, for a given
temperature, periods larger than in the corresponding Oosterhoff class I
clusters. (Sandage 1982)
Spectral Energy Distribution
Small Magellanic Cloud; The lesser of the two Magellanic Clouds —
irregular galaxies that are satellites of our own Milky Way Galaxy. The
SMC is about 10,000 light-years in diameter, has a visible mass of
about one-fiftieth that of the Milky Way, and, at a distance of some
210,000 light-years, is the third-nearest external galaxy after the
Sagittarius Dwarf Elliptical Galaxy and the Large Magellanic Cloud
(LMC). It contains fewer clusters and nebulae than does the LMC, and
relatively more gas and dust. However, like the LMC, it seems to have
experienced one burst of star formation early in its history followed by a
second much more recently. The SMC is important historically as the
location in which Henrietta Leavitt discovered the period-luminosity
relation of Cepheid variables.
Type Ia supernovae lack helium and present a silicon absorption line in
their spectra near peak light. The most commonly accepted theory of
this type of supernovae is that they are the result of a carbon-oxygen
white dwarf accreting matter from a nearby companion star, typically a
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red giant, until it nears the Chandrasekhar limit. The current view is that
this limit is never actually attained, so that the process of collapse is
never initiated. Instead, the increase in pressure raises the temperature
near the center, and a period of convection lasting approximately 100
years begins. At some point in this simmering phase, a deflagration
flame front powered by carbon fusion is born, although the details of the
ignition – the location and number of points where the flame begins – is
still unknown. Oxygen fusion is initiated shortly thereafter, but this fuel
is not consumed as completely as carbon. The flame accelerates
dramatically, through the Rayleigh-Taylor instability and interactions
with turbulence. It is still a matter of considerable debate as to whether
this flame transitions from a subsonic deflagration into a supersonic
detonation.
The energy release from the thermonuclear burning (~1044 joules)
causes the star to explode violently and to release a shock wave in
which matter is typically ejected at speeds on the order of 10,000 km/s.
The energy released in the explosion also causes an extreme increase
in luminosity. The typical absolute magnitude of Type Ia supernovae is
-19.5 (~5 billion times brighter than our Sun), with little variation.
The theory of this type of supernovae is similar to that of novae, in
which a white dwarf accretes matter more slowly and does not
approach the Chandrasekhar limit. In the case of a nova, the infalling
matter causes a hydrogen fusion surface explosion that does not
disrupt the star.
Type Ia supernovae have a characteristic light curve, their graph of
luminosity as a function of time after the explosion. Near the time of
maximum luminosity, the spectrum contains lines of intermediate-mass
elements from oxygen to calcium; these are the main constituents of the
outer layers of the star. Months after the explosion, when the outer
layers have expanded to the point of transparency, the spectrum is
dominated by light emitted by material near the core of the star, heavy
elements synthesized during the explosion, most prominently iron-group
elements. The radioactive decay of Nickel-56 through Cobalt-56 to
Iron-56 produces high-energy photons which dominate the energy
output of the ejecta at intermediate to late times.
Unlike the other types of supernovae, Type Ia supernovae are generally
found in all types of galaxies, including ellipticals. They show no
preference for regions of current star formation.
The similarity in the shapes of the luminosity profiles of all known Type
Ia supernovae has led to their use as a standard candle in extragalactic
astronomy. The cause of this similarity in the luminosity curve is still an
open question. In 1998, observations of Type Ia supernovae indicated
the unexpected result that the universe seems to undergo an
accelerating expansion.
SN Ib and SN Ic
The early spectra of Types Ib and Ic do not show lines of hydrogen nor the
strong silicon absorption feature near 615 nanometers. These events, like
supernovae of Type II, are probably massive stars running out of fuel at their
centers; however, the progenitors of Types Ib and Ic have lost most of their
envelopes due to strong stellar winds or interaction with a companion. Type Ib
supernovae are thought to be the result of a Wolf-Rayet star collapsing. There
is some evidence that Type Ic supernovae may be the progenitors of gamma
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ray bursts, though it is also thought that any core-collapse supernova (Type Ib,
Ic, or II) could be a GRB dependent upon the geometry of the explosion.
SN II
SPBs
Standstills
Starspots
Supergiants
Stars far more massive than the sun evolve in much more complex
fashions. In the core of the sun, hydrogen is fused into helium, releasing
energy which heats the sun's core, and providing pressure which
supports the sun's layers against collapse (see hydrostatic equilibrium).
The helium produced in the core accumulates there since temperatures
in the core are not yet high enough to cause it to fuse. Eventually, as
the hydrogen at the core is exhausted, fusion begins to slow down and
gravity begins to cause the core to contract. This contraction raises the
temperature high enough to initiate a shorter phase of helium fusion,
which accounts for less than 10% of the star's total lifetime. In stars
with less than ten solar masses, the carbon produced by helium fusion
does not fuse, and the star gradually cools to become a white dwarf.
White dwarf stars, if they have a near companion, may then become
Type Ia supernovae.
A much larger star, however, is massive enough to create temperatures
and pressures needed to cause the carbon in the core to begin to fuse
once the star contracts at the end of the helium-burning stage. The
cores of these massive stars become layered like onions as
progressively heavier atomic nuclei build up at the center, with an
outermost layer of hydrogen gas, surrounding a layer of hydrogen
fusing into helium, surrounding a layer of helium fusing into carbon (via
the triple-alpha process), surrounding layers that fuse to progressively
heavier elements. As a star this massive evolves, it undergoes
repeated stages where fusion in the core stops, and the core collapses
until the pressure and temperature is sufficient to begin the next stage
of fusion, re-igniting to halt collapse.
Slowly pulsating B stars
A standstill usually starts at the end of an outburst and consists of a
period of constant brightness, about one magnitude below maximum
light that may last from a few days to 1,000 days. The average energy
output in a standstill is larger than that during an outburst cycle.
Standstills occur when the mass transfer rate from the secondary star
into the accretion disc around the primary star is too large to produce
normal outbursts.
Analogous to our solar sun spots
With the exception of hypergiants, the brightest, largest kind of star.
Supergiants have luminosities of 10,000 to 100,000 solar luminosities
and radii of 20 to several hundred solar radii (about the size of Jupiter's
orbit). The two commonest types are red supergiants, exemplified by
Betelgeuse and Antares, and blue supergiants, exemplified by Rigel.
When a star of at least 15 solar masses exhausts the hydrogen in its
core, it first swells to become a red giant. But when it reaches the stage
of helium-to-carbon burning, by the triple-alpha process, it expands to
an even larger volume. This much brighter, but still reddened star is a
red supergiant. Through a vigorous stellar wind, red supergiants
steadily lose their extended atmospheres and turn into smaller but
much hotter blue supergiants. A blue supergiant may then develop a
fresh distended envelope and revert to the red supergiant phase. Both
types, red and blue, can explode as supernovae. Stellar evolution
theory had long taught that supernovae always come from the red
variety. However, the great Supernova 1987A was found to have had a
blue supergiant precursor.
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Superhumps
Superoutbursts
Synchrotron radiation
Triple-alpha process
An additional modulation of the light curve of an SU Ursae Majoris stars
caused by precession of the accretion disc. Superhumps show up in
the light curve of a superoutburst as a modulation with a period a few
percent longer than the orbital period. They continue until the star
returns to quiescence, although their period usually drifts to slightly
shorter periods and smaller amplitudes over time. Nicholas Vogt was
the first to propose that superhumps were caused by the disc becoming
elliptical during superoutburst. He suggested that such a disc would
precess, meaning that the direction in which the disc was elongated
would gradually rotate, on a timescale much longer than the orbit (in the
same way, the axis of a spinning top precesses, but more slowly than it
spins). The long precessional period of the disc would then interact
with the orbital cycle to create a new periodicity — the superhump.
Outbursts which are much brighter and less frequent than normal
outbursts but last several times longer as demonstrated in SU UMa
class stars.
Electromagnetic radiation emitted by electrons that are spiraling along,
and therefore being constantly accelerated, in a magnetic field at a rate
great enough for relativistic effects to be important. Predicted long ago,
this radiation was first encountered in the particle accelerator called the
synchrotron. Much of the radiation observed by radio astronomers
originates in this fashion.
The triple alpha process is the process by which three helium nuclei
(alpha particles) are transformed into carbon.
This nuclear fusion reaction can occur rapidly only at temperatures
above 100,000,000 kelvins and in stellar interiors having a high helium
abundance. As such, it occurs in older stars, where helium produced
by the proton-proton chain and the carbon nitrogen oxygen cycle (CNO
Cycle) has accumulated in the center of the star. After the completion
of hydrogen burning in the stellar core, the core will collapse until the
central temperature rises to the point where helium burning occurs.
4
He + 4He ↔ 8Be
Be + 4He ↔ 12C + γ + 7.367 MeV
8
The net energy release of the process is 7.275 MeV.
The 8Be produced in the first step is unstable and decays back into two
helium nuclei in 2.6×10-16 seconds. However, under the conditions of
helium burning a small equilibrium abundance of 8Be is formed; capture
of another alpha particle then leads to 12C. This conversion of three
alpha particles to 12C is called the triple-alpha process.
Because the triple-alpha process is unlikely, it requires a long period of
time to produce carbon. One consequence of this is that no carbon was
produced in the Big Bang because within minutes after the Big Bang,
the temperature fell below that necessary for nuclear fusion.
Ordinarily, the probability of the triple alpha process would be extremely
small. However, the beryllium-8 ground state has almost exactly the
energy of two alpha particles. In the second step, 8Be + 4He has almost
exactly the energy of an excited state of 12C. These resonances greatly
increase the probability that an incoming alpha particle will combine
with beryllium-8 to form carbon. The existence of this resonance was
predicted by Fred Hoyle before its actual observation based on its
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necessity for carbon to be formed.
As a side effect of the process, some carbon nuclei can fuse with
additional helium to produce a stable isotope of oxygen and release
energy:
12
C + 4He → 16O + γ
The next step of the chain in which oxygen combines with an alpha
particle to form neon turns out to be more difficult because of nuclear
spin rules, and as a result heavier elements cannot easily be formed in
stellar nucleosynthesis.
This creates a situation in which stellar nucleosynthesis produces large
amounts of carbon and oxygen but only a small fraction of these
elements is converted into neon and heavier elements. Both oxygen
and carbon make up the ash of helium burning. That nuclear
resonances sensitively are arranged to create large amounts of carbon
and oxygen, has been controversially cited as evidence of the anthropic
principle.
UBV system
WD
Fusion processes produce elements only up to iron; heavier elements
are created mainly by neutron capture. The slow capture of neutrons,
the S-process, produces about half of these heavy elements. The other
half are produced by rapid neutron capture, the R-process, which
probably occurs in a core-collapse supernova.
A system of stellar magnitudes devised by Harold Johnson (1921-1980)
and William Morgan at Yerkes Observatory, which consists of
measuring an object's apparent magnitude through three color filters:
the ultraviolet (U) at 3600 Å; the blue (B) at 4200 Å; and the visual (V) in
the green-yellow spectral region at 5400 Å. It is defined so that, for A0
stars, B - V = U - B = 0; it is negative for hotter stars and positive for
cooler stars. The Stebbins-Whitford-Kron six-color system (U, V, B, G,
R, I) is defined so that B + G + R = 0. The difference, B - V is a good
measure of a star's actual color. For example, Betelgeuse has B - V =
1.85, indicating that it is quite red. On the other hand, Rigel has B - V =
-0.03, indicating that it is bluish. Most stars fall between these
extremes, except for a few redder-than-red stars (mostly carbon stars)
and a few bluer-than-blue stars (mostly young, high-mass stars).
A white dwarf is an astronomical object which is produced when a low
or medium mass star dies. These stars are not heavy enough to
generate the core temperatures required to fuse carbon in
nucleosynthesis reactions. After such a star has become a red giant
during its helium-burning phase, it will shed its outer layers to form a
planetary nebula, leaving behind an inert core consisting mostly of
carbon and oxygen.
This core has no further source of energy, and so will gradually radiate
away its energy and cool down. The core, no longer supported against
gravitational collapse by fusion reactions, becomes extremely dense,
with a typical mass of that of the sun contained in a volume about equal
to that of the Earth. The white dwarf is supported only by electron
degeneracy pressure. The maximum mass of a white dwarf, beyond
which degeneracy pressure can no longer support it, is about 1.4 solar
masses. A white dwarf which approaches this limit (known as the
Chandrasekhar limit), typically by mass transfer from a companion star,
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may explode as a Type Ia supernova via a process known as carbon
detonation.
Eventually, over hundreds of billions of years, white dwarfs will cool to
temperatures at which they are no longer visible. However, over the
universe's lifetime to the present (about 13.7 billion years) even the
oldest white dwarfs still radiate at temperatures of a few thousand
kelvins.
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Greek Alphabet
Capital
Α
Β
Γ
∆
Ε
Ζ
Η
Θ
Ι
Κ
Λ
Μ
Ν
Ξ
Ο
Π
Ρ
Σ
Τ
Υ
Φ
Χ
Ψ
Ω
Low-case
α
β
γ
δ
ε
ζ
η
θ
ι
κ
λ
µ
ν
ξ
ο
π
ρ
σ
τ
υ
φ
χ
ψ
ω
Classification of Variable Stars, A Compilation of Information
John W Shepherd
Greek Name
Alpha
Beta
Gamma
Delta
Epsilon
Zeta
Eta
Theta
Iota
Kappa
Lambda
Mu
Nu
Xi
Omicron
Pi
Rho
Sigma
Tau
Upsilon
Phi
Chi
Psi
Omega
English
a
b
g
d
e
z
h
th
i
k
l
m
n
x
o
p
r
s
t
u
ph
ch
ps
o
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Constellations
Abbrev
And
Ant
Aps
Aqr
Aql
Ara
Ari
Aur
Boo
Cae
Cam
Cnc
CVn
CMa
CMi
Cap
Car
Cas
Cen
Cep
Cet
Cha
Cir
Col
Com
CrA
CrB
Crv
Crt
Cru
Cyg
Del
Dor
Dra
Equ
Eri
For
Gem
Gru
Her
Hor
Hya
Hyi
Ind
Name
Andromeda
Antlia
Apus
Aquarius
Aquila
Ara
Aries
Auriga
Bootes
Caelum
Camelopardalis
Cancer
Canes Venatici
Canis Major
Canis Minor
Capricornus
Carina
Cassiopeia
Centaurus
Cepheus
Cetus
Chamaeleon
Circinus
Columba
Coma Berenices
Corona Australis
Corona Borealis
Corvus
Crater
Crux
Cygnus
Delphinus
Dorado
Draco
Equuleus
Eridanus
Fornax
Gemini
Grus
Hercules
Horologium
Hydra
Hydrus
Indus
Classification of Variable Stars, A Compilation of Information
John W Shepherd
Abbrev
Lac
Leo
LMi
Lep
Lib
Lup
Lyn
Lyr
Men
Mic
Mon
Mus
Nor
Oct
Oph
Ori
Pav
Peg
Per
Phe
Pic
PsA
Psc
Pup
Pyx
Ret
Sge
Sgr
Sco
Scl
Sct
Ser
Sex
Tau
Tel
TrA
Tri
Tuc
UMa
UMi
Vel
Vir
Vol
Vul
Name
Lacerta
Leo
Leo Minor
Lepus
Libra
Lupus
Lynx
Lyra
Mensa
Microscopus
Monocerus
Musca
Norma
Octans
Ophiuchus
Orion
Pavo
Pegasus
Perseus
Phoenix
Pictor
Pisces Austrinus
Pisces
Puppis
Pyxis
Reticulum
Sagitta
Sagittarius
Scorpius
Sculptor
Scutum
Serpens
Sextans
Taurus
Telescopium
Triangulum Australis
Triangulum
Tucana
Ursa Major
Ursa Minor
Vela
Virgo
Volans
Vulpecula
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The Families
Intrinsic
These are stars which vary their light output, hence their brightness, by some change within the star itself.
They are an extremely important and useful group of stars to astronomers as they provide a wealth of
information about the internal structure of stars and models of stellar evolution. Perhaps their greatest
value is the role of some types such as Cepheids and supernovae in distance determination. Intrinsic
variables are further classified as to whether they exhibit periodic pulsations are more explosive or
eruptive events as in cataclysmic variables.
Eruptive Variables
According to the GCVS, eruptive variables are stars varying in brightness because of violent processes
and flares taking place in their chromospheres and coronae.
Luminous Blue Variables (LBVs)/ S Dor Stars
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Usually ‘hypergiants’
Some of the most massive and luminous (106 solar luminosities)
During an outburst, except for supernovae, are the visually brightest objects in the universe.
Sporadically show phenomenal mass-ejections (eruptions) followed by periods of quiescence.
Estimate that no more than 60 reside in our Galaxy.
Only a few dozen are currently known today.
Formation of a dusty envelope is characteristic of LBVs and one of the reasons of their variability.
Have strongest Balmer lines and He I lines in the visual spectrum.
Some LBVs have extended circumstellar shell or ring nebula of ejected nuclear-processed
material.
Suggestion that the LBV mechanism is an essential step to force massive stars to become WR
stars. (Wolf, Appenzeller et al. 1981; Maeder 1982)
Amplitude: (0.01 – several magnitudes)
Period: wide range of time scales (hours, over several decades, to centuries)
Variability is due primarily to rapid and unsteady mass loss.
There are three types of variations; variations that increase with time scales
• Large variations
• Associated with eruptions
• Seen in some but not all LBVs
• Occur on time scales of centuries
• Moderate variations
• Seen on time scales of decades
• Occur at irregular intervals
• Small-scale photometric variations
• Sometimes called micro-variations
• Found in all LBVs
• Micro-variations are not strictly periodic
• The characteristic period is not always visible
• Time scales are not constant in length
• Colors vary also but the amplitudes of variation are a few orders of magnitude smaller
than the light amplitudes.
• Color curves are usually in phase with the light curves
• The light amplitudes tend to increase with decreasing wavelength.
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•
Further discussions see the following (de Jager 1980; van Genderen and The 1984; Wolf 1986;
de Groot 1988; Humphreys 1989; Lamers 1989; Maeder 1989; Wolf 1989; Hillier 1992; Wolf
1992; Wolf 1992; de Koter 1993)
R Coronae Borealis Variables (RCB)
Unlike most variable stars, R Coronae stars spend most of their time at maximum brightness but
sometimes decrease in brightness by up to 9 magnitudes at irregular intervals. They take a few
months or a year to return to their normal maximum brightness. These rare stars are carbon-rich.
• Period: irregular
• Amplitude of variation: up to 9 magnitudes
• These are rare
• They are luminous, hydrogen-poor, carbon-rich, variables that spend most of their time at
maximum light, occasionally fading as much as nine magnitudes at irregular intervals.
• Typical rapid decline of 4 magnitude in 25 days followed by more gradual decline of about 3
magnitude in 120 days
• They then slowly recover to their maximum brightness after a few months to 3 years.
• A great deal of variety in light curve shape from one decline to the next
• New declines may take place before recovery or a new major decline may not take place for
many years.
• Decline of light is attributed to a cloud of carbon particles in ejecta from the stellar atmosphere.
• Light decline is taking place only close to the line of sight and not uniformly over the whole
surface.
• If this is the case then there will be times when carbon particle formation will be out of the line
of sight and not influencing the optical brightness.
• In this model the star is ejecting puffs of soot or other forms of carbon in random directions
and occasionally these are in the line of sight.
• Infrared observation indicates that RCB stars are surrounded by dust shells which are
presumably carbon particles at temperatures of 800 K.
• The infrared luminosities of these shells vary with quasi-periods of 1000 – 2000 days
• RCB stars show variability of a few tenths of a magnitude at optical wavelengths when not going
through an obscuration event.
• Variation seems to be semi-regular in nature and often has a quasi-period of the order of a
month.
• Radial observations show the star is still pulsating and infrared observations show these
pulsations continue uninterrupted when the star goes into an optical minimum
• It is generally assumed all stars of this class are pulsating and the initial ejection of material from
the star is connected with pulsational instability.
• Instability may include the propagation of shock waves through the stellar atmosphere.
• There is some speculation that obscuration events begin at a specific phase of the pulsation
cycle.
• Three RCB stars in the Large Magellanic Cloud are supergiants with absolute magnitudes of
about -5.
• Best known RCB stars have surface temperatures similar to F, G and K spectral types.
• There are some rare hot RCB stars as well with spectral types B and A
• Postulated RCB stars are in a rapid evolutionary phase from the top of the asymptotic giant
branch (AGB) towards the planetary nebula and white dwarf stages on the H-R diagram.
• Useful references are (Alexander, Andrews et al. 1972; Feast 1975; Hunger, Schoenberner et al.
1986)
Wolf-Rayet Stars (WR)
•
•
Very luminous hot Population I stars
Temperature (30000 – 70000 K)
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•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
Has a characteristic spectra composed of a broad and strong [C], [N], [O], [He] and [Si] emission
lines along with absorption lines corresponding to spectral type O or B.
• emission lines result from a shell of expelled gas expanding at speeds of up to 3000 km.s-1
Notorious for their high mass-loss (10-5 Msolar y-1)
About 150 are known in our Milky Way Galaxy
100 are known in the Large Magellanic Cloud
Only 12 have been identified in the Small Magellanic Cloud
WR stars forms an important evolutionary phase through which all massive stars above a certain
limiting mass pass when going from the main sequence to the end of their lives. (Sterken and
Jaschek 1996)
Discovered by Charles Wolf and Georges Rayet in 1866.
Composed of two sub-classes
• Carbon sequence (WC stars)
• WC4-WC9 with strong [C] and [O] emission lines
• Nitrogen sequence (WN stars)
• WN2-WN9 with strong [He] and [N] emission lines
Many WR stars are spectroscopic binaries.
About half of the WR stars show light variations with amplitudes of several hundredths of a
magnitude.
Light variations in some WR binaries are caused by phase-dependent occultation and tidal
effects.
Time scales (Vreux 1987)
• Milliseconds to seconds for pulsars in a WR binary
• Minutes to hours for flares and pulsations
• Hours to several days for their strongest variations
• Years with variable amplitudes
• Multiple periods are often present
Hard to separate the variations from the underlying continuum unless you use custom-designed
narrow-band filters.
(Moffat, Drissen et al. 1989) suggests that the most luminous WR stars of subtypes WN6-9 could
be post-LBV stars.
Additional reading on WR stars and variability can be obtained in (van der Hucht 1992; Gosset,
Rauw et al. 1994; Maeder and Conti 1994; van der Hucht, Williams et al. 1994)
Pre-main Sequence Stars (PMS)
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Young Stellar Object (YSO), coined by S. Strom (1972), is now widely used to designate all premain-sequence stellar objects, embedded or visible. (Strom 1972; Bertout 1989)
Pre-main sequence (PMS) stars are newly-formed stars from interstellar matter which has not yet
reached a high enough central temperature to ignite core hydrogen-burning.
Gain their energy from the release of gravitational energy called Kelvin-Helmholtz contraction.
PMS stars are eruptive variables.
A wealth of information has been obtained on the classification of PMS stars and their subclasses
over the past 20 years. (Bertout 1989)
GCVS sub-divides this class into many sub-groups (FU, IN, INA, INB, INT, INYY, and several
others)
• Classification is based on morphological properties only
• It is inconsistent and of very little value for real physical classification
• The classification would be better if based on intrinsic properties.
Now it is common practice to make a physical distinction between PMS stars by their mass.
• M <= 3 Msolar are T Tauri stars
• 4 Msolar <= M <= 8 Msolar are Herbig Ae/Be stars
• There is no clear-cut border between the groups but there is a smooth transition.
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T Tauri stars
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Low-mass PMS stars
• M <= 3 Msolar
More than 1000 known stars
First observed and named by Joy (Joy 1942)
Physical nature of the T Tauri was recognized by V. Ambartsumian (1947)
• Low-mass young stars that have not reached main sequence
• Often found in connection with groups of OB stars (Bertout 1989)
1962, Herbig defined the spectroscopic criteria for T Tauri stars
• Since then, further studies in the spectral ranges of millimeter, infrared, ultraviolet, and Xray have broadened our understanding of the T Tauri stars
Once thought as a distinct class separate from the others but is now considered a phase in
stellar evolution. (Bertout 1989)
• Represent a pivotal class between deeply embedded low-luminosity sources, which can
be studied only at infrared and radio wavelengths, and solar-type main sequence stars.
T Tauri stars are usually found near or in dark cloud complexes from which they were born1.
Variability is a defining characteristic of T Tauri stars
A classification exists based on the strength of the Hα emission line
• Line strength is measured by the width of the Hα line.
• Not a rigid division
• T Tauri stars can change spectroscopically such that the border W(Hα) = 10 Å is crossed
over. (Bertout 1989)
• Weak-Line T Tauri Stars (WTTS)
• W(Hα) < 10 Å
• When compared to CTTS, WTTS displays no UV excess, little or no infrared excess
and they show very weak, if any emission lines. (Montmerle, Feigelson et al. 1993)
• Classical T Tauri Stars (CTTS)
• W(Hα) > 10 Å.
• Optical spectroscopic definition of CTTS (Herbig 1962)
a. Hydrogen Balmer lines and [Ca II], [H] and [K] lines are in emission
b. Anomalous emission of [Fe I] λ4063, 4132 is often observed. Fluorescent
emission in these lines is probably excited either by [Ca II], [H] or [Hε] and are
only found in T Tauri stars.
c. Forbidden emission of [O I] and [S II] are usually observed but not always.
d. Probably [S II] λ 6717, 6731 and [O I] λ 6300, 6363 are also characteristic.
e. [Li I] λ6707 absorption is conspicuously strong.
Discussion of the above definition: After the hydrogen and [Ca II] lines, the
strongest emission lines are usually caused by [Fe II], [Ti II] and [He I]. The
emission line spectrum is superimposed on a continuous spectrum that may
range from a pure continuum (in extreme T Tauri stars) though a late-type
absorption spectrum with anomalous line strengths (in veiled T Tauri stars) to an
almost normal absorption spectrum of type F through M in moderate T Tauri
stars. (Bertout 1989)
• Bastian et al. (1983) found Herbig’s definition inadequate to define the CTTS in the
SIMBAD data base of the Centre de Données de Strasbourg because not all of the
above emission lines are found in all stars – in particular, [S II] and [Fe I] lines are
visible only in stars with strong emission spectra – and because intrinsic variability
implies not all of the criteria defined above need be fulfilled all the time. (Bastian,
Finkenzeller et al. 1983)
They propose instead to use as primary criteria:
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Editorial comment from Donn Starkey adding the definitive relationship of the T Tauri star and its
progenitor cloud association.
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a. Association with a region of obscuration,
b. Presence of [Hα] and [Ca II], [H] and [K] emission with Wλ(Hα) > 5 Å,
c. Spectral type later than F
Note on above proposal: these are the de facto criteria used in searches for faint T
Tauri stars. (Herbig 1962)
Show late type G – M photospheric absorption spectrum on which a continuous spectrum is
superimposed (Folha 1998)
• Sometimes so strong that it hides the absorption spectra
• Characteristic emission lines similar to solar emission lines
• Strongest are the hydrogen Balmer lines
• Singly ionized metals such as [Ca II], or [Fe II], and lines of neutral helium are also found
• Some T Tauri show forbidden emission lines which tells of an association with thin
circumstellar matter.
• Emission lines exhibit very complex profiles indicating mass flows in a circumstellar
surrounding.
• Strong excess radiation in the sub-millimeter and infrared wavelengths indicate large
amounts of circumstellar dust. (Beckwith and Sargent 1993; Strom, Edwards et al. 1993)
• Classification of IR spectra along with modeling of the particle composition has
provided some beginning understanding of the types of dust particles which make up
the disc. (Sargent, Forrest et al. 2006)
• Emission at 10 µm
• Smooth, narrow and featureless profiles indicate amorphous silicates
• Amorphous pyroxene: composition Mg0.8Fe0.2SiO3
• Amorphous olivine: composition MgFeSiO4
• Broader width of the 10 µm emission is indicative of larger grains
• Complex 10µm emissions are indicative of thermally processed silicates
• Crystalline pyroxene: composition Mg0.9Fe0.1SiO3
• Crystalline forsterite: composition Mg1.9Fe0.1SiO4
• α Quartz which is SiO2 (silica)
• Almost all T Tauri discs show some degree of silicate crystallinity irrespective of
star mass or age.
• Transitional discs, discs whose inner portions are either partially or nearly totally
cleared of small dust grains, usually indicate very few crystalline silicate grains.
• Crystalline pyroxene is usually accompanied by foresterite but the reverse is not
necessarily true.
• Very low mass stars can have relatively large amounts of crystalline silicates in
their surrounding discs.
• No clear trend exists between the mass fraction of crystalline silicates and the
disc-to-star mass ratio
• There is an indication that higher quartz mass fraction accompanies lower
amorphous olivine to amorphous pyroxene ratio.
• Clues to age of the T Tauri are found with the absorption line of lithium at 6707 Å.
• Lithium is rapidly depleted in older star atmospheres.
• Mass of the T Tauri accretion discs range from 0.001 – 1 Msolar and are 102 – 103 AU
large.
X-ray telescopes have identified a new class of T Tauri stars called weak-line T Tauri
• Have weak emission lines and no or very weak infrared excess emission
• Discovered based on their strong coronal X-ray emission
• Apparently have already lost most of their circumstellar material
• Still gain energy from their gravitational contraction and not from nuclear core
• Show strong lithium absorption
• Data from the ROSAT X-ray satellite show Weak-Line T Tauri are more numerous than
the classical T Tauri stars.
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As the evolution of the PMS star continues, it moves towards the main sequence in the H-R
diagram still gaining energy from gravitation contraction.
If temperature in the core gets high enough to ignite hydrogen burning then it becomes a
main sequence star and therefore star formation process ends.
Young rapidly rotating magnetized CTTSs spin down to their present slow rotation in less
than 106 yr (Romanova, Ustyugova et al. 2005)
General consensus is during the Classical T Tauri stage the circumstellar accretion discs are
places where planets could be formed later on. These discs are referred to as
‘protoplanetary’ discs.
• Accretion discs are created during the star formation process in the interstellar clouds
• Responsible for many of the characteristic properties of the T Tauri stars.
• Believed that outbursts of FU Ori type are due to instabilities in the accretion disc
Line profiles of the emission lines, somewhat resembles P Cygni profiles, show T Tauri stars
have stellar winds with velocities up to a few 100 km s-1
Mass loss: 10-8 – 10-7 Msolar y-1
Several T Tauri show a red-shifted absorption components called ‘inverse P Cygni profiles’
which indicate infall of matter onto the stellar surface.
The interaction of the T Tauri winds with the interstellar matter in which the T Tauri are
imbedded is the physical reason for phenomena like Herbig-Haro objects, jets, and bipolar
molecular outflows which are connected with the PMS stars.
Large variety of photometric variations is a characteristic property of T Tauri
Very complex photometric behavior in the sense that variations can have different character
at different wavelengths is a characteristic of T Tauri stars
Time scales of the variations can be minutes to decades or even centuries.
Brightness amplitudes (∆m) of the variations can be as large as 5 magnitudes or in
exceptional cases like FU Ori can be even somewhat larger.
Physical causes for the variations are still uncertain.
Possible mechanisms could be:
• Starspots
• instabilities in the circumstellar accretion disc
• magnetic flare activity
• obscuration by dust clouds which orbit around the star in Keplerian orbits in the outer part
of the circumstellar disc.
At least 5 types of optical variation and variations can be distinguished
• Irregular variation with large amplitudes on a long-term time scale
• Connected to the spectral appearance of the star
• Occur the most in T Tauri stars with strong emission lines in their spectrum and/or
inverse P Cygni profiles
• Example: YY Ori stars, DR Tau
• FU Ori type outbursts (FUors)
• Shows a strong increase by up to 6 magnitudes within a few months
• Slow decline on the time scale of years to decades
• Example: FU Ori, V1057 Cyg, V1515 Cyg, Z CMa
• EX Lup type outbursts (EXors)
• Brightness increases up to 5 magnitude, like the FU Ori type outbursts, within a few
months
• Decreases on the same time scale of a few months
• Example: EX Lup, V1647 Ori
• Irregular variations with low or moderate amplitude (∆m <= 2 magnitudes) on the time
scales of minutes to hours.
• Some of these outbursts could be due to solar-type flare activity
• Example: SU Aur
• Quasi-periodic variations on the time scales of 1 – 10 days
• Could represent the rotational period
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Assumed the variations are due to starspots which are the same as sunspots
Starspots of T Tauri should cover a much larger fraction of the stellar surface than
sunspots
Typical amplitudes are a few tenths of a magnitude.
Example: SY Cha, RY Lup, and V410 Tau
Herbig Ae/Be stars
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Approximately 50 known stars
First described in 1960
4 <= M <= 8 Msolar
Spectral type is A or earlier with emission lines
Star lies in an obscured region
Star illuminates fairly bright nebulosity in its immediate vicinity
• Distinction between a “normal” Be star and a “Herbig” Be star is the association with
nebulosity.
Have many of the same characteristics as T Tauri stars
• Emission line spectra in the optical and UV spectral range are similar
• Show strong hydrogen Balmer lines
• Show lines of singly-ionized metals
• Strong P Cygni profiles indicating mass outflows
• Large infrared and sub-millimeter excess that indicates substancial amount of mass of
circumstellar dust
• Inner parts of the disc are more crystalline than the outer parts due to the high
temperature processing and annealing of the dust particles from the constant
exposure to stellar heating. (Quanz, Henning et al. 2006)
• Dust can not exist in the inner 0.35 AU even on the disc surface because of the
high temperatures (>1500 K)
• Only the gaseous disc component can survive
• Found in the same places as T Tauri stars
Have higher luminosities because of the larger mass
One of the most remarkable properties of the Herbig Ae/Be stars is their irregular brightness
variation which can be up to 3 – 4 magnitudes for HAeBe stars of spectral type later than A0.
Physical reasons for the variation which occur on various time scales unclear but should be
the same in principle as T Tauri stars.
A working definition of the Herbig Ae/Be stars (Bastian, Finkenzeller et al. 1983)
“Stellar objects earlier than F0, associated with a region of obscuration and a
reflection nebula; in their spectrum they exhibit emission lines of the Balmer
series of hydrogen.”
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• Example: R Mon, and R CrA
Additional reading on PMS stars can be found in (Appenzeller and Mundt 1989; Bertout 1989;
Reipurth 1989)
Flare Stars
Per the AAVSO, ‘The following types of stars are not recommended for observation by inexperienced
observer due to either their irregularity, or the small amplitude of variation that they exhibit.’
A flare star is a variable star which can undergo unpredictable dramatic increases in brightness for a
few minutes or a few hours. The brightness increase is across the spectrum, from X-rays to radio
waves.
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Flare stars are dim red dwarfs, although recent research indicates a possibility that brown dwarfs
might also be capable of flaring.
• Belong the class of eruptive variables
• Late-type dwarf stars which undergo a sudden brightening at irregular time intervals.
• Spectral type K or M but most are Me stars
• Increase of brightness can be more than 6 magnitudes
• Amplitude of flare increases with decreasing wavelength
• It is stronger in the U band than in the V band
• Time intervals between consecutive flares can be very different
• Usually between several hours to several days
• Total energy in a flare can amount to 1034 erg (1027 J)
• These flares are in principle the same kind of phenomenon as solar flares but with much higher
energies involved
• Extreme solar flare does not exceed 1031 erg
• During a flare the stellar spectrum changes significantly
• Emission lines appear that are not in quiescent state spectra or are much weaker
• In the M emission line stars the emission lines are much weaker
• The strongest emission lines are the hydrogen Balmer series, helium and singly-ionized
metals like [Fe II].
• Flare spectrum is similar to the T Tauri flare spectrum.
• The flare phenomenon is directly related to stellar solar-type activity
• Similar type of flare activity has been found in T Tauri stars, RS CVn stars and Algol type
binaries.
• Flare stars are in the neighborhood of the galactic field
• These field stars are referred to as UV Ceti stars
• Distinction between flare stars and UV Ceti are
• Higher level of activity than the UV Ceti in open clusters and in associations
• Flare stars are younger than UV Ceti stars
• Flare activity depends on age of the star and decreases with increasing age
• Investigations of cluster flare stars have shown all late-type main-sequence stars in a young
cluster are flare stars
• It appears the flare stage is an evolutionary stage all low-mass stars undergo for some time.
• The flare stage is thought to last from a few hundred million to about one billion years
• Length depends on the mass of the star
• Period is longer for lower mass stars
• The rise time to maximum brightness of flares is very short
• Range from a few seconds to a few minutes
• Usually a gradient range from 0.05 – 0.2 mag s-1
• Extreme gradient range can be as high as 2.5 mag s-1
• Decay time has 2 ranges from maximum
• Long-delay – one hour or more
• Impulsive or Spike – a few minutes to a few tens of minutes
• Both type of these flare analogies exist with our Sun.
• The morphological differences probably indicate a real physical differences in the energy
release process
• Flares have been observed over wide spectral ranges from the radio to the X-ray regime
• X-ray observations have been very a powerful tool to study flare eruptions
• Flares are high-energy processes which release a significant part of their energy in the X-ray
regime.
• New type of short-term flare activity has been found called ‘micro-flares’ (Mirzoyan,
Ambaryan et al. 1989)
• Intensities are ten to a hundred times less than an ordinary flare
• Very frequent phenomenon
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Total integrated energy released by micro-flares is rather high
X-ray observation provides a way to estimate temperature, electron density, and size of
the flare region.
• Typical temperature: 20 – 30 x 106 K
• Typical electron density: 1011 – 1012 cm-3
• Typical size of flare region: 1027 – 1028 cm3
Flare activity is partially understood but to model the flare activity the following questions still
need to be answered
• Where the energy comes from
• How is the energy stored in the stellar atmosphere
• How this energy is release within a few seconds
• How the surrounding regions are heated to the high temperatures
For more general reading refer to (Mirzoian, Pettersen et al. 1990; Haisch, Strong et al. 1991)
Pulsating Variables
Pulsating Variables are stars that show periodic expansion and contraction of their surface layers.
Pulsations may be radial or non-radial. A radially pulsating star remains spherical in shape, while a star
experiencing non-radial pulsations may deviate from a sphere periodically. The following types of
pulsating variables may be distinguished by the pulsation period, the mass and evolutionary status of the
star, and the characteristics of their pulsations.
Cepheid Variables
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Period: 1 - 50 days with a few extreme examples up to 200 days.
The mass increases and the age decreases with increasing period
• Those which have periods of near 2 days have masses about 5 times that of the sun and
ages of about 108 years.
• Those which have periods of near 40 days have masses about 15 times that of the sun and
ages of about 107 years.
Amplitude of variation: 0.1 to 2.0 mag.
Classical Cepheids belong to Population I stars.
Relatively young massive stars have high luminosity and are of F spectral class at maximum, and
G to K at minimum.
Usually pulsating luminous white or yellow giants.
May form an evolutionary link between the red giant and main sequence-type phase.
The later the spectral class of a Cepheid, the longer is its period.
Cepheids obey a strict period-luminosity relationship. Higher luminosity will have longer periods.
In 1917 Harlow Shapley provided a method of extracting distances from the period-luminosity
relationship.
• Identify the star as a Cepheid variable by studying its spectrum (if possible) and/or by the
shape of its light curve.
• Calculate its period.
• Use the Period-Luminosity relationship to determine the absolute magnitude.
• Use the inverse-square law to calculate how far a star of that absolute magnitude would have
to be moved from the standard distance of 32.6 light-years to appear as a star of the
apparent magnitude observed.
Temperature between 5000 to 6000 K
Currently there are over 1000 Cepheids cataloged
"Probably all stars with masses more than three times that of our Sun - at least all that are not
close binaries - will go through this stage and will therefore become Cepheids."(PayneGaposchkin 1979)
(Turner 1998) further explains that Cepheids are post-main-sequence objects that begin their
lives as hydrogen-burning, B-type stars. At this stage, they have evolved such that hydrogen
burning ceases to take place in the core of the star, and so they are going through more
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advanced stages of nuclear fuel consumption. In addition, Turner states that "They become
unstable to radial pulsation perhaps five times during such stages: once during shell hydrogen
burning, twice more during core helium burning, and twice again during shell helium burning."
Majority of known extragalactic variables are believed to be of Cepheid type.
Cepheids can be further classified based on the amplitude of variation and period.
• DCEP - classical Cepheids, δ Cephei-type variables. Comparatively young objects which
have [left] the main sequence and are situated in the instability strip of the HertzsprungRussell diagram. They obey the well-known Cepheid Period-Luminosity relation, and belong
to the flat component of the Galaxy. DCEP stars are present in open clusters. They display
a certain relation between the shape of the light curve and the period value.
• CW - variables of W Virginis type. Pulsating variables of galactic spherical component or old
disc population with periods approximately from 0.8 – 35 day and amplitudes from 0.3 - 1.2
mag in V. obey a Period-Luminosity relation different from that for δ Cep variables. For an
equal period value the W Vir variables are fainter than δ Cep variables by 0.7 – 2
magnitudes. The light curves of W Vir variables for some intervals of periods differ from the
light curves of δ Cep variables for corresponding periods either by amplitudes or by the
presence of humps on the descending branch, sometimes turning into broad flat maxima. W
Vir variables are present in old globular clusters and under high galactic latitudes.
Stars in this class: (δ Cep, ζ Gem, X Cyg, W Virginis, TU Cas)
(Cox 1980; Madore 1985) provide useful summaries for the Cepheid class.
RR Lyrae Variables
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Period: 0.2 to 1 day (Kinemuchi, Smith et al. 2006) (RR Lyr itself has a period of 13 hr 36 min)2
Amplitude of variation: 0.2 to 0.4 magnitudes. (Nemec 2004)
Short-period, pulsating, white or yellow giant stars, usually of spectral class A2 – F6.
Lie in the Cepheid instability strip but are fainter than Type II Cepheids. (Matsunaga, Fukushi et
al. 2006)
Older and less massive than Cepheids
Radial pulsating
Population II stars in halos and globular clusters
Versatile objects for astronomical research as distance indicators and as probes for
understanding Galactic evolution and structure. (Kinemuchi, Smith et al. 2006)
S. I. Bailey divided RR Lyrae stars into 3 subclasses based on period-amplitude (Bailey 1902)
• Subclass a ... Increase of light very rapid. Decrease rapid, but much less rapid than the
increase. Light nearly constant at minimum for about one half of the full period, but perhaps
during this time the light changes slowly. In Omega Centauri the range is generally a little
more than a magnitude, and the period from twelve to fifteen hours.
• Subclass b ... Increase of light moderately rapid. Decrease is relatively slow and continues
with lessening rapidity till about the beginning of increase, except that in some cases there is
a tendency to a 'stillstand.' In Omega Centauri, the range is generally a little less than a
magnitude, and the period from fifteen to twenty hours ... This subclass is similar to subclass
a, of which it may be regarded as a modification.
• Subclass c... Light appears to be always changing, and with moderate rapidity. Increase of
light generally somewhat more rapid than the decrease, but in a few cases it appears to be of
only equal, or of less rapidity. In Omega Centauri the range is generally somewhat more
than half a magnitude, and the period from eight to ten hours...
(Preston 1959) discovered that the location of field RRab stars in the Bailey diagram (periodamplitude) was a function of metallicity.
• (Sandage, Katem et al. 1981) noted the same effect in RRab stars of globular clusters might
be explained if metal-poor RRab stars were brighter than their metal-rich counterparts.
• (Clement and Rowe 2000) furthered the argument that RRab stars of Oosterhoff type I and II
occupy separate and distinctive lines in the Bailey diagram.
Data from the AAVSO
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Bailey subclass a and subclass b exhibit mean periods of either near Pab = 0.55 day (Oosterhoff
class I) or near Pab = 0.65 day (Oosterhoff class II) as determined by (Oosterhoff 1939;
Oosterhoff 1944) and verified by subsequent observations. (Castellani and Quarta 1987; van den
Bergh 1993)
• Oosterhoff Class I
• Significantly more metal rich than Class II
• Much more likely to be on retrograde orbits than are Class II
• Those Oosterhoff Class I which are in retrograde orbits are found to be mainly
plunging with a 97.5 percent confidence. (van den Bergh 1993)
• See reference (Perek 1954) for discussion of plunging terminology.
• Clusters with high retrograde motions mainly have metallicities in the narrow range 1.65 <= [Fe/H] <= -1.33
• Oosterhoff Class II
• More luminous than class I
• More massive than class I
• Cooler than class I
• (Sandage 1982) reports a series of evidences suggesting that the mean period (Pab) in
Oosterhoff class II clusters is larger, just because all variables have, for a given temperature,
periods larger than in the corresponding Oosterhoff class I clusters.
• Referred to as the Sandage effect (Castellani and Quarta 1987)
• 9% are RRc
RR Lyrae stars are not close enough to Earth to have their distances and thus absolute
magnitudes measured directly by trigonometric parallax
• Although per (Alcock, Alves et al. 2004), the use of them as standard candles as they pertain
to the LMC is in practice.
• Physical parameters log M/Msolar, log L/Lsolar and Teff are dependent on metallicity (Lazaro,
Arellano Ferro et al. 2006)
• For the RRc stars:
• log M/Msolar = -(0.105 +/- 0.019) [Fe/H] – (0.381 +/- 0.032)
• log L/Lsolar = -(0.111 +/- 0.009) [Fe/H] + (1.554 +/- 0.016)
• log Teff = +(0.013 +/- 0.001) [Fe/H] + (3.882 +/- 0.002)
• For the RRab stars:
• log Teff = +(0.032 +/- 0.006) [Fe/H] + (3.852 +/- 0.008)
• Mv = +(0.191 +/- 0.037) [Fe/H] + (1.032 +/- 0.054)
Most RRab type pulsate in the fundamental mode
• Have a steep ascending branch large amplitude lightcurve when compared with RRc stars
Most RRc type stars pulsate in the first overtone mode.
• Have less amplitude variation as the RRab but are a more sinusoidal shaped lightcurve.
A number of RR Lyrae stars have been found that show mixed mode behavior, pulsating
simultaneously in the first overtone and fundamental modes. These are termed RRd stars.
No RR Lyraes have yet been identified with certainty as pulsating only in the second overtone.
Blazhko effect is occurs exclusively in RRab stars. Blazhko (Blazko 1907) discovered there were
periodic variations in the primary light curve shape of some RR Lyrae stars.
• Changes in the slope of rise to maximum
• Changes in the height of maximum
• Other changes of the shape of the light curve
• Periodic modulation of the primary light curve shape on a timescale typically around tens of
days.
• Found in 20-30% of the RRab stars and in about 5% of the RRc stars. (Szeidl 1988; Moskalik
and Poretti 2003)
• RR Lyr itself demonstrates a Blazhko cycle of about 40 days
RR Lyrae stars which exhibit secondary periodicities can be divided into two main groups:
• The so-called RRd stars which show a mixture of fundamental and first overtone radial
pulsation modes
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Stars which show the classical Blazhko Effect (long-term modulations of their light curves).
• No apparent correlation between the length of the primary period and the length of the
Blazhko period
• The modulation periods are generally in the range 20 to 200 days and the effect on the
light curve can be quite marked.
• A pronounced characteristic of the Blazhko effect is its irregularity.
• In some stars the Blazhko effect nearly vanishes some years, but is very strong in others.
• There is no accepted explanation for the Blazhko cycles but two mechanisms are
possible:
• Blazhko effect is the consequence of some type of mixing of pulsational modes
• Effect may be related to magnetic cycles in the stars, possibly coupled with rotation.
There was some concern RR Lyrae star’s use as a distance scale, as are the Cepheids, was in
jeopardy due to discrepancies in values obtained. There is good evidence that the absolute
magnitudes of the RR Lyraes depend on their metallicities. (Feast 1995; Lazaro, Arellano Ferro et
al. 2006)
RR Lyrae stars are thought to be radially pulsating evolved low-mass (~0.8 solar masses) stars in
the core helium burning stage of their evolution.
• On the horizontal branch in the Hertzsprung-Russell (H-R) diagram which is believed to occur
between the first and second assent of the giant branch of its evolutionary path.
• Exact evolutionary path depends upon mass and chemical composition as well as other
things, but in general: (Smith 1995)
• The progenitor of the RR Lyrae star spends most of its time burning hydrogen on the
main sequence
• After significant time (15 billion years), it ascends the red giant branch where it burns
hydrogen to helium in a shell around the helium core
• Temperatures in the helium core are not yet high enough to fuse helium atoms to form
heavier elements and the inert core collapses and becomes electron degenerate
• At the tip of the red giant branch the core temperature becomes hot enough to ignite
helium and a helium flash occurs as the star initiates its core helium-burning phase on
the zero-age horizontal branch.
• If the star falls within the bounds of the instability strip in the H-R diagram, it pulsates as
an RR Lyrae star.
• The RR Lyrae star is a giant at this point with a radius 4-6 times that of the sun
• Both its radius and luminosity are much reduced from what they were when at the tip
of the red giant branch.
• Eventually the helium source will run out and the star will leave the horizontal branch.
• It swells and cools again ascending the asymptotic red giant branch while making fuel
from hydrogen and helium burning in the shells around the core
• Probably the outer gaseous envelope is expelled as a planetary nebula
• Star continues to shine weakly as a white dwarf
• The white dwarf will gradually radiate its internal heat energy at a low rate
For a general discussion of RR Lyrae variables see (Nemec 1992).
AH Leo
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Primary period of 0.466 day
Vmin = 14.35 mag
∆V = 0.5 – 1.2 mag
Demonstrates Blazhko cycle
• Approx 25 day
RV Tauri Variables
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Classified by three parameters; distinct light curves, their periods, and spectral type.
Period: 30 to 150 days
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Amplitude of variation: up to 4.0 magnitudes
Yellow supergiants having a characteristic light variation with alternating deep and shallow
minima.
Found among the older Population II stars and are seen to congregate in the galactic halo or disc.
Periods are defined as the interval between two deep minima.
Temperature (3000-4000 K)
Absolute Magnitude (-2 to -6)
Luminosity (300-10000 Sun)
Some of these stars show long-term cyclic variations from hundreds to thousands of days.
Known to exist in Globular Clusters and therefore their distances are known.
Not found in Open Clusters, associations, binary star systems, or the Megellanic Clouds
according to Wahlgren. (Wahlgren 1983)
Generally, the spectral class ranges from F to G at minima and G to K at maxima.
Exhibit characteristics of luminosity class II-Ib and occasionally Ia.
RV Tauri stars are probably the low-mass, and in some cases the low metallicity portion of those
stars in transition from the asymptotic giant branch (AGB) to white dwarfs. Because of their
previously high mass-loss rates, many will probably become planetary nebulae. (Jura 1986)
RV Tauri stars can be further classified by their photometric behavior.
• RVa are RV Tauri type stars that do not vary in mean magnitude.
• RVb are RV Tauri type stars that vary in mean magnitude with periods of 600 to 1500 days
(or more), with amplitudes up to 2 magnitudes in V.
RV Tauri stars can be broken into three distinct groupings based on spectroscopic properties.
(Preston, Krzeminski et al. 1963)
• A Class
• typically include spectral types of G or K
• may present irregularities in the strength of the CH and CN bands
• show titanium oxide (TiO) bands at minimum
• Thought to be the younger and more rich in metals than those of C Class
• B Class
• Generally carbon-rich
• weak metallic absorption
• show strong bands of CH and CN between the secondary and primary maximum
• C Class
• Display weak metallic lines
• Resemble the B Class
• Absence of CH or CN bands
RV Tauri stars possess a large infrared excess which is generally associated with a circumstellar
dust shell.
“Based on the seemingly smooth transition between the RVa and RVb stars, Lloyd
Evans (1985) proposes that perhaps the two groups are not physically distinct. "The
RVb stars may be in an active phase in which the dust shell is replenished by dust
formation close to the star... The dust may be swept out with this gaseous outflow,
and in the absence of fresh dust production the star will become an RVa, with a much
less dense shell." The RVa-type stars may, in fact, have thinner dust shells or have
concentration of dense dust located at large radii. As an alternative, perhaps the two
classes may be successive evolutionary processes.
Jura (1986) points out that "analysis of IRAS data shows that the mass-loss rate from
RV Tau stars has apparently significantly decreased during the past ~500 yr... It
seems likely that these stars have just evolved from the phase of rapid mass loss,
characteristic of the last stages of the asymptotic giant branch." In the very late
stages of the AGB, stars undergo extensive mass loss which result in circumstellar
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envelopes. In the case of RV Tau stars, the consensus is that mass is not currently
being ejected.”
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Data indicates that RV Tauri stars may be an evolutionary link between the asymptotic giant
branch (AGB) and white dwarfs.
100 known members of this group include R Sct, U Mon, AC Her, V Vul, AR Sgr, SS Gem, R
Sge, AI Sco, TX Oph, RV Tau, UZ Oph, TW Cam, TT Oph, UY CMa, DF Cyg, CT Ori, SU Gem
α Cygni Variables
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Luminous variable B and A supergiants
Massive O and late type stars belong since these belong to the same evolutionary sequence.
Have the MK spectral-classification of classes Ib, Iab, Ia and Ia+ (in increasing order of
luminosity).
• The most luminous supergiants are also called “hypergiants”
• These “hypergiants” are in fact Luminous Blue Variables (LBVs).
• Ia supergiants are pre-LBV objects. (Sterken and Jaschek 1996)
Historically LBVs (S Dor) were classified as α Cygni class stars until their first eruption was
observed.
Luminous Blue Variable (LBV) classification should be read in parallel when referring to α Cygni
class stars since a lot of details are common to both classes.
All OBA supergiants are variable. (Rosendhal and Snowden 1971; Maeder and Rufener 1972;
Sterken 1977)
The amplitudes of the most luminous supergiants resemble the microvariations resemble the
microvariations observed in the Luminous Blue Variables during quiescence.
The level of variability increases in higher luminosities.
Some α Cygni stars can demonstrate variability of other classes.
• According to Balog et al., Cygnus X-1, O9.7 Iab supergiant with either a neutron star or a
black hole secondary, is not only an X-ray source but an ellipsoidal variable with a reflection
effect due to X-ray heating of the optical star. (Balog, Goncharskij et al. 1981)
β Cephei Variables
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Normal early B giants and subgiants
Also called β Canis Majoris stars
Show coherent short-period light and radial-velocity variations
Possess fundamental and overtone pulsations. (Gautschy and Saio 1993)
Period: 2 – 7 hours
Amplitude: 0.1 – 0.3 Mag
10 – 20 Msolar
The radial velocity was discovered by Frost at the turn of this century at Yerkes Observatory.
(Frost 1902; Frost 1906)
Determined the period of variability as 4h 34m
For decades these stars were labeled “β Canis Majoris stars”
There are over 50 known stars of this class.
No β Cephei have been identified in external galaxies but systematic searches have been limited
to mainly the LMC and SMC.
Grouped in a small cluster on the H-R diagram because of their small range of spectral types and
luminosities.
• Some Be stars share this area in the H-R diagram.
• Near the end of core hydrogen-burning stars
• Some stars observed as β Cep at one time may become Be stars at another
• BW Vul (B2III, V = 6.55) has the largest known amplitude of light variation and radial velocity
variation.
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Light curve is marked by a standstill phase, the beginning precedes time of maximum by
about 0.05 day, duration of standstill is close to 0.03 day.
• Peak-to-peak amplitude of light variation is approximately 0.2 Magnitude in the visual and
increases to about 1.2 Magnitudes at ultraviolet wavelengths.
• The period of variation is about 5 hours and is reported to be increasing at a rate of about
2 seconds per century.
The region of ionization of He+ responsible for destabilizing classical Cepheids, δ Scuti, RV
Tau and RR Lyr variables does not have any effect on β Cep variables. (Christy 1966)
The effects of spin-orbit interactions significantly enhance opacity in the region critical for
driving pulsations
Be Stars
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O6 – B9 stars with Luminosity class V to III that show (variable) emission in the Balmer lines
associated with a rapidly-rotating circumstellar envelope or shell.
• Morphology is reputed to be either a toroidal shaped ring or even a flattened ring structure.
(Chen, Marlborough et al. 1992; Owocki, Cranmer et al. 1996; Meilland, Stee et al. 2006)
• There is still much debate on the morphology of the circumstellar envelope and its
contributions to stellar mass-ejection.
Be stars are often called γ Cas stars or λ Eri stars if they are periodic. (Balona 1991)
• γ Cas was the first Be star discovered by Angelo Secchi in 1866 because of the Hβ emission
line while developing his spectral classification during 1863 – 1868.
• L. R. Wackerling published a catalogue in 1970 of over 5000 early-type stars whose spectra
have shown emission lines. (Slettebak 1979)
• Objects termed Be stars include at least the following five classes (Bidelman 1976)
1) Rapidly rotating single stars
2) Interacting binaries
• If consider ‘normal’ or ‘classical’ Be stars to be represented by B-type spectra of
luminosity class III to V with superposed Balmer and sometimes Fe II emission then
we are discussing class 1 and some representation of class 2.
3) Supergiants
• Early-type supergiant stars do occasionally show Hα emission but are very different
than the ‘classical’ Be stars.
4) Early-type nebular variables
• The early-type nebular variables are also a different class of star. These are the
Herbig Ae and Be stars which are young objects still embedded in the nebular
material from which they formed.
5) Quasi-planetary nebulae
• Quasi-planetary nebulae have been classified Bep and show the nebular lines as
well as Hα in emission. These are very different from the Be stars as defined. They
are radio emitters and apparently have very large circumstellar envelopes. (Purton
1976)
Struve’s famous paper ‘On the Origin of Bright Lines in Spectra of Stars of Class B’ provided the
first physical model of a Be star. (Struve 1931)
Be stars share the same approximate area on the H-R diagram as the β Cep and 53 Per/mid-B
stars
Stars seen as β Cep stars at one time may become Be stars at another.
Many Be stars display short or intermediate-term light variability.
Period: 0.4 – 3 days
• Multiple periods and double waves are found
Amplitude: 0.01 – 0.03 Magnitude
Be stars can be classified into two categories:
• Light curves resembling mild cases of nova outburst (e.g. γ Cas)
• Light curves which are the inverse of nova light curves resembling R CrB stars (e.g. BU Tau
and V477 Her). (Harmanec 1983)
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Specific information about variability of Be stars on the time scales of a couple hours to a couple
of days can be found in (Harmanec 1989).
A source of general reading on Be stars can be found in (Slettebak 1979).
See Stefl (1995) paper on non-radial pulsation (NRP) and rotational modulation (RM)
mechanisms for Be stars. (Stefl, Baade et al. 1995)
53 Per / mid-B / Slowly-Pulsating B Variables
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53 Per stars are O8 – B5 stars that show variability in line profiles with variable periods of the
order of a day.
53 Per stars are non-radial pulsators (Buta and Smith 1979; Smith 1980)
Waelkens and Rufener introduced the class of ‘mid-B’ variables. (Waelkens and Rufener 1985)
• B3 – B8 stars of luminosity class III – V
• Period: 1 – 3 days
• Amplitude: a few hundredths of a magnitude.
• Color variations are in phase with the light variations
• Color-to-light ratio remains constant despite variability in amplitude on a cycle-to-cycle and
even on a year-to-year base
Later inferred that 53 Per and mid-B variables are identical and supported by line-profile work.
Waelkens‘s later report from his personal observations of all mid-B stars reveal that all of these
stars were multi-periodic variables. (Waelkens 1991)
• Period: 1 – 4 days
• Multi-periodicity points to a non-radial pulsation
• Renames these stars to “slowly pulsating B stars” (SPBs)
• Theoretical calculations support this renamed class. (Gautschy and Saio 1993)
Still confusion on how to classify these types of variables.
δ Scuti Variables
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Pulsating variables
Period: < 0.3 day
Spectral types A or F
Amplitude: from a few thousandths to about 0.8 Magnitude
• Magnitude range of about 0.2 is typical for those currently known.
Stars form a group which lies in an instability strip in the H-R diagram which includes the classical
Cepheids at the bright end and the pulsating white dwarfs at its faintest limit.
Confusion exists on the nomenclature applicable to these stars. The broad class contains stars
belonging to both halo and young disc populations in our Galaxy.
Alternate names for all or some of these variables are: dwarf Cepheids, RRs variables, AI Vel
stars, SX Phe, and ultra-short period Cepheids.
δ Scuti stars display a very complex light variation.
• Some are pulsating in one radial mode only
• Others may be pulsating simultaneously in several radial and non-radial modes.
• It is possible in some case mode-switching takes place
Absolute magnitudes range from +3.0 – 0.0.
GCVS lists over 200 members of this and closely related classes.
Type II Cepheids
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Low mass analogues to the classical Cepheids
Reside in the Cepheid instability strip but belong to older populations than the classical Cepheids.
(Matsunaga, Fukushi et al. 2006)
Mass: in the order of 0.6 solar mass.
Period: 0.75 – 40 days
They are radial pulsators
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Found in the halo population of our Galaxy (including globular clusters), the bulge and in the olddisc population (thick disc region) but not in the thin disc or spiral arms.
Referred to as CW stars in the GCVS catalog
• Periods of less than 7 days (often called BL Her or CWB stars).
• Periods of greater than 7 days and less than 20 days (often called W Vir or CWA stars.
Diethelm classified type II Cepheids in the 1 to 3 day period range into 3 groups (Diethelm 1983)
and later renamed the groups (Diethelm 1990)
• RRd stars (smooth light curves) later to renamed AHB1
• CW (or W Vir) stars (a bump on the ascending branch) later to renamed AHB2
• BL Her stars (a bump on the descending branch) later to renamed AHB3
• Neither scheme is widely adopted
• It should be noted the letters RRd are commonly used in current literature to denote double
mode RR Lyrae stars
(Nemec and Matthews 1993) are attempting to revive Arp’s suggestion that not all Type II
Cepheids are pulsating in the fundamental mode.
Studies of their spectra show that shock waves are being propagated outwards through their
atmospheres during each pulsation cycle.
The shapes of the light curves show a general dependence on period similar to the Hertzsprung
progression in classical Cepheids. (Stobie 1973)
Bumps are generally in the descending branch for periods shorter than 1.5 days and on the
ascending branch in longer period stars. Interpretation is not yet clear why. (Petersen and
Diethelm 1986; Simon 1986; Petersen 1993)
Kwee divides Type II Cepheids with periods between 13 and 20 days into two groups (Kwee
1967)
• Those with flat-topped maxima
• Those with “crested” maxima, have a shoulder or hump on the falling branch.
Data shows there is a period-luminosity relation for Type II Cepheids similar to classical Cepheids
• Not yet well defined as it is for analogous classical Cepheids
• Could be due to the presence of overtone?
• Type II Cepheids are fainter than their classical analogues at a given period.
Semi-regular and Slow Irregular Variables
Irregular variable stars, which include the majority of red giants, are pulsating variables. As the name
implies, these stars show luminosity changes with either no periodicity or with a very slight periodicity.
• Period: 30-1000 days
• Amplitude of variation: 1.0 to 2.5 magnitudes
• Giants and supergiants showing appreciable periodicity accompanied by intervals of irregular light
variation
• Cool luminous stars
• TiO absorption becomes strong at low temperatures (minimum light) and thereby tends to
increase the amplitude of variability allowing such stars to meet the amplitude qualification of
Miras.
• GCVS classifies 4 classes of semi-regular variables:
• SRa
• Giants
• Visual light amplitude of less than 2.5 magnitudes and differ from Miras on this account.
• Spectral class M, S, and C
• May or may not show emission lines. Those that do tend to be similar to Miras
• More heterogeneous than Miras and include stars with a range of masses
• In globular clusters
• Kinematic studies of local SRa variables are younger than the globular clusters
• SRb
• Giants
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• Like SRa but with less obvious periodicity
• Spectral class M, S, and C
• May or may not show emission lines. Those that do tend to be similar to Miras
• More heterogeneous than Miras and include stars with a range of masses
• In globular clusters
• Kinematic studies of local SRb variables are younger than the globular clusters
• SRc
• Supergiants
• Fraction of carbon semi-regulars is much higher than the fraction of carbon Miras
• Largely a consequence of the way the atmospheric molecular absorption changes with
phase.
• Thought to be massive with progenitors in excess of 8 solar masses
• SRd
• Semi-regular giants and supergiants
• Spectral class F, G, and K sometimes with emission lines.
• Heterogeneous
• Poorly studied
• Those with emission lines and large amplitude variations have been suggested as a lowmetallicity analogue of the Mira variables.
• Found in globular clusters
• Others seem to more closely resemble RV Tau stars.
• A sub-group, UU Her, located at high galactic latitude has been proposed as a possible
transition phase between the asymptotic giant branch (AGB) and the white dwarf
evolutionary phases.
• Another possibility involves a close binary with a common envelope.
Irregular variables
• Slow varying with no evidence of periodicity
• GCVS uses the classifications Lb and Lc
• Lb
• Giants
• Lc
• Supergiants
Mira Variables (Long Period Variables (LPVs))
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Period: 80-2000 days
Amplitude of variation: 2.5 to 5.0 magnitudes
Giant red variables that show characteristic emission lines
The spectral classes range through Me, Ce, and Se.
Spectral type indicates that Mira atmospheres contain strong molecular absorption and are
therefore cool.
• Me usually indicate oxygen rich
• Ce usually indicate carbon rich
• Se probably indicates an intermediate
• The emission characteristic is an important signature of shock waves associated with
pulsation variability
Light curves in the infrared where most of the energy is emitted have smaller amplitudes than
visual but they are mostly over 0.5 magnitude
Large visual magnitude arise from the combination of the fact we are observing temperature
variations from the blue side of the star’s energy-distribution peak and from the changes in
molecular-band strengths associated with the temperature variations.
Very long periods indicate Miras with very large radii.
Miras are of great interest astrophysically
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Represent a short-lived phase in stellar evolution
They are found at the very tip of the asymptotic giant branch in the H-R diagram
Their next evolutionary step is expected to be the rapid move across the diagram to become
a planetary nebulae.
• Correlations in periods exist which suggests what population the Mira belongs to
• Periods of around 200 days belong to the same, old population as do the metal-rich
globular clusters.
• Longer period Miras are more massive and/or metal rich.
• There is no evidence that Miras systematically evolve to longer periods as they age.
• Miras are useful as distance indicators as they obey a period-luminosity relation
• Can be expressed in total (bolometric) luminosity
• Can be expressed in term of the near-infrared magnitude (usually K, 2.2 µm)
Still uncertain whether Miras pulsate in the fundamental or first over-tone modes.
• There are theoretical reasons for favoring the fundamental mode
• Observational evidence favors the overtone
Miras lose mass rapidly (10-8 – 10-4 solar mass per year)
Low mass loss rates are statistically correlated with the pulsation period, the bolometric light
amplitude and the shape of the light curve.
The most highly evolved Miras are surrounded by the material they have ejected, rendering them
optically faint but strong infrared sources.
The very long-period Miras which have evolved from the most massive progenitors and have the
most mass to lose, have particularly thick shells.
• Some of these circumstellar shells also produce SiO, H2O, and/or OH maser emission which
is detectable at radio frequencies.
Mira light curves are not identical from cycle to cycle
Brightness at maximum often varies by a magnitude or more from one cycle to the next.
Period changes are observed in certain stars and are particularly clearly in R Aql and R Hya
which may be undergoing helium shell flashes.
Additional readings (Campbell 1955; Johnson, Querci et al. 1986; Whitelock, Feast et al. 1994)
ZZ Ceti Variables
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Non-radially pulsating white dwarfs
Period: 30 sec – 25 minutes
Amplitude: can reach 0.2 magnitude
GCVS give 3 subtypes classified according to spectral type
• ZZA
• Spectral type DA
• White dwarfs with pure hydrogen absorption lines
• They have CO-nuclei
• Have thin hydrogen layer
• Have partial ionization zones of hydrogen in its surface layer
• Temperature 12000 Kelvin
• ZZ Cet example
• ZZB
• Spectral type DB
• White dwarfs with pure helium I absorption lines
• They have CO-nuclei
• Have thin helium layer
• Have partially ionized zones of helium in its surface layer
• Temperature 25000 K
• V777 Her example
• ZZO
• Spectral D0
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White dwarfs with continuous spectra or PNNV (variable planetary nebula nuclei)
• D0 displays He II, C IV, O IV
• PNNV displays He II, C IV, nebula
• Have partial ionization zones of carbon and oxygen in its surface layer
• It’s also possible that the κ-mechanism which is responsible for the Cepheid pulsations
operate in these layers
• Temperature > 100000 K
• GW Vir example
ZZ Ceti stars can not be radial pulsators since their periods are too long.
Multicolor observations have confirmed that the pulsations are nonradial gravity (=g) modes
• Unlike pressure (=p) modes, the g-modes are produced by fairly horizontal motions.
• Several periods are simultaneously excited, their frequencies are often split into close pairs
by the slow rotation of the star.
• Periods can be rather stable (∆P/P <= 10-12)
• Unstable periods with period changes occurring over a few hours are probably caused by
interactions of various periods (beating of closely-spaced frequencies).
The white dwarfs have masses near 0.6 solar mass
They have CO-nuclei
Pulsations of a thin CO-convection zone have been suggested for the behavior of all three groups
(Cox 1993)
First pulsating white dwarf was discovered by Landolt in 1986
GCVS lists 22 objects
• 5 occur in nova-like or dwarf nova systems
• Remaining 17 belong to the ZZA type
Cataclysmic Variables
Cataclysmic variables (also known as Eruptive variables), as the name implies, are stars that have
occasional violent outbursts caused by thermonuclear processes either in their surface layers or deep
within their interiors.
“The stars destined to become cataclysmic variables begin as binaries separated by a few hundred solar
radii, orbiting about every 10 years; one must be less than one solar mass and the other more massive.
The heavier star evolves more rapidly, since the greater weight on its core ensures a greater pressure
and temperature, and thus more vigorous nuclear reactions. Luminosity scale is proportional to the
(Mass)3 but the fuel reserves scale is proportional to the Mass, therefore the lifespan of the cataclysmic is
proportional to 1/(Mass)2. Eventually the massive star expands to become a red giant; it then overflows
its Roche lobe, transferring its outer layers to the lower-mass companion.
But this situation – the reverse of that in in a cataclysmic variable – is unstable. The heavier star is
nearer to the center of mass of the binary, so material transferred to its companion moves further from the
center of mass. This increases the angular momentum of the transferred material, and thus the stellar
separation decreases slightly, so that angular momentum is conserved overall. But the decrease is
separation decreases the Roche-lobe size; the heavier star finds itself overfilling the Roche lobe even
more, and yet more material is transferred. The result is a run-away feedback as the entire envelope of
the red giant is dumped onto the companion star, limited only by the speed at which the material can flow.
This might take only a few years, which is extraordinarily fast by the standards of stellar evolution!
The companion star cannot assimilate such an influx, so the material overfills both Roche lobes, and
forms a cloud surrounding the two stars. In this ‘common envelope’ phase the nascent cataclysmic
variable is effectively orbiting within a red giant. The effect is like swimming in treacle: the drag on the
stars as they orbit drains their orbital energy, causing then to spiral inwards. Their separation shrinks
from 100 Rsolar to 1 Rsolar in about 1000 years.
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From the point of view of the envelope, the binary acts as a propeller, expelling it outwards. The energy
extracted from the binary orbit pushes the envelope into interstellar space, forming a ‘planetary nebula’.
The now-naked binary is either a cataclysmic binary, or, if the separation is still too large for mass
transfer, a detached red-dwarf/white-dwarf binary.” (Hellier 2001)
Supernovae
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Period: none
Amplitude of variation: 20 magnitudes
Rare in occurrence
Frequencies of occurrence are dependent on the supernova type and the type of galaxy as well
as the luminosity of the galaxy
Discovery is influenced by the absolute brightness of the supernova, the dust absorption, and the
inclination of the host galaxy
Massive stars show sudden, dramatic, and final magnitude increases as a result of a catastrophic
stellar explosion.
One to several solar masses are expelled at velocities of several tens of thousands km s-1
Light curve in the declining part is powered by thermalized quanta released by the radioactive
decay of elements produced in the stellar collapse of mainly 56Co and 56Ni.
Ejected shell interacts with the interstellar medium and forms a SN remnant that can be observed
long after the explosion in radio, optical and X-ray regions.
Supernovae can be divided into two classes SN I and SN II (Nadyozhin and Imshennik 2005)
SN I
• Have fairly similar light curves and display a small spread in absolute magnitudes
• Spectra around maximum show absorption lines of [Ca II], [Si II], and [He I] but lacks lines of
hydrogen
• Occur in old and intermediate populations
• Their progenitor stars are not clearly identified
• massive white dwarfs (WDs) that accrete matter from a close companion and are pushed
over the Chandrasekhar limit are good candidates
• Could also be the fusion of a WD binary pair
• In either case the collapse of the white dwarf leads to an explosive burning of its carbon
• The released energy is sufficient to trigger a disintegration of the complete object.
• Evidence supports subdivision into subclass Ia, Ib, and Ic
• Light curves of all three are practically identical
• SN Ia
• A thermonuclear supernovae
• Belong to population II type stars
• Disintegration of the white dwarf triggers Ia
• Absolute magnitude: -19.9 mag
• Light curve is powered by the 56Ni -> 56Co -> 56Fe beta-decay
• An average of ~ 0.6 Msolar of 56Ni is synthesized as a result of explosive carbonoxygen (CO) burning in a degenerate Chandrasekhar mass (M ~ 1.4 Msolar)
• Total energy of the electromagnetic emission is ~ 6 x 1049 erg
• Most of the energy is radiated in optical and infrared wavelengths
• Only a fraction is X-rays and gamma photons which manage to escape the
scattering by the expanding envelope.
• The explosion energy Eexp ~ 1051 erg comes from the difference in nuclear binding
energies of the initial carbon-oxygen mixture and the final products of thermonuclear
burning.
• Mainly 56Ni – the most tightly bounded nucleus among all those consisting of
equal numbers of neutrons and protons.
• Almost all Eexp turns out to be converted into kinetic energy of expanding matter
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White dwarf is totally disrupted and no stellar remnant is left
Mean velocity of the expanding debris is estimated to be (u) = (2Eexp / M )0.5 ~
8000 km/s
• Although the above points of concept are observationally and theoretically is wellfounded conjecture the big unsolved problem relating to the mode of thermonuclear
CO-burning are unanswered.
• The most important issue is an interplay between the deflagration and detonation
regimes of burning which is controlled by different instabilities of turbulent
thermonuclear flame propagating in degenerate matter and by the behavior of
the white dwarf as a whole in response to the onset of the burning.
• Pre-expansion
• Radial pulsations
• Requires a sophisticated approach based on 3-dimensional modeling of the CO
ignition and propagation of the thermonuclear flame.
• Problems with convective instabilities
• Problems with Rayleigh-Taylor instabilities
• Problems with Landau-Darries instabilities
SN Ib
• A core-collapse supernovae
• Spectroscopically missing Si II absorption at 615 nm
• Absolute magnitude is approximately 1.5 magnitude below that of subtype a
• Belong to population I
• Disintegration of the white dwarf triggers Ib
• Takes place in massive, hydrogen poor star
• Absolute magnitude: -18 magnitude
SN Ic
• A core-collapse supernovae
• Similar to subtype b
• Spectra around maximum fail to show neither [Si II] at 615 nm nor [He I] at 587.6 nm
SN II
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A core-collapse supernovae
• Not all of the details are fully understood
• Most distinctive feature is an enormous energy of (3 – 5) x 1053 erg = (10 – 15)% MFec2
radiated in the form of neutrinos and antineutrinos of all flavors (e, µ, τ)
• Extensive hydrodynamical modeling during the past 30 years has demonstrated that it is
almost impossible to simulate the explosion by spherical symmetry.
• Based on this information, an empirical theorem can be constructed telling
• Spherically-symmetrical models do not result in expulsion of the envelope
• SN outburst does not happen
• Envelope falls back on the core
• There are 3 reasons under investigation why spherical symmetry breaks down.
• Large-scale neutrino-driven convection
• The accreting shock can obtain an additional energy necessary for
successful explosion from fast, possibly jet-like, subsonic streams of
neutrino-heated matter circulating under and over the neutrinosphere.
(Epstein 1979; Livio, Buchler et al. 1980; Lattimer and Mazurek 1981)
• Interaction between rotation and magnetic fields
• Hydrodynamical heterogeneity of the collapse results in a strong differential
rotation which could amplify toroidal magnetic field.
• Dense central stellar core layers contract increasingly faster than the
outer layers
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Under favorable conditions an excessive magneto-hydrodynamical pressure
could cause or assist in the expulsion of the SN envelope. (Bisnovatyi-Kogan
1970; Ardeljan, Bisnovatyi-Kogan et al. 2005; Moiseenko, Bisnovatyi-Kogan
et al. 2005)
• Rotational fragmentation followed by a neutron star explosion
• Massive fast-rotating collapsed core undergoes rotational fragmentation
generating a close neutron-star binary (Imshennik 1992; Imshennik and
Popov 1994)
• Driven by the emission of gravitational waves and mass-exchange
• Terminates in a low-mass neutron-star explosion (M ~ 0.1 Msolar)
Light curves show greater diversity than SN I
Occur in young stellar populations
Final stage of massive single stars following the red supergiant stage
• > 8 Msolar
Produces a neutron-star or black-hole remnant
Spread in absolute magnitude is broader than SN I
Cause is the depletion of stellar energy when an iron core is formed.
• Iron can not undergo nuclear fusion therefore absorbs available energy
• Since iron absorbs energy there is not sufficient energy to sustain stellar pressure
• Star collapses and forms a neutron star
• Outer stellar layers follows the collapse and bounces off the iron core and is ejected
• Neutrino pressure may play a role in the early stages of the explosion
• Spectra around maximum light has a blue shifted absorption lines of [H] and [He I]
• The [He I] emission line spectra is similar of a nova but has higher expansion velocities
Zampieri et al. (2003) breaks down into two categories based on plateau luminosity or the
expansion velocity measured at 50 days after explosion
Both High and Low Level SNe have progenitors with M >= 20 – 25 Msolar
• High Level luminosity (HL) as modeled by SN1992am
• 56Ni mass ejection increases with expansion velocity over several orders of
magnitude
• Large fraction of ejected envelope mass comes from the Carbon-Oxygen-Helium
layer
• Low Level luminosity (LL) as modeled by SN 1997D and 1999br
• Low level of 56Ni mass ejected
• Ejected mass comes mainly from the measurement of ejected Hydrogen
• Light curves are powered first by the shock heating, then by recombination of hydrogen,
and finally at their tail phase by the 56Co -> 56Fe decay of approximately 0.02 to 0.2 Msolar
of 56Co
• Initially 56Ni
• Total energy of the electromagnetic emission is ~ 1049 erg
• The explosive energy of the core-collapse SNe is typically (0.5 – 2) x 1051 ergs
• Comes from the shock wave that is launched somewhere at the boundary between
the “iron” core of a mass MFe = (1.2 – 2) Msolar
• Collapses into a neutron star
• The outer envelope is expelled
• Mean velocity of the expansion is 3000 – 5000 km/s depending on the mass of
the envelope expelled.
• Three subtypes exist
• IIP
• Plateau shaped light curves
• Contain ~10 Msolar of hydrogen in their envelopes
• IIL
• Linearly decaying light curves
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• Contain ~< 1 Msolar of hydrogen in their envelopes
IIn
• Contain some hydrogen in an extended envelope formed by dense stellar wind
Absolute magnitude: -17.8 magnitude
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Catalogs of supernovae are published (Barbon, Cappellaro et al. 1989; van den Bergh 1994)
Additional readings can be found in (Woosley and Weaver 1986; Petschek 1990; van den Bergh
and Tammann 1991; Woosley 1991; Zampieri, Ramina et al. 2003; Nadyozhin and Imshennik
2005)
Novae
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Period: 1-300+ days
Amplitude of variation: 7-16 magnitudes
These close binary systems consist of a main sequence, Sun-like star and a white dwarf.
• Primary massive white dwarf with chemical elements Carbon and Oxygen or Oxygen,
Magnesium, and Neon
• Cool dwarf star secondary of spectral type G or K
• Cool star overflows its critical volume and looses mass to the primary
• Matter forms an accretion disc around the primary and is finally accreted on its surface
• Instabilities in the accretion disc lead to short and long period photometric variability at the
stage of minimum light
Increase in brightness by 7 to 16 magnitudes in a matter of one to several hundred days.
After the outburst, the star fades slowly to the initial brightness over several years or decades.
Near maximum brightness, the spectrum is generally similar to that of an A or F giant star.
Cause for the nova outburst is a thermonuclear runaway reaction
• Occurs in the accreted hydrogen-rich layer near the surface of the massive white dwarf
• Carbon and Oxygen from the outer layers of the white dwarf are mixed with the accreted
hydrogen
• At a certain critical pressure hydrogen burning begins by the CNO cycle in the degenerate
hydrogen-rich outer layer
• A rapid increase in temperature leads to a lifting of the degeneracy forming a shock wave
• The shockwave in combination with radiation-driven mass-loss produces a large expanding
atmosphere of high absolute magnitude (Mv = -6 to -9) at maximum light
• The decrease in mass due to loss with the ongoing energy release causes a decline of the
visual output
• A shrinking of the photosphere
• Radiative heating of the ejected material giving an interesting spectroscopic phenomenon
Detailed light and spectral properties of novae are complex
• Depends on white dwarf mass and chemical composition
• Depends on the mixing of the accreted hydrogen-rich material with the CO-rich nuclei
• Depends on the dust formation in the ejected shell
Each nova has its unique characteristic photometric and spectroscopic evolution however novae
can be classified in 4 broad subgroups
NA – Fast Novae
• After maximum light it declines 3 magnitudes in visual light in 100 days or less
• Have unusually smooth light curves
• Have higher absolute magnitudes
• Considered as classical novae along with NB subgroup
NB – Slow Novae
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After maximum light it declines 3 magnitudes in visual light in more than 100 days
Fairly structure light curves
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Considered as classical novae along with NA subgroup
NC – Very Slow Novae
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Remain at near maximum light for years or even decades
The bulk of these objects are symbiotic stars
Sometimes referred to as symbiotic novae
These are accreting objects with late-type giant companions
NR – Recurrent Novae
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Period: time intervals of decades
Amplitude of variation: 7-16 magnitudes
Objects are similar to novae, but have repeated outbursts during their recorded history.
Usually these are fast novae
Often have giant companions
Accreting white dwarf is probably near the Chandrasekhar limit
• A position that allows explosions in degenerate material under high pressure
The ‘critical’ amount of accreted material which undergoes a thermonuclear runaway reaction
is about one-tenth of that for classical novae
Only eight have been found in the Galaxy, two in M31 and one in the Large Magellanic Cloud
Nova-like Stars
The GCVS has this group as ‘insufficiently studied objects resembling novae by the characteristics of
light changes or by special features. This type includes, besides variables showing nova-like bursts,
also objects with no bursts ever observed; the spectra of nova-like variables resemble those typical
for old novae at minimum light. Quite often a detailed investigation makes it possible to reclassify
some representatives of this highly inhomogeneous group into some other type of variable star.’
• Not known how novae look between the long interval between outbursts
• Hibernation hypothesis indicates if accretion is reduced then novae may not look like nova-likes
• Could be classified as dwarf novae if:
• Accretion rate and the magnetic field strength are low
• Quasi-periodic disc instabilities could occur
• Could be classified as nova if
• White dwarf mass high enough (MWD > 0.6 Msolar) nova explosions can occur
• If event has occurred in the last decades and was properly recorded
• In all other cases, when signatures of accretion on the white dwarf via a disc or accretion column
are present in the spectrum, and the object cannot be clearly classified as novae or dwarf novae,
it is then classified as nova-like.
• Subdivisions of nova-likes proposed by Ritter (Ritter 1990)
AC – AM CVn systems3
• Accretor is a CO core with a small Helium shell
• [He I] and [He II] greatly outweigh any Hydrogen in spectrum
• Photometric variability with a period in the range of minutes suggested binary nature in 1967
(Smak 1967)
• Composed of a white dwarf primary4 accreting from another white dwarf or a semidegenerate helium star semi-detached system.
• Direct spectroscopy of primary (Sion, Solheim et al. 2006)
• Spectroscopy of secondary (Nelemans, Portegies Zwart et al. 2001)
3
Personal communication with Donn Starkey provided additional understanding, embellishments and
resources on AM CVn.
4
Updated information from Donn Starkey to indicate a confirmed white dwarf binary for AM CVn systems.
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Evolution and mass transfer stability the mass-radius relationship must be known
• Dependent on the temperature, chemical composition, thickness of the envelope etc
• Model 1 – progenitors may be detached close double white dwarfs
• brought into contact by the loss of angular momentum due to gravitational wave
radiation (GWR)
• less massive white dwarf fills its Roche lobe
• AM CVn is born if the stars do not merge
• Model 2 – progenitor may be a semi-degenerate mass donor
• Starting with a low-mass, non-degenerate helium burning star and a white dwarf
companion.
• 2.3 – 5 Msolar
• Long lifetimes of helium stars enhances this scenario giving there is enough
time available to lose angular momentum by gravitational wave radiation and
start mass transfer before the helium burning stops
tHe ~ 107.15 MHe-3.7 yr
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Loss of angular momentum by GWR may result in the Roche lobe overflow
before the helium is consumed in the core if they are close enough
• Mass transfer is stable if the donor helium star mass ratio to the accreting white
dwarf is approximately smaller than 1.2
• When mass of the helium star decreases approximately below 0.2 Msolar the
helium core stops burning and the star becomes semi-degenerate
• Mass transfer causes the orbital period to increase
• Minimum period is approximately 10 minutes
• With a strongly decreasing mass transfer rate, the donor drops to 0.01 Msolar
in a few Gyr
• Period of the system increases up to approximately 1 hour
Light variation caused by rotational, pulsational, and accretion effects (flickering)
• Flickering first noted in AM CVn (Warner and Robinson 1972)
Orbital periods are extremely short, measured in minutes. (Hellier 2001)
7 known objects and one possible candidate: AM CVn, HP Lib, CR Boo, V803 Cen, CP Eri,
GP Com, RX J1914+24, and KL Dra5 (Nelemans, Portegies Zwart et al. 2001)
Undergo common envelope phase evolution (Iben and Livio 1993)
It is thought the evolutionary history which leads to their pure helium composition and the
physics of its accretion may contribute up to 25% of the Type Ia supernovae (Nelemans,
Portegies Zwart et al. 2001) although recent work suggests it less than 1%. (Solheim and
Yungelson 2005)
AM – AM Her systems (polars)
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Composed of a synchronously rotating, magnetized white dwarf (approx 1034 gauss cm3) and
a cool companion which is near main sequence
Magnetic accretion
• Accretion occurs towards the magnetic poles
• The accretion region is at or near the magnetic poles
• Location of the accretion region is determined by the threading region
• The region where material threads onto a field line at a given radius from the
white dwarf will follow the that field line until it plunges into the white dwarf at a
set distance from the magnetic pole
• Anticipated to be an arc near the magnetic pole
• Threading occurs at different locations depending on the density of the material
KL Dra is a candidate only.
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• Denser blobs arriving preferentially at one end of an arc
• More diffuse material arrives at the other end of the arc
• Nature of the impact with the white dwarf depends on the density of the accreting
material
• Diffuse mist accretion material
• Kinetic energy is converted to thermal energy heating it to X-ray
temperatures
• Forms a pool of accreted material which expands because it is hot
• Generates a hot dense accretion column
• Extends approx 0.1 RWD above the surface
• Incoming material slams into the top of the column
• Generates a shock
• Reduces the infall velocity by a factor of 4
• Liberated kinetic energy heats up the material to ~2 x 108 K (20 keV)
• Frequent collisions of electrons and ions produce emission of X-rays
by the bremsstrahlung process
• Material slows further while cooling and becoming more dense and
settles onto the white dwarf
• Accretion columns are strong sources for hard-X-ray emission
• Roughly half of the X-rays will be directed towards the white
dwarf
• Some will be reflected
• Majority will be absorbed and will heat the region around the
column until it glows
• Emits a blackbody radiation at ~200000 K (20 eV)
• Dense blob accretion material
• Not affected by accretion shock
• Have sufficient momentum to plunge straight into the white dwarf
• Bury themselves deep in white dwarf’s atmosphere
• Entire kinetic energy is absorbed by the white dwarf
• Percolates to the surface to emerge as more blackbody radiation at
200000 K
• Most accretion is by dense blobs in AM Her stars
• Dominant radiation is blackbody emission at soft-X-ray temperatures
• Some AM Her stars emit 50 times as much energy at soft X-rays as in hard
X-rays
A magnetic field affects the motion of charged particles, but the moving charges generate
magnetic fields.
Any interaction of a field with hot, ionized gas leads to a complex feed-back loop of
interactions.
End result can be summarized by two general principles
1) the field and the matter become frozen together
• The charged particles can move along the field lines but cannot easily cross them
• Any motion of material drags the field along with it
2) for the purposes of deducing the motion of the material, one can usually either ignore
the field, or ignore everything but the field
Accreting material far from a magnetic white dwarf
• The kinetic energy associated with the bulk flow of the gas will far exceed the energy
associated with the interaction with the field.
• The flow will continue as though there were no field
• The field will be dragged along with the flow but is too weak to affect it
Accreting material close to a magnetic white dwarf
• The energy of the matter-field interaction greatly exceeds the energy of bulk flow
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The field lines remain immovable and the material can do nothing but flow along the
field lines
The strength of a magnetic field decreases rapidly the farther away from the magnetic
white dwarf
• magnetic cataclysmic variables can often be thought to have an outer zone which
acts as a non-magnetic system, and
• a magnetically dominated magnetosphere surrounding the white dwarf
• Division is aided by an effect called ‘screening’
• At the magnetosphere boundary the field induces electric currents in the ionized
plasma; these currents counteract the effect of the field and so ‘screen’ the field
from the material further out
• Extent of magnetosphere is set mainly by the strength of the field and by the
accretion rate depending on whether the material is a confined stream or spreads out
into a disc
Inside the magnetosphere the material is locked to the field lines and is forced into corotation with the white dwarf completing one orbit every white-dwarf spin period
regardless of its radius
3) the spin period of the white dwarf tends to adjust itself so that the circular motion just
inside the magnetosphere equals the circular (~ Keplerian) motion of material just outside
the magnetosphere
• Implies the lowest-field white dwarfs will have the smallest magnetosphere
• Will be spinning the fastest
• Higher-field white dwarfs will spin more slowly
• Higher-field white dwarfs will find an equilibrium with the slower-moving outer parts of
the binary
The interaction between field strength, spin rate and mass-transfer rate determines the
subclass of magnetic cataclysmic variable
Accretes by streaming
• Stream is at first unaffected by the field and flows on a ‘ballistic’ trajectory as it would
in a non-magnetic system until nearer to the white dwarf
• If the magnetosphere extends out past the circularization radius the stream cannot
orbit freely and does not form a disc
• Where the magnetic field begins to dominate the stream changes direction and must
flow out of the plane to follow field lines for the rest of the trip
• Transition from ballistic to magnetically controlled flow is complex
• The increased magnetic pressure of the converging field lines as the stream
approaches the white dwarf squeezes the stream causing it to break up into
dense ‘blobs’ of material
• Field cannot easily penetrate the blobs because of screening so the continue
ballistically for a while
• Magnetic pressures increase and force blobs to change direction
• Collisions in the stream form shocks
• Energy is dissipated and radiated away
• Pool of material collect in a ‘stagnation’ or ‘threading’ region
• Extends over a range of radii relating to the range of blob densities
• Material from the pool (mixture of blobs and fine ‘mist’ of material stripped away
from the surface of the blobs) then diverts along the field lines and flows onto the
white dwarf
• Physical systems tend to settle into their lowest-energy configuration but diverting the
stream out of the plane requires energy
• It is found in many systems the magnetic field of the white dwarf has tilted over so
that one magnetic pole ‘points’ towards the direction of the oncoming stream to
minimize the energy required
• Preferentially material flows to one pole
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Material can flow to the other pole but it must take the long way around thus moving
further out of the plane
• Only a small fraction succeeds in doing this.
• If the dipole is offset from the white dwarf center one magnetic pole will be stronger
than the other.
• Stream will prefer to feed the weaker pole since it requires less of a diversion
Systems show polarized optical radiation
• Ionized material for AM Her systems do not simply follow a field line but spiral around the
field line.
• The motion of the charged particles in the stream is effectively an electric current
• Any electric current moving perpendicular to a field will experience a force
• Force is perpendicular to both the field line and direction of motion
• Causes the particle to move in a circle around the field line
• Motion in a circle involves constant acceleration and accelerating electrons emit
photons thus called cyclotron emission
• Occurs at a characteristic frequency for relatively slow-moving electrons called
cyclotron frequency
• Faster motion radiation occurs at integer multiples of the cyclotron frequency
called cyclotron harmonics
• Smeared out into broad humps around the frequency of each harmonic
• Spectra of AM Her contain cyclotron humps
• Measuring the wavelength of the humps and deducting which harmonic
creates each hump yields the field strength in the region where the
emission came from
• One of the primary methods of measuring field strength in these
stars
• Cyclotron emission is polarized
• Can be up to 50% of the total light from AM Her stars
• AM Her stars are the most polarized objects in the sky
• Polarization is very important to the study of AM Her stars
• From the ratio of linear to circular polarized light the determination of:
• The angle between the line-of-sight and the magnetic axis
• How the angle varies with orbital phase
• Gives insights to the binary inclination and tilt between the magnetic and spin
axis
• Modeling the polarization can also yield the strength of the field
• The geometries are often the best determined among the cataclysmic variables
• Zeeman splitting is another method for determining field strengths along with polarization
and cyclotron harmonics
• Orbits of electrons in atoms set by quantum mechanics are often oriented in a particular
direction
• Usually does not affect the energy of the orbits since one direction is as good as
another
• When a magnetic field is applied the energy of the orbit depends on its orientation
with respect to the field
• Spectral lines resulting from transitions to this orbit is slightly shifted and split into
several components depending on the possible orientations of the orbit
• Degree of Zeeman splitting depends on the magnetic field so measuring the spacing
of the Zeeman-split lines in a spectrum yields the magnetic field strength
Shows strong X-ray radiation
• The accretion pattern of funneling onto a small spot near one magnetic pole (some may
be flowing towards a similar spot at the opposite pole) leads to characteristic X-ray
lightcurves
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If accretion is entirely onto one pole when that pole is facing us we see plenty of Xrays, but we also see none when the pole is away from us
• Lightcurve looks like ST LMi or VV Pup with near-zero light flux for roughly half of the
cycle
• If the system was at low inclination, the accreting pole might always be visible
• X-ray flux would be roughly constant at all orbital phases
• If accretion went to the lower pole then it might never be visible and no X-rays would
be seen
• Some systems do show ‘dips’ in the X-ray lightcurves meaning the accretion stream
is temporarily blocking the accretion spot
• Lightcurve looks like QQ Vul or EF Eri where the accreting pole is always visible but
there are periodic dips where the accretion stream passes in front of the pole and
absorbing the X-rays
Has short-period modulations (orbital motion effects)
Has long-term bright and low states
Orbital periods are below 3.5 hours
17 known objects
See the following references for additional discussion (Cropper 1990; Schwope, Beuermann
et al. 1993; Patterson, Skillman et al. 1995; Schwope, Mantel et al. 1997; Harrop-Allin,
Cropper et al. 1999; Schmidt 1999; Kube, Gänsicke et al. 2000)
DQ – DQ Her systems (intermediate polars, IP)
• Composed of a non-synchronously rotating, magnetized white dwarf and a cool companion
which is near main sequence
• Magnetic moment approx one-tenth as strong as in the AM systems
• Field strength is typically 1 – 10 MG
• Accretion usually occurs in the outer regions via a disc
• Hallmark of an intermediate polar is the observation of pulsed X-rays
• Probably due to the magnetic dipole being slightly off-center to the axis of the white
dwarf.
• Could be the accretion regions have significant height above the white dwarf surface
also breaks symmetry
• Accretion region 0.1 white dwarf radii above surface allows X-rays to be seen for
0.07 cycle longer
• X-ray pulsations in intermediate polars are deeper at lower energies
• Characteristic of absorption of X-rays by material in the accretion flow
• Lower energy X-rays are absorbed more effectively
• Minimum of X-ray pulsation happens when the upper magnetic pole points toward us
and our view of the upper accretion region is obscured by infalling material. Half a
spin-cycle later the upper region is pointing away but our view of the accretion
regions are unobstructed and we see more X-rays.
• Accretion curtain model
• Explains the fact that spin-cycle pulsations are often seen in the optical
lightcurves of intermediate polars
• The dominance of spin-cycle pulses over beat-cycle pulses is the standard picture for an
intermediate polar
• At large radii there is very little difference from a non-magnetic system
• Inside the magnetosphere is where the disc is disrupted and replaced by inflow along
field lines
• In equilibrium a disc-fed white dwarf will co-rotate with the Keplerian motion at the
magnetosphere
• FO Aqr spin period wanders around what is perceived as the equilibrium value
changing from spinning down to spinning up on and approx 10 year timescale
• Accretion by disc-less intermediate polar (V2400 Oph)
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If we look at the lightcurve of V2400 Oph presented in the form of Fourier transforms we
can see the different frequencies that constitute the lightcurve similar to what a frequency
analyzer does for music.
• The circular polarized light varies with a period of 924 seconds
• Since polarization is caused by a field then this must be the which the magnetic
dipole and white dwarf is spinning
• X-ray flux varies with a period of 1003 seconds while the spectroscopy of the star
shows the orbital period of 3.4 hours.
• 1003 seconds is the beat period between the spin and orbital cycles
• The accretion stream is flipping between the two magnetic poles as the white
dwarf spins beneath it
• X-ray flux that is produced varies with the interaction period
ω and Ω are the spin and orbital frequencies respectively, beat frequency is ω - Ω.
Equivalently, 1/Pbeat = 1/Pspin – 1/Porb
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Confirmed by Doppler shifts of the emission lines
Spin period is approximately 8% of the orbital period
• The stream of material will emerge with an angular momentum appropriate to the
Lagrangian point
• Equivalent to that in a Keplerian orbit at the circularization radius
• White dwarf will tend to adjust its spin rate so that at circularization radius the
magnetic field lines are traveling at the same speed as the local Keplerian orbit
Close to the white dwarf the accretion disc is disrupted by the magnetic field and mass flows
via an accretion column towards its magnetic poles
Light variations are caused by eclipse effects and by rotationally moderated accretion effects
24 known objects and only a few have shown nova explosions
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Seen nearly edge on which creates a deep X-ray eclipse every 6.06 hour orbital cycle
• Lies behind a molecular cloud so it is not observable visually
• It emerges from eclipse and pulses at the 206 sec spin period
• Analysis shows the bulk of the X-ray flux emerges from eclipse in less than 2 secs
• The white dwarf takes approximately 30 secs to emerge from eclipse
• Implies that most of the X-rays originate from a small concentrated accretion
region
• Region is approximately 0.001 of the white dwarf surface
• Timing the eclipse egresses at different phases of the spin cycle give a good idea
of where the accretion region is located on the white dwarf surface.
• During half of the spin cycle the upper pole is visible then the lower pole
becomes visible during the remaining part of the spin cycle.
• Generates a nearly constant X-ray flux
• The low-level pulsation seen must then be due to a small asymmetry
between the poles such that the appearance and obscuration of the poles
are not quite synchronized
Also a dwarf nova
• Outer ring is capable of undergoing the dwarf nova instability(Hellier, Mukai et al.
1997)
• Inclination of 82o
• Quiescent magnetosphere extends out to 9 white-dwarf radii if it can be assumed
to co-rotate with the white dwarf spin period of 206 sec.
• Allows the bottom pole to be seen through the cleared center of the disc
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As the increased accumulation of material the increases the disc viscosity it
pushes an overwhelming flood of material towards the magnetosphere.
• Boosts the disc’s ram pressure to overwhelm the magnetic field and pushes
the magnetosphere inward.
• A 20 – 24 X increase in accretion rate drives the accretion disc to within
approximately 4 white dwarf radii and therefore our view of the lower pole in
the white dwarf is cut off.
• Symmetry of the quiescent state is disrupted by the disappearance of the
upper pole over the white dwarf limb
• No longer compensated with the appearance of the lower pole by the
obscuration caused by the collapse of the disc material on the
magnetosphere
Results in a strong AM Her-like observation.
EX Hya
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Consists of a white dwarf primary (Hoogerwerf, Brickhouse et al. 2004; Hoogerwerf,
Brickhouse et al. 2005)
• Spin period = 67 minutes
• Orbital period = 98 minutes
• Mass = 0.49 +/- 0.13 Msolar
• Radius = 1.0 +/- 0.2 x 109 cm
• Max rotation velocity = 15 km s-1
Secondary
• Mass = 0.078 +/- 0.014 Msolar
There is an angle of inclination such that the lower accretion pole of the white dwarf is
partially obscured by its companion as indicated by lightcurve data.
• Angle of incidence (i) = 77.2o +/- 0.6o
There seems to be a discrepancy for the various properties of the white dwarf based on
whether the calculations were performed using X-ray, optical photometry or optical
spectroscopy. (Belle, Howell et al. 2005)
• TWD = 23000 K using spectral models
• MWD = 0.9 Msolar using spectral models
• Accretion disc truncated at 2.5 RWD
AO Psc
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Primary (Hellier, Mukai et al. 1996)
• Curtin accretion model matches parameters obtained
• Spin period = 805 sec
• Orbital period = 3.59 hour
• 0.47 +/- 0.04 Msolar
• Angle of incidence ~ 60o
• Radius of the magnetosphere ~ 4 x 109 cm
Secondary
• Mass ~ 0.16 Msolar
AE Aqr
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A magnetic cataclysmic variable with a lot of peculiarities
• Unusually long orbital period of 9.9 hours.
• Short spin period at 33 seconds
• Implies a small magnetosphere with a large disc if the system were in equilibrium
with its accretion
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Optical light produced by the material transferred by the secondary indicates an
accretion flow of 1000 times greater than the actual mass accreting onto the white
dwarf by its weak X-ray flux.
Suggests a rapidly spinning field is ejecting the majority of the flow from the binary
• Causes the white dwarf to lose energy and reduces the rate at which it spins
Rotational energy is lost at 100 times the rate at which the accretion flow radiates
The magnetic field is spinning too rapidly for the larger magnetosphere and therefore
acts as a propeller.
Over time the energy drain will decrease until disc-fed accretion can resume (Wynn,
King et al. 1997)
WZ Sge
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Propeller may be operating as judged by the detection of pulsed X-rays with a period of
28 seconds
• If the 28 seconds can be considered the white dwarf spin period then this is faster than
any other magnetic cataclysmic variable
• 33 year intervals between superoutbursts with no intermittent outbursts
• Discussion of the mechanics of such a phenomenon is provided by (Hellier 2001) and is
outlined below:
• Can only be produced by invoking an exceptionally low viscosity in quiescence so
there is no diffusion into the inner disc and triggers an outburst
• A magnetic propeller would expel material from the inner disc preventing the buildup
that would trigger an outburst
• Material accumulates in outer disc where the mass required to trigger an outburst is
much larger greatly increasing inter-outbust intervals
• When outburst occur they involve sufficient material to become superoutbursts
• Inward surge of material in a superoutburst overwhelms the magnetic field
• Collapses the magnetosphere onto the white dwarf surface that allows accretion
For additional discussion please refer to the following references (Patterson 1979; Hellier
1991; Hellier, Cropper et al. 1991; Hellier 1993; Patterson 1994; Hellier, Mukai et al. 1996;
Hellier 1997; Hellier, Mukai et al. 1997; Hellier 1998; Patterson, Kemp et al. 1998; Hellier,
Kemp et al. 2000)
UX – UX UMa systems
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Systems have bright accretion discs caused by high accretion rates
Eclipse effects are often observed in the light curves
Some systems resemble novae at minima
15 known objects
VY – VY Scl stars (anti-dwarf novae)
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Similar to UX subdivision but spend most of their time in ‘high state’.
Candidates for systems entering the ‘period gap’ of 2 – 3 hours
There are 11 objects which from time to time fade by several magnitudes and remain in the low
state for days to months.
Most have orbital periods of around 3 hours
Additional reading on novae, nova-like stars and dwarf novae can be obtained from (Mauche
1990; Ritter 1990; Hack, Ladous et al. 1993)
Available catalogs (Ritter 1990; Downes and Shara 1993)
Dwarf Novae
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Close binary system
Orbital periods between 80 minutes and 14 hours
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Consists of a white dwarf primary and a red main-sequence star of spectral type between G and
M as secondary
Companion is so close to the primary (within the Roche lobe) that it continuously loses matter
from its surface towards the white dwarf
• The stream of matter cannot hit the white dwarf directly due to its large angular momentum
• The angular momentum forces the matter to form an accretion disc around the white dwarf by
keplerian orbit
• Light variations observed are caused by the rather complex behavior of the accretion disc
Characterized by semi-regular outbursts of sudden brightening by 3 – 8 magnitudes in a day, a
bright phase of 3 – 10 days and a subsequent decline of a few days
Outbursts repeat at mean intervals or cycle periods characteristic for each star
Shortest cycles are about 10 days
Typical cycle lengths are from 20 – 200 days
Extreme cycle length are up to 33 years as seen in WZ Sge (Osaki 1995)
In quiescent state emission-line spectra with broad and often doubled Balmer and He I lines
• Formed in and around the accretion disc
Disappear during outburst when they are replaced with very broad Balmer absorption lines
• Originate in the disc
• Disc is much brighter and optically thick
Outbursts are due to the release of potential energy within the accretion disc
• Change in viscosity in the disc (sudden)
• Outer disc matter falls into the white dwarf
• Energy released when matter hits the surface (“accretion”)
• Released in the form of radiation in the optical, ultraviolet, and X-ray range
• Controversy exists over the reason for this change
• Most people favor disc instabilities such as the change from radiative to convective disc
structure (Meyer and Meyer-Hofmeister 1981; Ludwig, Meyer-Hofmeister et al. 1994)
• Others defend an alternative view of mass flow towards the disc is variable due to an
unknown instability of the red secondary star (Bath, Clarke et al. 1986)
Reference for further reading and catalogs are given at the close of Nova-like section
3 sub-classes
SS Cygni (UGSS)
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Have orbital periods of greater than 3 hours
Show outbursts with typical intervals of 30 – 100 days
Each outburst last for about 3 – 10 days
Obeys Kukarkin-Parengo relation
• Relationship between outburst amplitude and the mean time interval between two
subsequent outbursts (cycle length)
75% show clear division between wide and narrow outbursts
• Bimodal width distribution
• Total outburst increases the width ratio (of wide to narrow) decreases with orbital period
70% show occasional ‘anomalous outbursts’ characterized by an abnormally-slow rise phase
and lasts nearly as long as the decline giving a symmetric appearance to the light curve.
For orbital periods of > 10 hour, anomalous outbursts seem to be usual if not exclusive type
of outbursts
Anomalous outbursts may be either wide or narrow.
• No obvious explanation
U Geminorum (U Gem)
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First dwarf nova detected
An eclipsing system with partial eclipses of the accretion disc
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SS Cygni (SS Cyg)
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Brightest and best observed of all dwarf novae
BV Centauri (BV Cen)
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Has the longest orbital period (14.64 hours)
Shows short ‘standstills’ in the rising branch of outburst
Has a typical hump light curve
Z Camelopardis (UGZ)
• These systems show cyclic variations, interrupted by intervals of constant brightness called
“standstills”.
• Standstills are characteristic of UGZ stars
• standstills last the equivalent of several cycles, with the star “stuck” at the brightness
approximately one-third of the way from maximum to minimum.
• Standstills are interpreted as a period of stabilization of the mass transfer and the mass
transfer rate (Meyer and Meyer-Hofmeister 1983)
• The standstill always ends with a return to quiescent state and the subsequent recovery of
the outburst
• Spectra in standstill is similar to the spectra of a dwarf nova in outburst with the broad Balmer
absorption
• (General observation of the visual light curve of Z Cam) The light curve goes through several
oscillations between min and max over several cycles (a few weeks to months) and then
goes into the standstill phase with minor oscillations representing more or less ‘noise’ about
one-third of the way down from maximum (several months). The standstill phase ends
dropping to minimum and beginning its cycle of several oscillations from min to max.
• Examples are Z Cam and RX And
SU Ursae Majoris (UGSU)
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These systems have two distinct kinds of outbursts:
• One is faint, frequent, and short, with a duration of 1 to 2 days which repeat at intervals of
15 – 40 days
• The other (“superoutburst”) is bright, less frequent, and long, with duration of 10 to 20
days and occur at intervals of 6 months to several years.
During superoutbursts, small periodic modulations (“superhumps”) appear.
Superhumps appear shortly after passing maximum
• Repeats with a period that is 3 – 5% longer than the orbital period
Generally have orbital periods below the period gap (< 2 hr) or in a few cases near the upper
border of approximately 3 hr
Typical mass-transfer rate ~ 5 x 1012 kg s-1 (10-10 Msolar yr-1)
Superhumps were first observed spectroscopically in Z Cha during outburst (Vogt 1982)
• Orbital disc motion showed large displacements (several 100 km s-1) in the zero term of
the radial velocity curve
• Varied with the beat period between orbital and superhump periods
• Direct evidence for an elliptical deformity in the accretion disc during superoutburst
• The disc is slowly processing in the inertial frame of reference
• Subsequent theoretical calculations and modeling showed that the eccentric disc is a
natural consequence of its expansion toward critical radius of the 3:1 resonance
• A precessing eccentric develops due to tidally-driven instability
• Periodic tidal stressing of the eccentric disc by the orbiting secondary gives rise to the
superhump light variation (Whitehurst 1988; Ichikawa, Hirose et al. 1993)
• Tidal instability implies binary systems with extreme mass ratios of 4 or greater
Compilation of all known SU UMa stars and their characteristics is available (Molnar and
Kobulnicky 1992)
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VW Hyi
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Brightest and best studied SU UMa star that shows an ‘orbital hump’ in the light curve at
quiescence
ER UMa
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Sometimes referenced as RZ LMi type
Short orbital period (Porb < 92 mins)
Shortest supercycle system known
• Supercycle 20 – 50 days
• Between superoutbursts a rapid succession of normal outbursts
• ~ one every 4 days
Has approx 10 times the mass-transfer rate as SU UMa which explains rapid succession
of outbursts to contend with the increased transfer rate.
• ~ 4 x 1013 kg s-1
• If the rate of mass transfer increased more the superoutburst would lengthen being
sustained by increased flow of accretion material.
• With high enough mass transfer the star would become stuck in permanent
superoutburst and be similar to a novalike.
Understanding the behavior is still not completely understood
• Why the superoutburst shuts down before it has drained the disc of material before it
starts another outburst just as it reaches quiescence?
• Osaki’s standard tidal-thermal-instability model does not answer issue because
superhumps are observed at nearly all phases of the supercycle.
Z Cha
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SU UMa star with total eclipses of white dwarf and hot spot
WZ Sge
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White dwarf with the longest-known super cycle system (32 yr)
Shortest-known orbital period (1.36 hr)
An eclipsing system
Mass-transfer rate in the neighborhood of 1012 kg s-1
• Takes decades to accumulate sufficient material for a superoutburst
• Unknown why that during the accumulation of material there are no or very few
normal outbursts.
• Probability the disc viscosity is extremely low ( < 0.001)
• Normal disc viscosity during quiescence is ~ 0.01 – 0.05
Peculiarity is the observation of bright humps in the lightcurve recurring with the orbital
period and not the superhump period.
Some discussion if WZ Sge should be its own class (Hellier 2001)
Examples: EG Cnc and WZ Sge
Symbiotic Stars
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Period: semi-periodic
Amplitude of variation: up to 3 magnitudes
There are over 150 stars that have been classified as symbiotic
Defining characteristics
• Erratic photometric variability
• Spectra simultaneously show:
• Spectral signature of a cool giant (molecular absorption features)
• Spectral signature of high-temperature plasma (high-excitation emission lines)
A mass transfer system composed of three components:
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Cool giant or super-giant mass donor
• Usually spectral class K or M
• If has Mira-type variability then has usually has a large infrared excess (Kenyon,
Fernandez-Castro et al. 1988)
• A circumstellar ionized nebula
• Has electron temperature of approximately 17000 K
• Mass-accreting secondary
• A degenerate star
• White dwarf or sub-dwarf
• Effective temperature of approximately 100000 K
• Neutron star
• Accretion rate 10-9 – 10-7 Msolar yr-1
• Example: V2116 Oph (Chakrabarty and Roche 1997)
• Main-sequence star
• Roche lobe filling
• >= 10-5 Msolaryr-1 mass-transfer rate (Iben and Tutukov 1996)
Close binary systems consist of a red giant and a hot blue star, both embedded in nebulosity (i.e.
interacting binary system)
Have been often misclassified as peculiar planetary nebula using limited wavelength regions
Molecular absorption features are only present in the infrared spectra
The symbiotic phenomenon with erratic variability and high-excitation emission lines occurs when
mass is transferred from the giant to the other star
Accretion occurs in two possible ways
• Main-sequence star accretion by direct tidal overflow (Roche-lobe overflow) from the giant
• White dwarf accretion from the giant’s stellar wind
Many systems show evidence of accretion disc
Process of mass transfer gives rise to a ‘hot spot’.
• Hot spot produces the temperature necessary to ionize part of the circumstellar environment
• Hot spot produces the emission lines
Symbiotic stars are closely related to the VV Cep systems (rare) which a late-type supergiant
interacts with a O or B star
Level of symbiotic activity depends on the separation and the evolutionary states of the two stars
Time scales are from seconds (flickering) to decades although the most studied are on a time
scale of days to tens of days
Variations due to orbital modulation are seen
Orbital periods range from 100 days to many years
Some show eclipsing
• Examples AP Pav and CI Cyg
Techniques are available and used to determine good orbits for the giants but orbits of the hot
companion are more difficult
• In best cases velocities of emission features thought to be associated with the hot component
have been measured and mass ratios of the stars have been computed. Then various
assumptions have been used to estimate the masses, radii, separation of the components,
and the Roche-lobe radius of the cool giant.
• Only about 12 of the 150 known symbiotic stars currently have been reasonably welldefined orbit of the cool giants (Seal 1997)
• Problems in observation:
• Visual observation is hampered by both emission-line spectrum and scattering by dust, if
present, from the cool star.
• 1 – 2 m region of the IR spectrum offers a window with much-reduced dust extinction
that is merely free from contamination by the hot star
• D-type or “dusty” symbiotic stars contain Mira variables
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IR spectroscopy of Mira variables clearly demonstrate the benefits of observing these
stars near the H- opacity minimum at 1.6 m.
• Spectra of Mira variables at the 1 – 2 m IR show cyclically repeatable large
amplitude (20 – 30 km-s-1) velocity changes during a pulsation period.
Blue spectra is dominated by emission lines makes it difficult to put observation on a
standard UBV or ubvy system
Variations among instruments prevent the compilation of results
• Would require a single instrument to perform large numbers of measurements to
obtain any detail
Very Slow Novae
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Examples: RR Tel, V1016 Cyg and AG Peg
Have undergone outbursts which take years to decades to decay
Outbursts are thought to be runaway thermonuclear reaction in the accreted material on the
surface of a white dwarf
Closely related to the recurrent novae (RS Oph and T CrB)
Mira or D-type
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Distinguished by their near-infrared color that indicate the presence of dust
Indicate the Miras are normal
Subject to higher circumstellar extinction than typical single stars
Mira-like variability is clearly marked only in the infrared
Mira symbiotics probably have the longest orbital periods of all known interacting binaries
Mira (o Ceti) is a binary system with its white dwarf but is widely separated and relatively low
interaction is probably the reason why it is not classified as a symbiotic.
S-type
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Have stellar infrared color
A cool absorption spectrum is present from the M giant component of the system
Near the 1 µm there are a number of strong transitions of hydrogen and of both neutral and
ionizied helium which can be used to study and classify. (Baratta, Neto et al. 1991)
• [Fe II] at λ 999.7 nm has a strong fluorescence line
• [H I] at λ 1005 and λ 1094 nm (P7 and P6 respectively)
• [He I] at λ 1083 nm
• [He II] at λ 1012 nm
CI Cyg
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Eclipsing system
812 day orbital period
Components: Roche-lobe filling M4 giant and a main sequence accretor
Has undergone several outbursts but no two are identical
Shows some flickering
AR Pav
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Eclipsing system
605 day orbital period
Components: Roche-lobe filling M3 giant and a main sequence accretor
AG Peg
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A bright 8.4 magnitude system
816.5 day orbital period
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Components: Roche-lobe filling M3 giant and a white dwarf accretor
Underwent a nova-like outburst in the 1950s and still appears to be decaying
RR Tel
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Symbiotic Mira and a very slow nova
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Extrinsic
Extrinsic variables are those in which the light output varies either due to processes external to the star
itself or due to the rotation of the star. The two main classes of extrinsic stars are the eclipsing binaries
and rotating variables.
Rotating Variables
Rotating stars show small changes in light that may be due to dark or bright spots, or patches on their
stellar surfaces (“starspots”). Rotating stars are often binary systems.
Ap and roAp Stars
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Ap star surface is depleted in He at the same time overabundance of Iron, Silicon and Chromium
in spots
• A chemically peculiar (CP) star in the spectral class B2 – F in which the spectra signatures of
chemical peculiarities, i.e. strongly-enhanced spectral lines of Fe and rare-earth elements
• Has global surface magnetic fields of 0.3 to 30 kG (thousands of times stronger than the Sun)
• Effective magnetic-field strength varies with rotation
• Time scales of light variation ranges from minutes to decades
• Intrinsically slow rotators but hotter stars rotate faster than cooler stars.
• Length of rotation period can be derived as the aspect of their spotted surface varies
periodically with time
• Most periods are from one day to one week
• Surface inhomogeneities and the magnetic structures on Ap stars seem to be quite stable
over the years
• CP stars are also variable in the infrared
• Near-infrared light curves seem to be phase related to the magnetic field variations in the
sense that magnetic-field extrema might coincide in time with the infrared light extrema
Rapidly-oscillating Ap (roAP) stars are cool magnetic AP SrCrEu stars which pulsate in highovertone, low-degree non-radial modes with periods from 5 minutes to less than 20 minutes
(Kurtz 1982)
• Amplitudes of light are less than a few millimag
• Pulsations are dominated by strong global magnetic fields of the Ap stars
• Amplitude is modulated with rotation in phase with the magnetic-field modulation
• Less than 30 roAp stars are known
• Located in the lower δ Scuti-star instability strip
• Have intrinsic cyclic frequency-variability on a time scale of hundreds of days to years. (Kurtz
and Martinez 1994)
• Suggests a magnetic cycle may be in operation
Oblique Pulsator Model
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Proposed by Kurtz (1982) assumes the pulsation and magnetic axes are aligned and oblique
to the rotational axis
Rotational modulation of the light variation is caused by the varying aspect of non-radial
pulsation modes (Kurtz 1990; Shibahashi and Takata 1993; Kurtz and Martinez 1994)
Spotted Pulsator Model
• Assumes the pulsation axis coincides with the rotation axis of the star so that the pulsation
modes are always seen from some viewing angle
• The ratio of flux to radius variations and phase lag between the flux and radius variations are
variable over the surface as a function of magnetic-field strength (Mathys 1985)
For a general review of A stars, Ap stars and the oblique-rotating model refer to the following
reference (Wolff 1972)
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For general discussion of the magnetic fields in all stars see the following reference (Landstreet
1992)
For reviews of the roAp stars see the following references (Shibahashi 1987; Kurtz 1990;
Matthews 1991)
Ellipsoidal Variables
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Subgroup of rotating variable stars
Subgroup needs to be updated in some catalogs especially GCVS
Non-eclipsing binaries which neither, one or both stars are elongated by mutual tidal forces
As the binary orbits the elongated star rotates producing two maxima and two minima per orbit
• Most eclipsing binaries show this behavior
• GCVS does not specify them as ‘ELL’
• Stronger limb-darkening on the pointed end of the more elongated produces one minima
deeper than the other
Although the GCVS does not list this classification, there is another mechanism which would
produce the same light curve
• A system which the reflection effect greatly increases the lamination of one of the
component’s one hemisphere
• Examples would be HZ Her and BH CVn
At least a half-dozen ellipsoidal variables are known to approach 0.4 magnitude variation
although the GCVS states the light amplitudes in ellipsoidals do not exceed 0.1 mag (Hall 1990)
Systems in which neither one nor both components are evolved which are detached or semidetached
Spectral types from O to M
Examples
• ο Persei:
• A B1 III + B2 III 4.42-day binary system
• Both components contribute to the ellipticity effect of 0.07 magnitude in V
• Minima are equal
• IW Persei:
• Spectral type A5m 0.92-day system
• Full ellipticity effect is 0.05 magnitude in V
• Minima are equal
• V350 Lacertae:
• Spectral type K2 III 17.755-day single-lined binary system
• K2 giant is chromospherically active, the GCVS added ‘RS’ classification (Crews, Hall et
al. 1995)
• Starspots contribute a great deal to its variability
• Full amplitude is 0.075 magnitude in V with one minima about 0.01 magnitude deeper
• Due to limb-darkening because the K2 giant fills only 75% of its Roche lobe
Further reading on the ellipticity effect and ellipsoidal variables are in the following references
(Wilson and Fox 1981; Morris 1985; Lines, Lines et al. 1987; Lines, Lines et al. 1988; Hall 1990)
BY Draconis Variables
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Subgroup of rotating variable stars
A historical discussion is offered by (Hall 1994)
Physically a dKe and dMe stars
• Late dwarfs with hydrogen lines in their spectra
Axial rotation of a star with uneven surface brightness produces variability
• Apparently a region of cool spots on one hemisphere
Can be classified as a RS CVn binary because of its chromospheric activity but unlike RS CVn
they can be either binary or single
Was thought one of phenomenon contributed to by binaries was starspots
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Found that singles with an equatorial rotation rate of 5 km s-1 or faster was required (Bopp and
Fekel 1977)
The companion star in binaries is only indirectly important to speed up rotation by spin-orbit
coupling mechanism
Several show UV Ceti-type flares giving the ‘UV’ classification by GCVS
A few stars classified as BY in GCVS probably should be classified as FK Comae-type variables
• Single star, spotted, and varying due to rotational modulation but not the ‘proper’ spectral
type and/or luminosity class for BY variables
• Examples: OP And (gK1), V390 Aur (K0 III), EK Eri (G8 IV-III), etc
Examples
• BY Dra:
• A K4 V + K7.5 V 5.975-day non-eclipsing binary system
• Starspot wave period is 3.827 days
• Ratio between orbital period and wave period is indicative of a pseudo-synchronous
rotation with eccentricity of e = 0.31
• Systems mean brightness varies with a 50 – 60 year cycle
• CC Eri:
• A K7 Ve + ? 1.56-day non-eclipsing binary system
• Discovered before it was accepted that starspots produced variability (1959)
• OU Gem:
• A K3 V + K5 V 6.99-day non-eclipsing binary system
• Wave period is 7.36 days longer than the orbital period
• Non-synchronous rotation and relatively young
Additional reading on chromospheric activity and BY Dra-type variables in the following
references: (Bopp and Fekel 1977; Linsky 1980; Byrne and Rodono 1983; Baliunas and Vaughan
1985; Hall 1986; Strassmeier, Hall et al. 1993)
FK Comae Variables
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Rapid rotating giants
Possess uneven surface brightness on one hemisphere (starspots)
Late-type giants with very short rotation period (high values of v sin i)
Extreme chromospheric activity
No indication of large velocity variations
GCVS allows binaries in this classification
FK Comae rotates so fast the most reasonable evolutionary scenario involves the coalescence of
a W UMa-type binary and an optically thick spun-up envelope
Other stars assigned the this class do not spin as fast
May be an evolved single A-type star that have not lost their rapid main-sequence rotation
If binaries were allowed the their rapid rotation would be by synchronization with a short orbital
period
Only 4 stars appear in the 4th edition of the GCVS but a few more have appeared in lists
Examples
UZ Lib:
• A K2 III + (dwarf M?) 4.768-day binary system
• Photometric period is 4.75 +/- 0.01 day
• Starspots produce a large variation (approx 0.35 magnitude in V)
OU And:
• A G1 III single giant
• Rotation period of 23 days
• Variability 0.04 magnitude in V
• Lies in the Hertzsprung gap
• May have evolved from a rapid rotating single A-type main-sequence star but not having
passed the rotational break that happens between G0 III and G3 III
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References for further reading (Bopp and Stencel 1981; Fekel, Moffett et al. 1986; Strassmeier
and Hall 1988; Gray 1989)
Pulsars
Pulsars are rotating neutron stars that are observable as sources of electromagnetic radiation in radio
wavebands. The radiation intensity varies with a regular period, believed to correspond to the rotation
period of the star. Pulsars also create what is called the lighthouse effect, this is when the light from a
pulsar is only seen at a specific position and not all of the time. Werner Becker of the Max Planck
Institut für extraterrestrische Physik recently said,
"The theory of how pulsars emit their radiation is still in its infancy, even after nearly forty years of
work.. There are many models but no accepted theory."6
The first pulsar was discovered in 1967, by Jocelyn Bell Burnell and Antony Hewish of the University
of Cambridge, UK.7 Initially baffled as to the unnaturally regular nature of its emissions, the pair
dubbed their discovery LGM-1, for "little green men"; their pulsar was later dubbed CP 1919, and is
now known by a number of designators including PSR 1919+21. The word pulsar is a contraction of
"pulsating star", and first appeared in print in 1968:
"An entirely novel kind of star... came to light on Aug. 6 last year and, ... was referred to by
astronomers as LGM (Little Green Men). Now... it is thought to be a novel type between a white
dwarf and a neutron [sic]. The name Pulsar (Pulsating Star) is likely to be given to it. ... Dr. A.
Hewish ... told me yesterday: '... I am sure that today every radio telescope is looking at the
Pulsars."8
CP 1919 emits in radio wavelengths, but pulsars have subsequently been found to emit in the X-ray
and/or gamma ray wavelengths. Hewish received the 1974 Nobel Prize in Physics for this and related
radio astronomy work.
Three distinct classes of pulsars are currently known to astronomers, according to the source of
energy that powers the radiation:
a) Rotation-powered pulsars, where the loss of rotational energy of the star powers the radiation
b) Accretion-powered pulsars (accounting for most but not all X-ray pulsars), where the gravitational
potential energy of accreted matter is the energy source (producing X-rays that are observable
from Earth), and
c) Magnetars, where the decay of an extremely strong magnetic field powers the radiation.
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Rapid rotation neutron stars that emit very regular pulses with periods between 1.558 ms and
4.308 seconds
Most pulsars are found by their radio emission
Very few emit pulses in the optical spectral range
Usually called ‘radiopulsars’
Should not confuse radiopulsars with X-ray pulsars
Assuming a supernovae is the transition from ordinary star to neutron star
Neutron stars 1st postulated in 1932
1st model in 1939 by Oppenheimer and Volkoff
1st radiopulsar discovery in 1967 by Jocelyn Bell
Nature of the neutron star settled in 1968 with the discovery of a pulsar residing in the middle of
the Crab Nebula
6
European Space Agency, press release, "Old pulsars still have new tricks to teach us", 26 July 2006
Hewish, A.; Bell, S. J.; Pilkington, J. D.; Scott, P. F.; Collins, R. A., "Observation of a Rapidly Pulsating
Radio Source" (1968) Nature, Vol. 217, pp. 709
8
Daily Telegraph 5 Mar 1968 21/3
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500+ are now known
Neutron stars are the final products in the evolution of a star
• Formed in a SN II explosion with the collapse of the iron core in the progenitor
• The rapid spin is a direct result of the conservation of angular momentum during the collapse
phase
• The angular velocity increases inversely proportional to the square of the stellar radius by a
factor of 1010
• Since the magnetic field is frozen in the stellar matter during the collapse a similar
amplification of the magnetic field happens producing field strengths of about 109 tesla or 1013
gauss
Basic processes of the pulsed radiation is somewhat understood
• Prerequisite is both the rapid rotation and the strong magnetic fields
• If the rotation axis and the axis of the magnetic field are tilted with respect to each other a
huge electric field is generated in the immediate neighborhood of the neutron star
• Generated fields are accelerating the free electrons and protons present at the surface of the
neutron star to relativistic velocities
• This plasma moves away from the neutron star along the magnetic field lines which are not
closed at the polar region
• Relativistic electrons emit non-thermal synchrotron radiation in a narrow cone like a beacon
light
• Cone is rotating with the angular velocity of the pulsar
• A pulse is received if the observer is in the line of sight of the observer
Synchrotron radiation comes from the rotational energy of the spinning neutron star
There is a constant conversion of rotational energy to radiant energy of the synchrotron radiation
All pulsars are slowing down at a rate that is proportional to the dissipated energy
• With this in mind the fastest pulsars should be the youngest
• With the increasing period the energy output decreases to where it can no longer be
measured (several millions of years)
For radio pulsars the duty cycle is of the order of several percent
Refer to the references listed to obtain a general background (Taylor and Stinebring 1986;
Srinivasan 1989; Lyne and Graham-Smith 1990; Ventura and Pines 1991)
Eclipsing Binary Systems
These are binary systems of stars with an orbital plane lying near the line-of-sight of the observer. The
components periodically eclipse one another, causing a decrease in the apparent brightness of the
system as seen by the observer. The period of the eclipse, which coincides with the orbital period of the
system, can range from minutes to years.
Algol Type Eclipsing Binaries (EA)
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First EA discovered was Algol (β Persei)
• Discovered by John Goodricke in 1783
• First to determine its strict periodicity of 2.867 day
• First to propose eclipses as a mechanism for its variability
• Has partial eclipses
• Semi-detached
• Undergoes mass transfer
• Has a chromospherically active secondary which emits radio waves and X-rays
• Belongs to a triple system
• Orbital period of 1.783 year cycle as it orbits around Algol C
• Has a 32 year magnetic cycle
EA Variables are segregated according to light curve shape
Moments of beginning and end of eclipse can be determined from the light curve
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Eclipses may be partial giving only a 0.01 magnitude variation or it could be total giving several
magnitude variation
Light curve shape is characteristic if both stars are nearly spherical or slightly ellipsoidal.
• Possibility of one star could be highly distorted and even filling its Roche lobe provided it
does not contribute to the system’s total brightness
• This is the case for 50% of the known EA variables
Orbital periods of EA variables can be determined by accurately timing the sharp eclipses
Period variations are found and can be attributed to apsidal motion, orbit around a third body,
mass loss and/or mass transfer, and solar-type magnetic cycles.
Evolutionary status of EA variables (Sterken and Jaschek 1996)
• State 1:
• Binaries containing two main-sequence stars of any spectral type form O to M
• IQ Persei:
• A B7 V + A2 V 1.74-day system
• Primary eclipse is annular while secondary is total
• A moderate orbital eccentricity displaces secondary eclipse from phase 0.5
• Period has been constant
• State 2:
• Binaries in which one or both components are evolved but have not yet overflowed their
Roche lobes
• RT Andromedae:
• An F8 V + G5 V 0.63-day system
• At least one of the two stars are chromospherically active and produces a starspot
wave in the light curve
• Also classified as RS
• Orbital period is decreasing monotonically
• State 3:
• Binaries with one star unevolved and the other overflowing its Roche lobe and causing
mass transfer
• MR Cygni:
• A B3 V + B8 V 1.677-day system
• May be semi-detached or nearly so
• Ellipticity effect and reflection effect are noticeable
• Orbital period is constant
• State 4:
• Binaries with one star highly evolved (hot subdwarf or white dwarf) and the other less
evolved
• VW Cygni:
• An A3e + K1 IV 8.43-day system
• Semi-detached (listed as detached in GCVS)
• Primary eclipse is total and deep but appears slightly rounded during totality because
of photometric effects due to circumstellar material
• Orbital period has at times decreased and increased
• State 5:
• Not evolved at all
• RS Cephei:
• An A5 IIIe + G8 IV-III 12.42-day system
• Semi-detached (listed as detached in GCVS)
• Primary eclipse is deep but appears slightly rounded during totality because of
photometric effects of circumstellar material
• Period has increased
• More details on these can be found in the following references (Thomas 1977;
Sahade and Wood 1978; Soderhjelm 1980; Olson 1985; Batten 1989; Hall 1990)
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β Lyrae Type Eclipsing Binaries (EB)
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EB Variables are segregated according to light curve shape
The light curve varies continuously between eclipses making it hard to determine the moment it
begins and ends
Have primary and secondary eclipses significantly different in depth
Orbital periods longer than a day
Spectral types B or A
The light curves are suppose to me made by an eclipsing binary which one or both components is
highly ellipsoidal
One of the components may be filling its Roche lobe
Evolutionary status of EB variables (Sterken and Jaschek 1996)
• State 1:
• Unevolved binaries consisting of two main sequence stars but a relative short orbital
period
• β Lyrae:
• A B8 II + F 12.94-day system
• At the deeper minimum the B8 star is partially eclipsed by the accretion disc
• The F spectral type refers to the average surface temperature of the edge of the disc
• The underlying star is 10 Msolar and would appear to be an early B spectral type if not
obscured
• DO Cassiopeiae:
• A A2 V + G V 0.685-day system
• GCVS has this classified as a contact binary
• State 2:
• Binaries in which one or both components is evolved but not yet filling the Roche lobe
• State 3:
• Semi-detached binaries undergoing mass transfer from the evolved to the unevolved star
• State 4:
• Binaries with one star highly evolved (hot subdwarf or white dwarf) and the evolved
producing the ellipticity effect
Some binaries classified as EB are not eclipsing
• The light variation is produced entirely by the ellipicity effect
• The two minima are unequal as a result of greater limb-darkening effects on the pointed
end of the highly distorted star
First EB discovered was β Lyrae by John Goodricke in 1784
β Lyrae is extremely complex
• The brighter star fills its Roche lobe and is transferring matter to the other star so rapidly that
a thick optically and a thick geometrically disc is built up which almost obscures the mass
gaining star
• The mass causes the orbital period to increase
• From 1784 to 1996 the period has increased from 12.8925 day to 12.93854 day (approx
0.35%)
• Additional examples:
ζ Andromedae:
• A single-lined binary pair K1 III 17.77-day system
• The giant K nearly but not quite fills its Roche lobe
• K giant is chromosherically active and the GCVS added the ‘RS’ classification but later it
was shown that starspots contribute a little to its variability
• There are no evidence that eclipses occur
• Primarily an ellipsoidal variable
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Single-lined semi-detached binary pair K1 III 96.71-day system
All light variation is produced by the ellipicity effect and therefore may not be eclipsing at
all
• The pointed-end effect causes one minimum to be deeper than the other
More details on these can be found in the following references (Sahade and Wood 1978; Plavec
1983; Plavec 1985)
RS Canum Venaticorum Eclipsing Binaries (RS)
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RS appears in the GCVS twice in two of their main classes
First appears as one type of ‘eruptive variable stars’.
• Misleading because variability is caused by rotational modulation with the surface having cool
spots distributed randomly in longitude which do not radiate the same intensity of energy.
• Strange that it does not appear as one of the type of ‘rotating variable stars’.
Second, it appears as a type of ‘close binary eclipsing systems’ by its physical characteristics of
the two stars.
• Misleading as well because more than 50% of the variables classified in the GCVS as RS are
not eclipsing
Classification per D. S. Hall
• Binaries which the hotter of the two is F or G
• [Ca II], [H] and [K] lines show strong emission reversals at all phases
• Have one component off the main sequence but not yet filling its Roche lobe
• Emit intense coronal X-ray and radio radiation
• Have strong emission lines in the far ultraviolet
• Lose mass in an enhanced wind
• Have variable orbital periods
• Show a starspot wave
• Undergo more gradual changes in the mean brightness
• May indicate a magnetic cycle similar to our sun’s 11-year cycle
Starspot wave is the principle source for variation
• Usually sinusoidal in shape
One-fifth of the RS cases the wave period is not in sync with the orbital period and varies greatly
Four-fifths of the RS cases the orbital period and the wave period are in sync with only small
variations
Measured amplitude range from 0.01 – 0.6 magnitude in V
• The larger the variation the more surface is covered by starspots
All of the characteristics are considered the phenomenon of chromospheric activity is thought to
rise from enhanced dynamo action
• Corresponds to rapid rotation and a deep convective zone
Explains why chromospheric activity is found in many separately defined groups of both single
and binary stars of diverse evolutionary state:
• RS CVn binaries
• Binaries which are similar except the unspotted star is highly evolved like a white dwarf or hot
subdwarf
• BY Dra variables
• UV Cet variables
• Single solar-type dwarfs
• T Tau variables
• W UMa binaries
• FK Com stars
• Other single giants not rapidly rotating
• The cool contact component in semi-detached Algol-type binaries
• Cool component in old novae and cataclysmic variables
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The four following non-eclipsing systems are examples that demonstrate starspot variability in the
RS CVn type binaries
• V1762 Cyg:
• Non-eclipsing K1 IV-III SB1 28.59-day system
• Light curve has a nearly sinusoidal starspot wave and double wave in others telling that
there are two starspots on opposites hemispheres of the K giant
• V1764 Cyg:
• Non-eclipsing K1 III SB1 40.14-day system
• Although classified as RS its variation comes from the ellipticity effect
• Amplitude 0.125 magnitude in V
• Starspot wave is present with an amplitude between 0.02 – 0.09 mag
• Period is 65% shorter than the orbital period
• V1149 Ori:
• Non-eclipsing K1 III SB1 53.58-day system
• Since discovery of variability the light curve has increased in amplitude from 0.05 – 0.40
magnitude in V
• Has displayed a double and a single starspot wave
• DM UMa:
• Non-eclipsing K1 IV-III SB1 7.492-day system
• Has shown both single and double starspot wave at various epochs
• Largest amplitude observed 0.32 magnitude in V
Additional reading can be obtained in the following references: (Sahade and Wood 1978; Zeilik,
Hall et al. 1979; Linsky 1980; Baliunas and Vaughan 1985; Strassmeier, Hall et al. 1993)
W UMa Type Variables (EW)
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Characterized by continuous light changes due to eclipses and to changing aspects of tidally
distorted stars
Minima are almost always equal in depth indicative of both stars are in contact
• Since the mass ratio of the two components would most likely not be unity, one would expect
the components would have different temperatures giving unequal minima on the light curve,
and thus a classification of EB which is not the case
• Both are contained within a common envelope
• The more massive is transferring luminosity to the smaller within the envelope equalizing the
surface temperatures
Signifies the temperatures of both components are similar
Periods are short (7 hr – 1 day)
EW systems cannot directly be compared to single main sequence stars
• Both members violate the mass-luminosity relation because of the luminosity transfer
• They are useful in determination of masses, temperature and radii
Ellipsoidal surfaces with varying gravity and luminosity because of the strong tidal effects
Light curve synthesis program as developed by Wilson and Devinney (1971) for interpretation of
MR Cygni provides good approximations of mass ratio, fractional radii, inclination and
temperature difference (Wilson and Devinney 1971)
• The occurrence of spots can also be considered
Efforts of using spectroscopic observation to determine masses and absolute dimensions is
marginal because of the diffuse spectral lines produced by rapidly rotating contact binaries
• Cross-correlation methods give better and more reliable results
Two subclasses can be distinguished
• A-type
• More massive stars
• Early spectral type (A – F)
• Longer orbital periods
• Deeper minimum caused by a transit of the smaller, cooler star in front of the larger
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• Period-color relation (0.4 – 0.8 day) (Mochnacki 1985)
W-type
• Less massive
• Later spectral type (G – K)
• Shorter orbital periods
• Deeper minimum caused by an occultation of the smaller, hotter star by the larger
• Period-color relation (0.22 – 0.4 day) (Mochnacki 1985)
• Some systems in the intermediate region with unstable light curves can change from A-type
to a W-type over a periods of months or years and back again (TZ Boo, 44i Boo)
Period changes are observed in all EW systems
• Connected with the ongoing mass circulation that transports the luminosity from the primary
to secondary
• Long term evolution should result in mass loss in the secondary
• Longer orbital period
• EW systems show a complex behavior of periods lengthening and shortening with in
interrupting phases of constant period of which there are no repeating patterns
EW systems are only known in our solar neighborhood because of their low luminosity
EW systems have a high space density (estimated at 2.5 X 10-5 pc-3 or one out of 500 main
sequence stars with spectral types between late A to early K is a W UMa system)
GCVS lists 542 EW systems
Examples:
• ER Ori:
• A F8 0.4234-day system
• AE Phe:
• A G0 0.3624-day system with a peculiar light curve probably due to spot activity
• 44i Boo
• A G2 0.2678-day system with a very unstable light curve
For more detailed reading refer to (Mochnacki 1985; Rucinski 1992)
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X-ray Binaries
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Classification is ambiguous
Some classify based on any kind of close binary with a compact degenerate object (white dwarf,
neutron star, or black hole)
More specific definition would be a close binary system which contains a neutron star or black
hole
• The white dwarf is not included because they are usually called cataclysmic variables
• The main difference between X-ray binaries and cataclysmic variables is X-ray luminosity
• X-ray binaries: X-ray luminosity (Lx = 1035 – 1038 erg s-1 or 1028 – 1031 W)
• Corresponds to 25 – 25000 times the total solar luminosity
• Cataclysmic variables: Lx <= 1034 erg s-1 or 1027 W
X-ray binaries are discovered by their strong X-ray emission
Close binary system
Components are a normal main-sequence star (giant) filling its Roche lobe and transferring
matter to the compact object (neutron star or black hole)
• Usually called a detached system
• Due to angular momentum the matter can not fall directly on the degenerate but forms an
accretion disc
• Due to internal friction in the accretion disc (viscosity) the matter spiral inward until it falls on
the compact object
• With some neutron stars with high magnetic fields not accretion disc exists
• Accretion takes place along the magnetic field lines onto the poles of the neutron star
• The matter close to the neutron star is heated to temperatures 107 K or more
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Most of the energy is radiated away as thermal radiation (blackbody and bremsstrahlung)
in the X-ray range
The physical mechanism for the high X-ray luminosities is the transformation of gravitational
energy into kinetic energy
Accretion is an efficient tool for converting gravitational energy into kinetic energy
• Accretion energy Eacc is proportional to (Mdot m)/Rdot with Mdot and Rdot being the mass and
radius of the accreting object respectively and m being the mass of the accreted material
• For a given unit of mass of one gram one obtains Eacc = 1020 erg g-1 or Eacc approx equal
0.15mc2
• From a neutron star, 15% of the rest energy mc2 can be released which is 20 times
as much as one can gain from nuclear fusion of the same amount of pure hydrogen
into helium
• Eacc for white dwarfs is lower since the radius of white dwarf is about 1000 times larger than
the radius of a neutron star
X-ray binaries can be divided into two distinct populations
• LMXRB (low-mass X-ray binary)
• Ratio of the X-ray to optical flux (Lx/Lopt) = 10 - 104
• These are optically dim
• HMXRB (high-mass X-ray binary)
• Sometimes called massive X-ray binaries
• Ratio of the X-ray to optical flux (Lx/Lopt) = 10-3 - 10
• These are optically bright
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Bibliography
Alcock, C., D. R. Alves, et al. (2004). "The MACHO Project Large Magellanic Cloud Variable-Star
Inventory. XIII. Fourier Parameters for the First-Overtone RR Lyrae Variables and the LMC
Distance." Astronomical Journal 127: 334-354.
Alexander, J. B., P. J. Andrews, et al. (1972). "A spectroscopic and photometric study of the pulsating R
CrB type variable, RY Sgr." Monthly Notices of the Royal Astronomical Society 158: 305.
Appenzeller, I. and R. Mundt (1989). "T Tauri stars." Astronomy and Astrophysics Review 1: 291-334.
Ardeljan, N. V., G. S. Bisnovatyi-Kogan, et al. (2005). "Magnetorotational supernovae." Monthly Notices of
the Royal Astronomical Society 359: 333-344.
Bailey, S. I. (1902). Harvard College Observatory Annual Report: 132 and 208.
Baliunas, S. L. and A. H. Vaughan (1985). "Stellar activity cycles." Annual Review of Astronomy and
Astrophysics 23: 379-412.
Balog, N. I., A. V. Goncharskij, et al. (1981). "On the possibility of optical eclipse in the Cygnus X-1
system." Soviet Astronomy Letters 7: 336-339.
Balona, L. A. (1991). Rotational Modulation and the Line Profile Variables. Rapid Variability of OB-stars:
Nature and Diagnostic Value.
Baratta, G. B., A. D. Neto, et al. (1991). "The 990-1100 NM spectrum of representative S-type symbiotic
stars." Astronomy and Astrophysics 251: 75-78.
Barbon, R., E. Cappellaro, et al. (1989). "The Asiago Supernova Catalogue." Astronomy and Astrophysics
Supplement Series 81: 421.
Bastian, U., U. Finkenzeller, et al. (1983). "The definition of T Tauri and Herbig Ae/Be stars." Astronomy
and Astrophysics 126: 438.
Bath, G. T., C. J. Clarke, et al. (1986). "The light-curve properties of mass-transfer events in cataclysmic
variables." Monthly Notices of the Royal Astronomical Society 221: 269-278.
Batten, A. H. (1989). "Algols; Proceedings of the 107th IAU Colloquium, Sidney, Canada, Aug. 15-19,
1988." Space Science Reviews 50.
Beckwith, S. V. W. and A. I. Sargent (1993). The occurrence and properties of disks around young stars.
Protostars and Planets III.
Belle, K. E., S. B. Howell, et al. (2005). "Simultaneous X-Ray and Optical Observations of EX Hydrae."
Astronomical Journal 129: 1985-1992.
Bertout, C. (1989). "T Tauri stars - Wild as dust." Annual Review of Astronomy and Astrophysics 27: 351395.
Bidelman, W. P. (1976). A list of early-type shell stars. IAU Symp. 70: Be and Shell Stars.
Bisnovatyi-Kogan, G. S. (1970). "The Explosion of a Rotating Star As a Supernova Mechanism."
Astronomicheskii Zhurnal 47: 813.
Blazko, S. (1907). "Mitteilung über veränderliche Sterne." Astronomische Nachrichten 175: 327.
Bopp, B. W. and F. Fekel, Jr. (1977). "Binary incidence among the BY Draconis variables." Astronomical
Journal 82: 490-494.
Bopp, B. W. and R. E. Stencel (1981). "The FK Comae stars." Astrophysical Journal 247: L131-L134.
Buta, R. J. and M. A. Smith (1979). "The light variations of nonradial pulsators - Theory and application to
the line profile variable 53 Persei." Astrophysical Journal 232: 213-235.
Byrne, P. B. and M. Rodono (1983). Activity in red-dwarf stars; Proceedings of the Seventy-first
Colloquium, Catania, Italy, August 10-13, 1982. ASSL Vol. 102: IAU Colloq. 71: Activity in RedDwarf Stars.
Campbell, L. (1955). Studies of Long Period Variables. Cambridge, American Association of Variable Star
Observers.
Castellani, V. and M. L. Quarta (1987). "The Oosterhoff dichotomy revisited. I - The ranking of RR Lyrae
periods versus metallicity." Astronomy and Astrophysics Supplement Series 71: 1-10.
Chakrabarty, D. and P. Roche (1997). "The Symbiotic Neutron Star Binary GX 1+4/V2116 Ophiuchi."
Astrophysical Journal 489: 254.
Chen, H., J. M. Marlborough, et al. (1992). "Dynamics of the envelopes of Be stars in the equatorial
plane." Astrophysical Journal 384: 605-612.
Christy, R. F. (1966). "Pulsation Theory." Annual Review of Astronomy and Astrophysics 4: 353.
Classification of Variable Stars, A Compilation of Information
John W Shepherd
Page 71 of 82
Last Modification 8/25/2006
Clement, C. M. and J. Rowe (2000). "The Globular Cluster omega Centauri and the Oosterhoff
Dichotomy." Astronomical Journal 120: 2579-2593.
Cox, A. N. (1993). White Dwarf and Pre-White Dwarf Oscillations. IAU Colloq. 139: New Perspectives on
Stellar Pulsation and Pulsating Variable Stars.
Cox, J. P. (1980). Theory of stellar pulsation.
Crews, L. J., D. S. Hall, et al. (1995). "Starspots found on the ellipsoidal variable V350 lacertae = HR
8575." Astronomical Journal 109: 1346-1351.
Cropper, M. (1990). "The Polars." Space Science Reviews 54: 195-295.
de Groot, M. (1988). "The most luminous stars in the universe." Irish Astronomical Journal 18: 163-170.
de Jager, C. (1980). "The brightest stars." Geophysics and Astrophysics Monographs 19.
de Koter, A. (1993). "Studies of the Variability of Luminous Blue Variable Stars." Ph.D. Thesis: 154.
Diethelm, R. (1983). "A photometric classification of pulsating variables with periods between one and
three days." Astronomy and Astrophysics 124: 108-115.
Diethelm, R. (1990). "Physical parameters of pulsating variables with periods between one and three
days. II - Fundamental parameters." Astronomy and Astrophysics 239: 186-192.
Downes, R. A. and M. M. Shara (1993). "A catalog and atlas of cataclysmic variables." Publications of the
Astronomical Society of the Pacific 105: 127-245.
Epstein, R. I. (1979). "Lepton-driven convection in supernovae." Monthly Notices of the Royal
Astronomical Society 188: 305-325.
Feast, M. (1995). Pulsating Stars and the Distance Scale - II. ASP Conf. Ser. 83: IAU Colloq. 155:
Astrophysical Applications of Stellar Pulsation.
Feast, M. W. (1975). The R Coronae Borealis type variables. IAU Symp. 67: Variable Stars and Stellar
Evolution.
Fekel, F. C., T. J. Moffett, et al. (1986). "A survey of chromospherically active stars." Astrophysical
Journal Supplement Series 60: 551-576.
Folha, D. F. M. (1998). "Near Infrared Hydrogen Lines as Diagnostic of Accretion and Winds in Young
Stellar Objects." Ph.D. Thesis: 11.
Frost, E. B. (1902). "The sprectroscopic binary beta Cephei." Astrophysical Journal 15: 340-341.
Frost, E. B. (1906). "The period of beta Cephei." Astrophysical Journal 24: 259-262.
Gautschy, A. and H. Saio (1993). "On non-radial oscillations of B-type stars." Monthly Notices of the
Royal Astronomical Society 262: 213-219.
Gosset, E., G. Rauw, et al. (1994). Photometric monitoring of Wolf-Rayet stars: Strömgren uvby and
narrow-band photometry. NATO ASIC Proc. 436: The Impact of Long-Term Monitoring on
Variable Star Research: Astrophysics.
Gray, D. F. (1989). "The rotational break for G giants." Astrophysical Journal 347: 1021-1029.
Hack, M., C. Ladous, et al. (1993). Cataclysmic variables and related objects. Monograph Series on
Nonthermal Phenomena in Stellar Atmospheres - NASA SP, Paris: Centre National de la
Recherche Scientifique; Washington, D.C.: NASA, |c1993.
Haisch, B., K. T. Strong, et al. (1991). "Flares on the sun and other stars." Annual Review of Astronomy
and Astrophysics 29: 275-324.
Hall, D. S. (1986). "Pseudosynchronization found in binaries with eccentric orbits." Astrophysical Journal
309: L83-L85.
Hall, D. S. (1990). "Masses and radii for thirteen chromospherically active ellipsoidal variables."
Astronomical Journal 100: 554-558.
Hall, D. S. (1990). Period Changes and Magnetic Cycles. NATO ASIC Proc. 319: Active Close Binaries
Proceedings, NATO Advanced Study Institute.
Hall, D. S. (1994). "The History of the Discovery of Starspots." International Amateur-Professional
Photoelectric Photometry Communications 54: 1.
Harmanec, P. (1983). "Review of observational facts about Be stars." Hvar Observatory Bulletin 7: 55-88.
Harmanec, P. (1989). "Towards understanding rapid line-profile and light variations of early-type stars. I General considerations and a critical re-analysis of the data on 13 Zeta OPH and 45 Epsilon Per."
Bulletin of the Astronomical Institutes of Czechoslovakia 40: 201-261.
Harrop-Allin, M. K., M. Cropper, et al. (1999). "Indirect imaging of the accretion stream in eclipsing polars
- II. HU Aquarii." Monthly Notices of the Royal Astronomical Society 308: 807-817.
Hellier, C. (1991). "Do observations reveal accretion discs in intermediate polars?" Monthly Notices of the
Royal Astronomical Society 251: 693-697.
Classification of Variable Stars, A Compilation of Information
John W Shepherd
Page 72 of 82
Last Modification 8/25/2006
Hellier, C. (1993). "Disc-overflow accretion in the intermediate polar FO Aquarii." Monthly Notices of the
Royal Astronomical Society 265: L35-L39.
Hellier, C. (1997). "The size of the accretion region in intermediate polars: eclipses of XY ARIETIS
observed with RXTE." Monthly Notices of the Royal Astronomical Society 291: 71-80.
Hellier, C. (1998). "Disc-overflow accretion in intermediate polars." Advances in Space Research 22: 973980.
Hellier, C. (2001). Cataclysmic Variable Stars: how and why they vary. Chichester, UK, Praxis Publishing
Ltd.
Hellier, C., M. Cropper, et al. (1991). "Optical and X-ray observations of AO PISCIUM and the origin of
the spin pulse in intermediate polars." Monthly Notices of the Royal Astronomical Society 248:
233-255.
Hellier, C., J. Kemp, et al. (2000). "Outbursts of EX Hydrae: mass-transfer events or disc instabilities?"
Monthly Notices of the Royal Astronomical Society 313: 703-710.
Hellier, C., K. Mukai, et al. (1997). "An outburst of the magnetic cataclysmic variable XY ARIETIS
observed with RXTE." Monthly Notices of the Royal Astronomical Society 292: 397.
Hellier, C., K. Mukai, et al. (1996). "The X-ray spectrum of the intermediate polar AO Piscium." Monthly
Notices of the Royal Astronomical Society 280: 877-887.
Herbig, G. H. (1962). "The properties and problems of T Tauri stars and related objects." Advances in
Astronomy and Astrophysics 1: 47-103.
Hillier, D. J. (1992). "Luminous blue variables (review)." LNP Vol. 401: The Atmospheres of Early-Type
Stars 401: 105.
Hoogerwerf, R., N. S. Brickhouse, et al. (2004). "The Radial Velocity and Mass of the White Dwarf of EX
Hydrae Measured with Chandra." Astrophysical Journal 610: 411-415.
Hoogerwerf, R., N. S. Brickhouse, et al. (2005). "X-Ray Light Curves and Accretion Disk Structure of EX
Hydrae." Astrophysical Journal 628: 946-952.
Humphreys, R. M. (1989). What are LBVs? - Their characteristics and role in the upper H-R diagram.
ASSL Vol. 157: IAU Colloq. 113: Physics of Luminous Blue Variables.
Hunger, K., D. Schoenberner, et al. (1986). Hydrogen deficient stars and related objects; Proceedings of
the Eighty-seventh IAU Colloquium, Mysore, India, Nov. 10-15, 1985. ASSL Vol. 128: IAU Colloq.
87: Hydrogen Deficient Stars and Related Objects.
Iben, I., Jr. and M. Livio (1993). "Common envelopes in binary star evolution." Publications of the
Astronomical Society of the Pacific 105: 1373-1406.
Iben, I., Jr. and A. V. Tutukov (1996). "On the Evolution of Symbiotic Stars and Other Binaries with
Accreting Degenerate Dwarfs." Astrophysical Journal Supplement Series 105: 145.
Iben, I. J. S. N. A. D. S. A. S. W. E. M. a. l. a. v. a. h. S. N. A. D. S. A. S. W. E. M. M., A. D. S. Sitemap, et
al. "Common envelopes in binary star evolution."
Ichikawa, S., M. Hirose, et al. (1993). "Superoutburst and superhump phenomena in SU Ursae Majoris
stars - Enhanced mass-transfer episode or pure disk phenomenon?" Publications of the
Astronomical Society of Japan 45: 243-253.
Imshennik, V. S. (1992). "A possible scenario of a supernova explosion as a result of the gravitational
collapse of a massive stellar core." Soviet Astronomy Letters 18: 194.
Imshennik, V. S. and D. V. Popov (1994). "Evolution of eccentric orbits of neutron star binaries emitting
gravitational waves." Astronomy Letters 20: 529-537.
Johnson, H. R., F. R. Querci, et al. (1986). The M-type stars.
Joy, A. H. (1942). "Spectral Criteria in the Classification of Variable Stars." Publications of the
Astronomical Society of the Pacific 54: 15.
Jura, M. (1986). "Mass loss from carbon stars." Astrophysical Journal 303: 327-332.
Kenyon, S. J., T. Fernandez-Castro, et al. (1988). "Far-infrared data for symbiotic stars. II - The IRAS
survey observations." Astronomical Journal 95: 1817-1827.
Kinemuchi, K., H. A. Smith, et al. (2006). Analysis of RR Lyrae Stars in the Northern Sky Variability
Survey.
Kube, J., B. T. Gänsicke, et al. (2000). "Eclipse mapping of the accretion stream in UZ Fornacis."
Astronomy and Astrophysics 356: 490-500.
Kurtz, D. W. (1982). "The Delta Scuti variability of three stars with AP spectral classifications, HR 151,
239 and 7461." Monthly Notices of the Royal Astronomical Society 200: 503-507.
Classification of Variable Stars, A Compilation of Information
John W Shepherd
Page 73 of 82
Last Modification 8/25/2006
Kurtz, D. W. (1990). "Rapidly oscillating AP stars." Annual Review of Astronomy and Astrophysics 28:
607-655.
Kurtz, D. W. and P. Martinez (1994). Long-term monitoring of cyclic frequency variability in roAP stars at
the Southerland station of the South African Astronomical Observatory. NATO ASIC Proc. 436:
The Impact of Long-Term Monitoring on Variable Star Research: Astrophysics.
Kwee, K. K. (1967). "Investigations on Population II Cepheids. III. Light-curves and two-colour diagrams."
Bulletin of the Astronomical Institutes of the Netherlands 19: 260.
Lamers, H. J. G. L. M. (1989). Mass loss from luminous blue variables. ASSL Vol. 157: IAU Colloq. 113:
Physics of Luminous Blue Variables.
Landstreet, J. D. (1992). "Magnetic fields at the surfaces of stars." Astronomy and Astrophysics Review 4:
35-77.
Lattimer, J. M. and T. J. Mazurek (1981). "Leptonic overturn and shocks in collapsing stellar cores."
Astrophysical Journal 246: 955-965.
Lazaro, C., A. Arellano Ferro, et al. (2006). CCD Photometry of the globular cluster M2. RR Lyrae
physical parameters and new variables.
Lines, H. C., R. D. Lines, et al. (1987). "Ellipticity and starspots in the RS CVn binary HD 185151 = V1764
CYG." Astronomical Journal 93: 430-432.
Lines, H. C., R. D. Lines, et al. (1988). "UBVRI photometry of the recurrent nova T coronae borealis."
Astronomical Journal 95: 1505-1509.
Linsky, J. L. (1980). "Stellar chromospheres." Annual Review of Astronomy and Astrophysics 18: 439488.
Livio, M., J. R. Buchler, et al. (1980). "Rayleigh-Taylor driven supernova explosions - A two-dimensional
numerical study." Astrophysical Journal 238: L139-L143.
Ludwig, K., E. Meyer-Hofmeister, et al. (1994). "Systematics of dwarf nova outbursts: a parameter study
in the framework of the disk-instability model." Astronomy and Astrophysics 290: 473-486.
Lyne, A. G. and F. Graham-Smith (1990). Pulsar astronomy.
Madore, B. F. (1985). Cepheids: Theory and observations; Proceedings of the Colloquium, Toronto,
Canada, May 29-June 1, 1984. IAU Colloq. 82: Cepheids: Theory and Observation.
Maeder, A. (1982). "Evolutionary scenarios leading massive stars to WR stars - Their mutual importance;
the role of mixing." Astronomy and Astrophysics 105: 149-158.
Maeder, A. (1989). On the evolutionary status and instability mechanism of the luminous blue variables
(LBV). ASSL Vol. 157: IAU Colloq. 113: Physics of Luminous Blue Variables.
Maeder, A. and P. S. Conti (1994). "Massive Star Populations in Nearby Galaxies." Annual Review of
Astronomy and Astrophysics 32: 227-275.
Maeder, A. and F. Rufener (1972). "Variable stars of small amplitude 1: supergiants and OB stars."
Astronomy and Astrophysics 20: 437.
Mathys, G. (1985). "The influence of surface inhomogeneities on the rapid light variations of AP stars."
Astronomy and Astrophysics 151: 315-321.
Matsunaga, N., H. Fukushi, et al. (2006). "The period-luminosity relation for type II Cepheids in globular
clusters." Monthly Notices of the Royal Astronomical Society 370: 1979-1990.
Matthews, J. M. (1991). "Stellar seismology and the pulsating AP stars." Publications of the Astronomical
Society of the Pacific 103: 5-19.
Mauche, C. W. (1990). Accretion-powered compact binaries. Accretion-Powered Compact Binaries.
Meilland, A., P. Stee, et al. (2006). Be stars: one ring to rule them all?
Meyer, F. and E. Meyer-Hofmeister (1981). "On the Elusive Cause of Cataclysmic Variable Outbursts."
Astronomy and Astrophysics 104: L10.
Meyer, F. and E. Meyer-Hofmeister (1983). "A model for the standstill of the Z Camelopardalis variables."
Astronomy and Astrophysics 121: 29-34.
Mirzoian, L. V., B. R. Pettersen, et al. (1990). Flare stars in star clusters, associations and the solar
vicinity; Proceedings of the 137th IAU Symposium, Byurakan, Armenian SSR, Oct. 23-27, 1989.
IAU Symp. 137: Flare Stars in Star Clusters, Associations and the Solar Vicinity.
Mirzoyan, L. V., V. V. Ambaryan, et al. (1989). "Statistical Investigation of Flare Stars - Part Three - Flare
Stars in the General Galactic Star Field." Astrophysics 29: 736.
Mochnacki, S. W. (1985). Observational evidence for the evolution of contact binary stars. NATO ASIC
Proc. 150: Interacting Binaries.
Classification of Variable Stars, A Compilation of Information
John W Shepherd
Page 74 of 82
Last Modification 8/25/2006
Moffat, A. F. J., L. Drissen, et al. (1989). Observational connections between LBV's and other stars, with
emphasis on Wolf-Rayet stars. ASSL Vol. 157: IAU Colloq. 113: Physics of Luminous Blue
Variables.
Moiseenko, S. G., G. S. Bisnovatyi-Kogan, et al. (2005). Magnetorotational Supernova Simulations. ASP
Conf. Ser. 342: 1604-2004: Supernovae as Cosmological Lighthouses.
Molnar, L. A. and H. A. Kobulnicky (1992). "Superhump timing in SU Ursae Majoris systems - Implications
of the data for the processing disk model." Astrophysical Journal 392: 678-690.
Montmerle, T., E. D. Feigelson, et al. (1993). Magnetic fields, activity and circumstellar material around
young stellar objects. Protostars and Planets III.
Morris, S. L. (1985). "The ellipsoidal variable stars." Astrophysical Journal 295: 143-152.
Moskalik, P. and E. Poretti (2003). "Fourier decomposition and frequency analysis of the pulsating stars
with P < 1 d in the OGLE database. II. Multiperiodic RR Lyrae variables in the Galactic Bulge."
Astronomy and Astrophysics 398: 213-222.
Nadyozhin, D. K. and V. S. Imshennik (2005). "Physics of Supernovae." International Journal of Modern
Physics A 20: 6597-6611.
Nelemans, G., S. F. Portegies Zwart, et al. (2001). "Population synthesis for double white dwarfs. II.
Semi-detached systems: AM CVn stars." Astronomy and Astrophysics 368: 939-949.
Nemec, J. M. (1992). The Astronomy and Astrophysics Encyclopedia. S. P. Maran. Cambridge,
Cambridge University Press: 789.
Nemec, J. M. (2004). "Physical Characteristics of the RR Lyrae Stars in the Very Metal Poor Globular
Cluster NGC 5053." Astronomical Journal 127: 2185-2209.
Nemec, J. M. and J. M. Matthews (1993). New Perspectives on Stellar Pulsation and Pulsating Variable
Stars. IAU Colloq. 139: New Perspectives on Stellar Pulsation and Pulsating Variable Stars.
Olson, E. C. (1985). Photometry of active ALGOLS. NATO ASIC Proc. 150: Interacting Binaries.
Oosterhoff, P. T. (1939). "Some remarks on the variable stars in globular clusters." The Observatory 62:
104-109.
Oosterhoff, P. T. (1944). "The periods of the variables 8, 9, 11 and 12 in the globular cluster M 92."
Bulletin of the Astronomical Institutes of the Netherlands 10: 55.
Osaki, Y. (1995). "A model for WZ Sagittae-type dwarf novae: SU UMa/WZ SGE connection."
Publications of the Astronomical Society of Japan 47: 47-58.
Owocki, S. P., S. R. Cranmer, et al. (1996). "Inhibition FO Wind Compressed Disk Formation by
Nonradial Line-Forces in Rotating Hot-Star Winds." Astrophysical Journal 472: L115.
Patterson, J. (1979). "Rapid oscillations in cataclysmic variables. III - an oblique rotator in an AE Aquarii."
Astrophysical Journal 234: 978-992.
Patterson, J. (1994). "The DQ Herculis stars." Publications of the Astronomical Society of the Pacific 106:
209-238.
Patterson, J., J. Kemp, et al. (1998). "Rapid Oscillations in Cataclysmic Variables. XIV. Orbital and Spin
Ephemerides of FO Aquarii." Publications of the Astronomical Society of the Pacific 110: 415419.
Patterson, J., D. R. Skillman, et al. (1995). "The Remarkable Eclipsing Asynchronous AM Herculis Binary
RX J19402-1025." Publications of the Astronomical Society of the Pacific 107: 307.
Payne-Gaposchkin, C. (1979). Stars and clusters.
Petersen, J. O. (1993). On Period Ratios and Resonance Sequences. IAU Colloq. 139: New Perspectives
on Stellar Pulsation and Pulsating Variable Stars.
Petersen, J. O. and R. Diethelm (1986). "Studies of Cepheid-type variability. III - Fourier description of
light curves of Type II Cepheids of periods 1-3 days." Astronomy and Astrophysics 156: 337-346.
Petschek, A. G. (1990). Supernovae.
Plavec, M. J. (1983). "IUE looks at the Algol paradox." Sky and Telescope 65: 413-416.
Plavec, M. J. (1985). From Algol to Beta Lyrae. NATO ASIC Proc. 150: Interacting Binaries.
Preston, G., W. Krzeminski, et al. (1963). "A Spectroscopic and Photoelectric Survey of the RV Tauri
Stars." Astrophysical Journal 137: 401-430.
Preston, G. W. (1959). "A Spectroscopic Study of the RR Lyrae Stars." Astrophysical Journal 130: 507.
Purton, C. R. (1976). Radio Observations of be Stars (review Paper). IAU Symp. 70: Be and Shell Stars.
Quanz, S. P., T. Henning, et al. (2006). FU Orionis - The MIDI/VLTI Perspective.
Classification of Variable Stars, A Compilation of Information
John W Shepherd
Page 75 of 82
Last Modification 8/25/2006
Reipurth, B. (1989). Proceedings of the ESO Workshop on Low Mass Star Formation and Pre-main
Sequence Objects, held in Garching bei Munchen, F.R.G., July 11-13, 1989. Low Mass Star
Formation and Pre-main Sequence Objects.
Ritter, H. (1990). "Catalogue of cataclysmic binaries, low-mass X-ray binaries and related objects (Fifth
edition)." Astronomy and Astrophysics Supplement Series 85: 1179-1256.
Romanova, M. M., G. V. Ustyugova, et al. (2005). "Propeller-driven Outflows and Disk Oscillations."
Astrophysical Journal 635: L165-L168.
Rosendhal, J. D. and M. S. Snowden (1971). Astrophysics 169: 281.
Rucinski, S. M. (1992). Contact Binaries of the W UMa Type. ASSL Vol. 177: The Realm of Interacting
Binary Stars.
Sahade, J. and F. B. Wood (1978). Interacting binary stars.
Sandage, A. (1982). "The Oosterhoff period groups and the age of globular clusters. III - The age of the
globular cluster system." Astrophysical Journal 252: 553-581.
Sandage, A., B. Katem, et al. (1981). "The Oosterhoff period groups and the age of globular clusters. I
Photometry of cluster variables in M15." Astrophysical Journal Supplement Series 46: 41-74.
Sargent, B., W. J. Forrest, et al. (2006). Dust Processing in Disks around T Tauri Stars.
Schmidt, G. D. (1999). Accretion in High Magnetic Fields: The Stellar Interaction. ASP Conf. Ser. 157:
Annapolis Workshop on Magnetic Cataclysmic Variables.
Schwope, A. D., K. Beuermann, et al. (1993). "Cyclotron and Zeeman spectroscopy of MR Serpentis in
low and high states of accretion." Astronomy and Astrophysics 278: 487-498.
Schwope, A. D., K. H. Mantel, et al. (1997). "Phase-resolved high-resolution spectrophotometry of the
eclipsing polar HU Aquarii." Astronomy and Astrophysics 319: 894-908.
Seal, P. (1997). "The masses and radii of the components of symbiotic stars." Astrophysics and Space
Science 254: 85-96.
Shibahashi, H. (1987). "Rapidly oscillating AP stars and Delta Scuti variables." LNP Vol. 274: Stellar
Pulsation 274: 112-121.
Shibahashi, H. and M. Takata (1993). "Theory for the distorted dipole modes of the rapidly oscillating AP
stars: A refinement of the oblique pulsator model." Publications of the Astronomical Society of
Japan 45: 617-641.
Simon, N. R. (1986). "On the short-period type II Cepheid field stars." Astrophysical Journal 311: 305-316.
Sion, E. M., J.-E. Solheim, et al. (2006). "The First Direct Spectroscopic Detection of a White Dwarf
Primary in an AM CVn System." Astrophysical Journal 636: L125-L128.
Slettebak, A. (1979). "The Be stars." Space Science Reviews 23: 541-580.
Smak, J. (1967). "Light variability of HZ 29." Acta Astronomica 17: 255.
Smith, H. A. (1995). RR Lyrae Stars. New York, NY, Cambridge University Press.
Smith, M. A. (1980). "Pulsation modes in B stars with variable line profiles." Lecture Notes in Physics,
Berlin Springer Verlag 125: 60-75.
Soderhjelm, S. (1980). "Geometry and dynamics of the Algol system." Astronomy and Astrophysics 89:
100-112.
Solheim, J. E. and L. R. Yungelson (2005). The White Dwarfs in AM CVn Systems -- Candidates for SN
Ia? ASP Conf. Ser. 334: 14th European Workshop on White Dwarfs.
Srinivasan, G. (1989). "Pulsars - Their origin and evolution." Astronomy and Astrophysics Review 1: 209260.
Stefl, S., D. Baade, et al. (1995). "Simultaneous photometric and spectroscopic monitoring of rapid
variations of the Be star eta Centauri." Astronomy and Astrophysics 294: 135-154.
Sterken, C. (1977). Astronomy and Astrophysics 57: 361.
Sterken, C. and C. Jaschek (1996). Light Curves of Variable Stars, A Pictorial Atlas.
Stobie, R. S. (1973). "On the existence of a Hertzsprung progression in the halo/old disk Cepheids." The
Observatory 93: 111-114.
Strassmeier, K. G. and D. S. Hall (1988). "Photometric variability in chromospherically active stars. II The rapidly rotating single stars." Astrophysical Journal Supplement Series 67: 453-460.
Strassmeier, K. G., D. S. Hall, et al. (1993). "A catalog of chromospherically active binary stars (second
edition)." Astronomy and Astrophysics Supplement Series 100: 173-225.
Strom, S. E. (1972). "Optical and Infrared Observations of Young Stellar Objects - an Informal Review."
Publications of the Astronomical Society of the Pacific 84: 745.
Classification of Variable Stars, A Compilation of Information
John W Shepherd
Page 76 of 82
Last Modification 8/25/2006
Strom, S. E., S. Edwards, et al. (1993). Evolutionary time scales for circumstellar disks associated with
intermediate- and solar-type stars. Protostars and Planets III.
Struve, O. (1931). "On the Origin of Bright Lines in Spectra of Stars of Class B." Astrophysical Journal 73:
94.
Szeidl, B. (1988). R Lyrae Stars: Beat and Blazhko Effect. Multimode Stellar Pulsations.
Taylor, J. H. and D. R. Stinebring (1986). "Recent progress in the understanding of pulsars." Annual
Review of Astronomy and Astrophysics 24: 285-327.
Thomas, H. C. (1977). "Consequences of mass transfer in close binary systems." Annual Review of
Astronomy and Astrophysics 15: 127-151.
Turner, D. G. (1998). "Monitoring the Evolution of Cepheid Variables." Journal of the American
Association of Variable Star Observers (JAAVSO) 26: 101-111.
van den Bergh, S. (1993). "The Oosterhoff effect." Monthly Notices of the Royal Astronomical Society
262: 588-590.
van den Bergh, S. (1994). "A catalog of recent supernovae." Astrophysical Journal Supplement Series 92:
219-227.
van den Bergh, S. and G. A. Tammann (1991). "Galactic and extragalactic supernova rates." Annual
Review of Astronomy and Astrophysics 29: 363-407.
van der Hucht, K. A. (1992). "Wolf-Rayet stars." Astronomy and Astrophysics Review 4: 123-159.
van der Hucht, K. A., P. M. Williams, et al. (1994). Long-term radio monitoring of Wolf-Rayet stars with
non-thermal emission. NATO ASIC Proc. 436: The Impact of Long-Term Monitoring on Variable
Star Research: Astrophysics.
van Genderen, A. M. and P. S. The (1984). "Characteristics and interpretation of the photometric
variability of Eta Carinae and its nebula." Space Science Reviews 39: 317-373.
Ventura, J. and D. Pines (1991). Neutron stars. NATO ASIC Proc. 344: Neutron Stars.
Vogt, N. (1982). "Z Chamaeleontis - Evidence for an eccentric disk during supermaximum." Astrophysical
Journal 252: 653-667.
Vreux, J.-M. (1987). Observed variations in Wolf-Rayet stars. ASSL Vol. 136: Instabilities in Luminous
Early Type Stars.
Waelkens, C. (1991). "Slowly pulsating B stars." Astronomy and Astrophysics 246: 453-468.
Waelkens, C. and F. Rufener (1985). "Photometric variability of mid-B stars." Astronomy and Astrophysics
152: 6-14.
Wahlgren, G. M., Ed. (1983). The RV Tauri and SRd Variables. Luminous High-Latitude Stars, ASP
Conference Series. San Francisco, BookCrafters, Inc.
Warner, B. and E. L. Robinson (1972). "Observations of rapid blue variables.- IX.- AM CVn (HZ 29)."
Monthly Notices of the Royal Astronomical Society 159: 101-111.
Whitehurst, R. (1988). "Numerical simulations of accretion disks. I - Superhumps - A tidal phenomenon of
accretion disks." Monthly Notices of the Royal Astronomical Society 232: 35-51.
Whitelock, P. A., M. W. Feast, et al. (1994). "Variability of Eta-Carinae." Monthly Notices of the Royal
Astronomical Society 270: 364.
Wilson, R. E. and E. J. Devinney (1971). "Realization of Accurate Close-Binary Light Curves: Application
to MR Cygni." Astrophysical Journal 166: 605.
Wilson, R. E. and R. K. Fox (1981). "Evidence for apsidal motion in the Cygnus X-1 system and a thirdbody interpretation." Astronomical Journal 86: 1259-1266.
Wolf, B. (1986). S-Doradus Type - Hubble-Sandage Variables. IAU Symp. 116: Luminous Stars and
Associations in Galaxies.
Wolf, B. (1989). 'Normal' LBV eruptions a la S Doradus. ASSL Vol. 157: IAU Colloq. 113: Physics of
Luminous Blue Variables.
Wolf, B. (1992). "Luminous Blue Variables; Quiescent and Eruptive States." Reviews of Modern
Astronomy 5: 1-15.
Wolf, B. (1992). Luminous Blue Variables; quiescent and Eruptive States (Invited Paper). ASP Conf. Ser.
22: Nonisotropic and Variable Outflows from Stars.
Wolf, B., I. Appenzeller, et al. (1981). "IUE and ground-based spectroscopic observations of the S Dortype LMC variable R 71 during minimum state." Astronomy and Astrophysics 103: 94-102.
Wolff, C. L. (1972). "The Five-Minute Oscillations as Nonradial Pulsations of the Entire Sun."
Astrophysical Journal 177: L87.
Classification of Variable Stars, A Compilation of Information
John W Shepherd
Page 77 of 82
Last Modification 8/25/2006
Woosley, S. E. (1991). Supernovae: 10th Santa Cruz Workship. Supernovae. The Tenth Santa Cruz
Workshop in Astronomy and Astrophysics, held July 9-21, 1989, Lick Observatory. Editor, S.E.
Woosley; Publisher, Springer-Verlag, New York, 1991. LC # QB856.S26 1989. ISBN #
0387970711.
Woosley, S. E. and T. A. Weaver (1986). "The physics of supernova explosions." Annual Review of
Astronomy and Astrophysics 24: 205-253.
Wynn, G. A., A. R. King, et al. (1997). "A magnetic propeller in the cataclysmic variable AE Aquarii."
Monthly Notices of the Royal Astronomical Society 286: 436-446.
Zampieri, L., M. Ramina, et al. (2003). Understanding Type II Supernovae.
Zeilik, M., D. S. Hall, et al. (1979). "The strange RS Canum Venaticorum binary stars." Sky and
Telescope 57: 132-137.
Classification of Variable Stars, A Compilation of Information
John W Shepherd
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Index
[C].....................................................................23
[Ca II]..............................................24, 25, 41, 67
[Fe II] ....................................................24, 25, 28
[H]...................................................24, 25, 43, 67
[He I]...............................................24, 41, 43, 45
[He II]................................................................45
[He]...................................................................23
[K] .........................................................24, 25, 67
[N].....................................................................23
[O].....................................................................23
[Si] ....................................................................23
12
C ................................................................8, 16
44i Boo .............................................................69
4
He ...................................................................16
53 Per.........................................................35, 36
56
Co ............................................................41, 43
56
Ni .............................................................41, 43
8
Be....................................................................16
AC Her..............................................................34
accretion disc 2, 7, 15, 16, 25, 26, 44, 51, 52, 53,
54, 55, 57, 66, 69
AE Aqr ..............................................................52
AE Phe .............................................................69
AG Peg.............................................................58
AGB..................................... 7, 22, 33, 34, 38, 39
AHB1 ................................................................37
AHB2 ................................................................37
AHB3 ................................................................37
AI Sco...............................................................34
AI Vel Star ........................................................36
Algol .....................................................28, 64, 67
AM CVn ..................................................2, 45, 46
AM Her ...................................... 2, 46, 47, 49, 52
Angular momentum........... 40, 46, 51, 54, 64, 69
AO Psc .............................................................52
AP Pav .............................................................57
AP Pis...............................................................66
Ap Star .............................................................60
AR Sgr..............................................................34
Balmer ........... 6, 7, 21, 24, 25, 27, 28, 35, 54, 55
Balmer lines ........................ 7, 21, 24, 25, 27, 35
Be Star .......................... 2, 10, 23, 27, 34, 35, 36
BH CVn ............................................................61
BL Her ..............................................................37
AHB3 stars...................................................37
CWB stars....................................................37
black hole .....................................8, 9, 34, 43, 69
blackbody ...............................................7, 47, 70
Blazhko Effect ........................................7, 31, 32
Blazhko Period .................................................32
bolometric.........................................................39
bremsstrahlung ......................................7, 47, 70
BV Cen .............................................................55
BW Vul .............................................................34
Classification of Variable Stars, A Compilation of Information
John W Shepherd
BY Dra .................................................61, 62, 67
BY Draconis Variable....................................... 61
BY Dra .............................................61, 62, 67
CC Eri .......................................................... 62
dKe .............................................................. 61
dMe.............................................................. 61
OU Gem ...................................................... 62
Carbon .............................................8, 23, 43, 44
Cataclysmic Variable ..21, 40, 48, 49, 52, 53, 67,
69
Eruptive variable.......................................... 40
CC Eri .............................................................. 62
Cepheid........9, 13, 21, 29, 30, 32, 35, 36, 37, 40
Chandrasekhar limit ...............................8, 41, 45
Chromium ........................................................ 60
CI Cyg ........................................................ 57, 58
Close binary .............................13, 38, 44, 67, 69
close binary eclipsing system .......................... 67
Close binary eclipsing system ......................... 67
CNO cycle.................................................... 8, 44
CO-nuclei ................................................... 39, 40
CP ..........................................................8, 46, 60
CP stars ........................................................... 60
Crab Nebula..................................................... 63
CT Ori .............................................................. 34
CWB................................................................. 37
Cyclotron.......................................................... 49
Cygnus X-1 ...................................................... 34
DF Cyg............................................................. 34
Dipole...................................................49, 50, 51
DM Uma........................................................... 68
DM UMa........................................................... 68
DO Cas ............................................................ 66
DQ Her............................................................. 50
DR Tau............................................................. 26
Dust...7, 8, 10, 11, 13, 22, 25, 26, 27, 33, 41, 44,
58
dwarf Cepheid.................................................. 36
Dwarf Novae .................................................... 53
UGSS........................................................... 54
BV Cen .................................................... 55
BV Centauri............................................. 55
SS Cyg .............................................. 54, 55
SS Cygni ...........................................54, 55
U Gem ...............................................34, 54
U Geminorum .......................................... 54
UGSU .......................................................... 55
SU UMa............................................. 55, 56
SU Ursae Majoris .............................. 16, 55
VW Hyi .................................................... 56
WZ Sge .......................................53, 54, 56
Z Cha.................................................55, 56
UGZ ............................................................. 55
RX And .................................................... 55
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Z Cam......................................................55
Z Camelopardis .......................................55
dwarf star....................................................28, 44
Eclipsing Binary System...................................64
EA ..........................................................64, 65
Algol Type................................................64
IQ Persei..................................................65
MR Cygni...........................................65, 68
RS Cephei ...............................................65
RT Andromedae ......................................65
VW Cygni.................................................65
EB ..........................................................66, 68
AP Piscium ..............................................66
DO Cassiopeiae ......................................66
EF Eri ...............................................................50
EK Eri ...............................................................62
Ellipsoidal Variable...........................................61
BH CVn ........................................................61
HZ Her .........................................................61
IW Persei .....................................................61
V350 Lacertae..............................................61
ER Ori...............................................................69
ER UMa............................................................56
Eruptive variable ..............................................40
EX Hya .............................................................52
EX Lup..............................................................26
FK Com ......................................................62, 67
FK Comae Variable..........................................62
FK Com..................................................62, 67
OU And ........................................................62
UZ Lib ..........................................................62
Flare Star....................................................27, 28
Flickering ..............................................46, 57, 58
FO Aqr..............................................................50
FU Ori...........................................................2, 26
Giant... 7, 8, 9, 13, 15, 22, 29, 30, 32, 33, 34, 38,
39, 40, 44, 45, 56, 57, 58, 59, 61, 62, 66, 68,
69
Gravitational Wave Radiation...........................46
GW Vir..............................................................40
GWR.................................................................46
Helium .... 7, 8, 10, 11, 13, 15, 25, 28, 30, 32, 39,
45, 46, 70
helium core.................................................32, 46
Helium shell......................................................45
Herbig Ae/Be..........................................8, 23, 27
Herbig Ae/Be star...................................8, 23, 27
H-R (diagram) ......... 9, 22, 26, 32, 34, 35, 36, 39
Hydrogen.... 6, 7, 8, 9, 10, 11, 13, 15, 22, 23, 24,
25, 26, 27, 28, 29, 32, 34, 39, 41, 42, 44, 61,
70
hypergiant.........................................9, 15, 21, 34
HZ Her..............................................................61
Hα ...........................................................7, 24, 25
Hβ .......................................................................7
Hδ .......................................................................7
Classification of Variable Stars, A Compilation of Information
John W Shepherd
Hγ ....................................................................... 7
Intermediate polar ............................................ 50
IQ Per............................................................... 65
Iron.......................................................43, 60, 64
Irregular Variable ....................................... 37, 38
Lb ................................................................ 38
Lc ................................................................ 38
IW Per .............................................................. 61
Kelvin-Helmholtz contraction ........................... 23
Keplerian....................................9, 26, 48, 50, 51
Kinetic energy ............................................ 47, 70
Landau-Darries instability ................................ 42
Large Magellanic Cloud .......9, 13, 22, 23, 34, 45
LBV ..................................................9, 21, 23, 34
Lightcurve ................................31, 49, 50, 51, 56
LPV .................................................................. 38
Luminous Blue Variable...................9, 21, 23, 34
Magnesium ...................................................... 44
Magnetosphere ........................48, 50, 51, 52, 53
main-sequence 10, 23, 28, 29, 54, 57, 62, 65, 69
Mass transfer ...15, 41, 46, 55, 56, 57, 64, 65, 66
Mira ..........................................38, 39, 57, 58, 59
Mira Variable..................................37, 38, 39, 58
MR Cyg ...................................................... 65, 68
Neon ................................................................ 44
neutron star....................8, 34, 43, 63, 64, 69, 70
Novae.................................44, 45, 53, 55, 58, 67
NA.......................................................... 44, 45
NB................................................................ 44
NC................................................................ 45
NR................................................................ 45
Nova-like Star ............................................ 45, 53
AC.......................................................... 34, 45
AM .............................2, 45, 46, 47, 49, 50, 52
AM Her ..................................2, 46, 47, 49, 52
DQ ............................................................... 50
DQ Her ........................................................ 50
UX................................................................ 53
UX Uma ....................................................... 53
UX UMa ....................................................... 53
VY ................................................................ 53
VY Scl .......................................................... 53
Omega Centauri............................................... 30
Oosterhoff Class I ............................................ 31
Oosterhoff Class II ........................................... 31
OP And ............................................................ 62
Orbital period ..16, 46, 51, 52, 53, 54, 55, 56, 58,
62, 64, 65, 66, 67, 68, 69
OU And ............................................................ 62
OU Gem........................................................... 62
Outburst 9, 15, 16, 21, 26, 35, 40, 44, 45, 53, 54,
55, 56, 58, 59
Oxygen...................................................8, 43, 44
P Cyg ......................................................... 26, 27
Polar................................................................. 64
Polarized .................................................... 49, 51
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Population I stars .................................10, 22, 29
Population II stars ..........................10, 11, 30, 33
Population III stars ...........................................11
Pre-main Sequence Star (PMS) ....23, 24, 26, 27
YSO .............................................................23
protoplanetary disc.....................................10, 11
Pulsars .................................................23, 63, 64
radiopulsar ...................................................63
pulsating variable ...................................7, 29, 37
QQ Vul..............................................................50
R Aql.................................................................39
R Coronae Borealis (RCB)...............................22
R CrA................................................................27
R Hya ...............................................................39
R Mon...............................................................27
R Sge ...............................................................34
Rayleigh-Taylor instability ....................12, 13, 42
roAp Star ....................................................60, 61
Roche lobe ...... 13, 40, 46, 54, 61, 65, 66, 67, 69
RR Lyr ........................... 7, 13, 30, 31, 32, 35, 37
RR Lyrae star ............................ 7, 30, 31, 32, 37
RR Tel ........................................................58, 59
RRd ......................................................13, 31, 37
AHB1 stars...................................................37
RS Canum Venaticorum Eclipsing Binary...6, 28,
58, 61, 65, 66, 67, 68
RS Cep.............................................................65
RS CVn ..........................................28, 61, 67, 68
RT And .............................................................65
RV Tau .................................... 32, 33, 34, 35, 38
RV Tauri Variable.............................................32
RVa-type stars .................................................33
RX And .............................................................55
RY Lup .............................................................27
S Dor ......................................................9, 21, 34
Sandage Effect.................................................13
Semi-regular Variable
SRa ........................................................37, 38
SRb ........................................................37, 38
SRc ..............................................................38
SRd ..............................................................38
Silicon...............................................................60
Slow Pulsating Binary (SPB)......................15, 36
Small Magellanic Cloud........................13, 23, 34
SN I ................................... 13, 15, 41, 42, 43, 64
SN II ...............................................15, 41, 42, 64
Spectroscopy .............................................45, 51
Spin period .............................. 48, 50, 51, 52, 53
SS Cyg .......................................................54, 55
SS Gem............................................................34
ST LMi ..............................................................50
standstill ...............................................15, 35, 55
starspots................ 15, 27, 60, 61, 62, 66, 67, 68
SU Aur..............................................................26
SU Gem............................................................34
Supercycle........................................................56
Classification of Variable Stars, A Compilation of Information
John W Shepherd
supergiant 8, 9, 13, 15, 22, 33, 34, 37, 38, 43, 57
superhump ...........................................16, 55, 56
Supernovae..............7, 13, 15, 21, 41, 44, 46, 63
SN I................................13, 15, 41, 42, 43, 64
SN Ia................................................13, 41, 76
SN Ib...................................................... 14, 42
SN Ic ...................................................... 14, 42
SN II...........................................15, 41, 42, 64
superoutburst .................................16, 53, 55, 56
SX Phe............................................................. 36
SY Cha............................................................. 27
Symbiotic Star.................................................. 56
eclipsing
AP Pav .................................................... 57
CI Cyg ............................................... 57, 58
Mira.............................................................. 58
Very Slow Novae ................................... 45, 58
AG Peg.................................................... 58
RR Tel ...............................................58, 59
V1016 Cyg .............................................. 58
synchrotron radiation ................................. 16, 64
T CrB................................................................ 58
T Tau..................2, 10, 23, 24, 25, 26, 27, 28, 67
T Tauri................2, 10, 23, 24, 25, 26, 27, 28, 67
T Tauri star...............2, 10, 23, 24, 25, 26, 27, 28
TiO ............................................................. 33, 37
Triple-alpha process ........................................ 16
TT Oph............................................................. 34
TW Cam........................................................... 34
TX Oph............................................................. 34
Type II Cepheid.......................................... 36, 37
U Gem........................................................34, 54
U Mon .............................................................. 34
UBV............................................................ 17, 58
ubvy ................................................................. 58
UU Her ............................................................. 38
UV Cet .................................................28, 62, 67
UV Ceti star................................................ 28, 62
UY CMa ........................................................... 34
UZ Lib .............................................................. 62
UZ Oph ............................................................ 34
V Vul ................................................................ 34
V1016 Cyg ....................................................... 58
V1057 Cyg ....................................................... 26
V1149 Ori......................................................... 68
V1762 Cyg ....................................................... 68
V1764 Cyg ....................................................... 68
V2400 Oph................................................. 50, 51
V350 Lac.......................................................... 61
V390 Aur .......................................................... 62
V410 Tau ......................................................... 27
V477 Her.......................................................... 35
V777 Her.......................................................... 39
variable planetary nebula nuclei ................ 10, 40
VV Cep............................................................. 57
VV Pup............................................................. 50
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VW Cyg ............................................................65
VW Hyi .............................................................56
VY Scl...............................................................53
W UMa Type Variable ................................68, 69
44i Boo.........................................................69
AE Phe.........................................................69
A-Type subclass ..............................62, 68, 69
ER Ori ..........................................................69
W-Type subclass .........................................69
W Vir...........................................................30, 37
AHB2 stars...................................................37
CWA stars....................................................37
WD ...................................................................17
white dwarf7, 8, 9, 17, 22, 32, 33, 34, 36, 38, 39,
40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 51, 52,
53, 54, 56, 57, 58, 59, 65, 66, 67, 69, 70
Wolf-Rayet star (WR) .......................6, 21, 22, 23
WZ Sge ................................................53, 54, 56
X Cyg................................................................30
X-ray... 24, 25, 28, 29, 34, 41, 47, 49, 50, 51, 53,
54, 63, 67, 69, 70
X-ray Binary .....................................................69
HMXRB ........................................................70
Classification of Variable Stars, A Compilation of Information
John W Shepherd
LMXRB ........................................................ 70
XY Ari............................................................... 51
YSO ................................................................. 23
YY Ori .............................................................. 26
Z Cam .............................................................. 55
Z Cha .........................................................55, 56
ZZ Ceti star ...................................................... 40
ZZ Ceti Variable ............................................... 39
ZZA ........................................................ 39, 40
ZZB .............................................................. 39
ZZO.............................................................. 39
α Cygni............................................................. 34
β Cep ......................................................... 34, 35
β Cephei........................................................... 34
β Lyrae ............................................................. 66
β Persei............................................................ 64
δ Cep................................................................ 30
δ Scuti ..................................................35, 36, 60
γ Cas ................................................................ 35
λ Eri.................................................................. 35
ζ Andromedae.................................................. 66
ζ Gem .............................................................. 30
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