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Univerzita Karlova v Praze
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,
DIPLOMOV A PRACE
Markéta Tukinská
Novy v galaxii M31
Astronomický ústav UK
Vedoucí diplomové práce Doc. RNDr. Marek Wolf, CSc.
Studijní program: astronom:ie a astrofyzika
./
/ r •
Věnování
Ráda bych tuto práci věnovala jako další dlažební kámen na cestě vědy. Možná jen
kamínek, ale i ty jsou potřeba, aby bylo nač pokládat hlavní desky. Doufám, že se
nebude příliš viklat.
1
Poděkování
Děkuji
Doc. Marku Wolfovi za odborné vedení, cenné rady a pomoc
diplomové práce a také za jeho
při
zpracování
neobyčejnou trpělivost.
Mé poděkování také patří Kamilu Hornochovi, bez jehož rad a zkušeností s" lovením"
nov a zpracováním dat bych tuto práci jen
těžko
dokázala napsat a za poskytnutá
data.
Děkuji kolegům, kteří
mi po celou dobu odpovídali na
v8etečné
především slečně Azře
Avdibegovié, Davidu Schmoranzerovi, Martinu "Matesovi"
dotazy. Z
těchto
Jelínkovi, Michalu Švandovi, Jaroslavě Schovancové, Jiřímu "Luinarovi" Peškovi a
Petru Scheirichovi.
Prohla.<íuji, že jRem svou diplomovou práci napsala
s použitím citovaných pramenú. Souhlasím se
V Praze dne .4. ~ !f.„~ 0 '.:l
samostatně
zapújčováním
výhradní'.~
a
práce.
:.\tiarkéta T\1ki11ská
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Contents
1
Introduction
5
2
Cataclysmic variable stars
6
2.1
White d w a r f s ...............................................................................................
7
2.2
Red dwarfs
2.3
Roche geometry and mass transfer
2.4
The accretion disk
3
4
5
8
.........................................................
8
..................................................................................... 11
2.4.1
The bright s p o t ............................................................................... 12
2.4.2
Disk in sta b ility ............................................................................... 12
2.5
Evolution of cataclysmic variable s t a r s ...................................................
2.6
Spectral characteristics............................................................................... 13
12
Novae
15
3.1
Classical N o v a e ............................................................................................15
3.2
Recurrent novae............................................................................................19
3.3
Novae as standard c a n d le s .........................................................................20
3.4
Supernovae type l a ..................................................................................... 21
Novae in M 31
22
4.1
M 3 1 .............................................................................................................. 22
4.2
Novae in M 3 1 ...............................................................................................23
Observations and Results
5.1
26
Review of n ovae............................................................................................26
5.2
Spectrum of nova 2005-01a.........................................................................30
5.3
The Geom etry...............................................................................................37
5.4
6
..................................................................................... ...
Photometry and light cu rv es..................................................................... 39
Conclusions
42
3
Abstrakt
Název práce: Novy v galaxii M31
Autor: Markéta Tukinská
Katedra (ústav): Astronomický ústav Univerzity Karlovy
Vedoucí diplomové práce: Doc. RNDr. Marek Wolf. CSc.
e-mail vedoucího: [email protected]
Abstrakt: V práci je podán přehled a statistika nov objevených v galaxii M31.
Většina nov
v M31 náleží do centrální výdutě či disku. Přesnější určení poměru mezi těmito dvěma popu­
lacemi je vzhledem ke sklonu galaxie a zatížení dat výběrovým efektem obtížné. Spektrum novy
2005-01a odpovídá v systému z observatoře Cerro Tololo třídě
otázkou však zůstává místo
původu této novy, neboť vzdálenost vypočtená pomocí standardních vztahu ~ 460 kpc neodpovídá
předpokládané vzdálenosti M31 (770 kpc). Nova 2007-lla, jejíhož pozorování 65-cm dalekohledem
na Ondřejovské observatoři jsem se zúčastnila, náleží do třídy rychlých nov, neboť
*3
~
11
dnů.
Předpokládalo se, že novy se bu dou vhodné standardní svíčky, avšak postu pem času se ukázalo,
že mnohem vhodnější je použít Cepheidy či supernovy.
Klíčová slova: kataklysmická proměnná, nova, M31
Abstract
Title: Novae in M31
Author: Markéta Tukinská
Department: The Astronomical Institute of Charles University
Supervisor: Doc. RNDr. Marek Wolf, CSc.
Supervisor’s e-mail address: [email protected]
Abstract: In this Thesis, a list of novae found in M31 is presented. Most o f these novae belong
either to the bulge or disk population. It is very difficult to establish the exact ratio o f these
two populations because o f the inclination of M31 and the bias cause by the selection effect. The
spectrum of nova 2005-01a belongs to the P*je class in the Cerro Tololo observatory system. The
distance of this nova remains questionable because from the standard relations we obtain ~460 kpc,
but the distance o f M31 is about 770 kpc. I took part in the observation o f nova 2007-1 la at the
Ondrejov observatory. This nova belongs to the fast novae class, because
<3 ~ 1 1
days. It was
assumed that novae could make excellent standard candles, but it appeared that Ccpheids and
supemovae would be better.
Keywords: cataclysmic variable, nova, M31
4
1
Introduction
Classical novae are a sub-class of cataclysmic variables. They exhibit typical out­
burst magnitudes of 8-15. A classical nova is a result of a thermonuclear runaway
on a mass-accreting white dwarf in a close binary star. There axe many theoretical
studies about nova cycles, novae’s recurrence and the dependence of maximum light
on the rate of decline. The known relation between maximum magnitude versus rate
of decline makes novae good distance indicators. The spatial distribution of novae
in galaxies is another often discussed question. The properties of novae may vary
between different Hubble types of galaxies. There are two populations of novae in
galaxies, bulge and disk population. It is assumed that most novae (~ 70%) belong
to the bulge population. The proximity of M31 and its relatively high nova rate
makes M31 one of the most important galaxies for the study of classical novae. M31
has been observed since the beginning of the 20th century. The first surveys were
made by Hubble (1929), Arp (1956), Ciardullo (1987), Rosino (1964, 1970, 1987).
Presently, M31 is observed by many astronomers almost every night. It is assumed
that the nova rate in M31 is about 35 novae per year. There are about 20 novae
observed each year, but in 2007, 29 novae were found in M31 as per November 29th.
5
2
Cataclysmic variable stars
Cataclysmic variable stars (hereafter CVs) are binary stars consisting of an accreting
white dwarf primary and a companion, usually a low-mass main sequence secondary
star (red dwarf).
In some cases the secondary star is another white dwarf or a
slightly evolved star (subgiant). The stars are close together, so the matter flowe
from the secondary the primary one. In most cases, the infalling matter forms an
accretion disk around the white dwarf, which emits UV or X-ray radiation.
There are several, possibly overlapping, smaller groups of CV stars, named
after a bright prototype star characteristic of each class:
• SS Cygni
• U Geminorum
• Z Camelopardalis
• SU Ursae Majoris
• AM Herculis
• DQ Herculis
• VY Sculptoris
• AM Canum Venaticorum
• SW Sextantis
It is also possible to divide CV stars according to their principal energy source
(NASA Classification, 2006):
1
. Fusion-dominated phase
a. Classical novae
b. Super Soft Sources
2. Accretion-dominated phase
a. Dwarf novae
b. Polars (AM Her systems)
c. Intermediate Polars (DQ Her systems)
6
2.1
White dwarfs
The primary star in the CV stars is a white dwarf. It is the burnt-out core of a star
nearing the end of its life.
The main-sequence stars are basically balls of hot gas. They mostly consist
of hydrogen which is fused to helium. The pull of gravity, which would cause the
star to collapse, is balanced by the pressure of radiation. Because of the pressure,
the gas is heated to tens of millions of degrees in the centre of star. This is the
temperature needed for nuclear fusion, which makes hydrogen burn to helium (and
possibly carbon, oxygen and heavier nuclei). The ash from the nuclear furnace sinks
and collects in the core. There is a huge pull caused by the surrounded matter which
causes huge densities, so the electrons of adjacent atoms nearly overlap. However,
because of the Pauli’s exclusion principle, which prevents two electrons from being
at the same place at the same time, thus forces the atoms apart, and halts further
contraction, the growing ash core stays inert.
After its hydrogen-fusing lifetime, the main-sequence star of a low or medium
mass will expand to a red giant which fuses helium to carbon and oxygen. It pushes
its envelope far from the core, the outer layers are no longer bound strongly and due
to the pressure of radiation they will eventually form a planetary nebula. The hot,
dense core of ash becomes exposed and is observed as a white dwarf.
Usually white dwarfs are composed of oxygen and carbon.
Sometimes
there are helium dwarfs(formed by mass loss in a binary system) or oxygen-neonmagnesium white dwarfs (if the core temperature is sufficient to fuse carbon, but
not neon). C -0 white dwarfs are final stages of stars with initial masses in the range
of 1-8 M© and O-Ne-Mg ones with initial masses 8-12 M© (Barkat et al., 1974).
No white dwarf can be heavier than the Chandrasekhar limit, about 1.4 times the
mass of the Sun, or else the pressure of gravity would force the electrons into the
nuclei, because there is no radiation pressure to balance it. Because of the elec­
tron degeneracy pressure, the mass comparable to the Sim’s will be contained in a
volume comparable to Earth’s, with an extreme density. If the star exceeded this
value, the electrons would combine with the protons to form neutrons and the white
7
dwarf would then collapse into a neutron star. The common mass of white dwarf is
about 0.5-0.6 M© and almost all of them are in the range of 0.3-1.3 M0 . The white
dwarf is originally very hot, but it has no internal source of energy, so it cools down
eventually.
2.2
Red dwarfs
The most common companion of the white dwarf in CV stars is the red dwarf. Red
dwarfs are relatively small and very dim /cool stars of the main sequence. Its spec­
tral type is late K or M. Red dwarfs are smaller than the Sun, their mass varies
from 0.075 M© to 0.5 M0 (these are called brown dwarves). With less matter the
pull of gravity on the core is lower and accordingly there is a lower temperature
in the core. Thus the rate of the nuclear reactions in a red dwarf is a thousandth
of that in our Sun and the temperature is lower, only about 3 500 K in the centre
and 2 900 K on the surface. In general, red dwarves transport energy to surface via
thermal convection. Their life span tends to be billions up to trillions years. They
are the most common of all stars.
When orbiting near the white dwarf, the red dwarf is blasted by its 60 000 K
radiation, which heats the side facing the white dwarf to 7 500 K. This causes a
reflection effect in the C V ’s light curve. A red dwarf in a CV star is called secondary.
2.3
Roche geometry and mass transfer
In a cataclysmic variable, the stars are close together and the gravitation of the
primary is distorting the secondary. When two stars are moving closer, the secondary
becomes more and more distorted until the material in the outer layers, which is
nearest the primary, experiences a greater gravitational attraction towards the white
dwarf then back towards its own star. In this case, material flows between the two
stars, which is a characteristic of cataclysmic variables. The outline of a star at the
critical point, when the mass-transfer to the companion is just possible, is called the
Roche lobe. The inner Lagrangian point (L i) is the apex of the Roche lobe on the
simplest path by which material can flow between the stars.
The red dwarf that fills its Roche lobe spins at the same rate as it orbits,
8
Figuře 1: The equipotentials in Roche geometry, from Mikulášek (2000). where L„
are the Lagrangian points, Mi is the centre of gravity of the primary, M 2 is the
centre of gravity of the secondary and X is the centre of gravity of the whole binary
system.
this is called tidal locking. In other cases there would be continual tidal flows of
material into and out of the bulges of the Roche lobe, accompanied with enormous
energy losses. The shape of the Roche lobes is determined solely by the mass ratio
q, defined q = M2jM \ where M\ is the mass of the primary and M2 the mass of the
secondary.
The analysis of the geometry of two orbiting stars is quite complicated. This
problem can be simplified when we consider stars as mass points that are following
circular orbits around a common centre of gravity, with an angular frequency ω.
Then we can write the gravitational potential Φ at a point specified by the vector r
as the sum of the potentials of the two stars (with masses M i, M2 located at rj.ra)
and of the term corresponding to the centrifugal force. Thus
9
Figuře 2: The Roche lobes can be visualised as gravitational wells in which matter
flows downhill. When the red dwarf overfills its Roche lobe, m atter flows over the
Li point into the Roche lobe of the white dwarf (Hellier, 2001).
where G is the gravitational constant, r is the position vector of the centre of mass,
Γι is the position vector of the primary, ra is the position vector of secondary and
ω is the angular frequency of the orbit.
The equipotentials are illustrated in Figure 1.
As Φ increases, the equipotentials of two stars first touch and then merge.
The Roche lobe is the critical surface where the equipotentials first touch. In 1955
the Czech astronomer Zdenek Kopal (1914-1995) established the evolutionary clas­
sification of binary stars according to their Roche lobes:
• d e ta c h e d sy ste m s - both surfaces are inside their Roche lobes
• sem id etach ed sy stem s - one component fills its Roche lobe. Mass transfer
is present in these systems.
• c o n ta c t sy ste m s - both components are overfilling their Roche lobes. These
systems may have a joint atmosphere.
10
Figure 3: Kopal's evolutionary classification of binary stars; 1. detached system,
2. semidetached system, 3. contact system.
2.4
The accretion disk
The material flowing from the secondary star forms an accretion disk, it orbits at
a radius with the same angular momentum as the material at L \ . This is known as
the circularisation radius. Material in smaller orbits moves faster (from 2nd Kepler's
law), but has a lower angular momentum. To conserve angular momentum, some
material has to move to larger orbits. This causes the ring to spread out into a thin
disk. The differences in velocity cause friction and turbulence, which heats the gas,
and the excess energy is radiated away. This energy comes from the gravitational
field, and it is converted into X-rays during the accretion process. On one side of
the disk, near the primary, the material falls onto the primary. On the other side
the angular momentum is transferred through the disk back to the secondary, due
to tidal interactions. The region where material is slowed down to the speed of the
white dwarf is called the boundary layer. In this region kinetic energy is converted
to heat and radiated away; the hot boundary layer can thus emit up to half the total
radiation. The disc is replenished by the mass-transfer stream form the secondary.
11
2.4.1
The bright spot
The bright spot is the place on the disk, where the stream of the infalling material
hits the disc edge. The kinetic energy of the falling material is converted to heat
and radiated away during the encounter, so that in some CV the collision region
emits ~ 30% of the total light of the system (Hellier, 2001). We know this thanks
to observation of orbital humps.
2.4.2
Disk instability
CV are named after the outburst, which brings brightening by several magnitudes
and then some time of quiescence. In 1974, Yoji Osaki suggested that an instability
in the accretion disc is as a cause for the outburst. When the mass transfer rate from
the secondary star is higher than the amount of material that could be transported
through the disk by viscous interactions then the material will pile up in the disc and
might cause the disc to become unstable, boosting the viscosity, increasing angular
momentum transport and so spreading the matter. There are two causes for the
disk instability: the viscosity in an accretion disk and magnetic turbulence which
leads to the Balbus-Hawley instability and to thermal instability.
2.5
Evolution of cataclysmic variable stars
A cataclysmic variable begins its life as a binary star, whose components are se­
parated only by a few hundred solar radii and which orbit every ~ 10 years. One
component must be less then M0 and the other one more massive. In the end, the
more massive one will expand to a red giant and overfill its Roche lobe and transfer
its outer layers to the lower-mass companion. However, this situation is unstable,
because the material is transferred further from the centre of mass of the binary
system and so the angular momentum of this material is increasing. To conserve
angular momentum, the separation of the stars is decreasing. The result is that both
stars are orbiting inside the envelope of the red giant, because the companion star
cannot assimilate such an influx. Orbiting inside the material is draining orbital
energy from the stars, so the separation shrinks from ~ 100 R© to ~ 1 R© in about
1000 years. Eventually, the envelope forms a ’planetary nebula’ (Hellier, 2001).
12
In the opposite situation, where material flows from the secondary to the
white dwarf, it is necessary to increase the separation of the stars in order to conserve
the angular momentum. However, the secondary detaches from its Roche lobe then
and prevents further mass loss. To explain how we can observe steady, long-lived
mass transfer, we could assume that the secondary is becoming a red giant. However,
the Universe is not old enough for many observed secondaries to evolve into red
giants. Another way is to suppose a gradual loss of angular momentum from the
binary system. There are two main mechanisms by which cataclysmic binaries lose
angular momentum: gravitational radiation and magnetic braking.
2.6
Spectral characteristics
Most photons in the Universe come from thermal energy.
This process can be
described by using an idealised entity called a blackbody. There is probably no
natural thing (except for black holes) which is a genuine blackbody, but most axe
near enough so that blackbody behaviour is a good approximation. To describe a
blackbody spectrum we use the Max Planck equation
where T is the thermodynamic temperature in Kelvins, v is the frequency of the
emitted radiation, h is the Planck constant, h = 6.626 176 · 10-34 J s and k is the
Boltzmann constant, k = 1.380 662 · 10-23 J K “ 1. The total amount of energy
radiated by the blackbody depends only on its temperature. This is described by
the Stefan-Boltzmann law
The emission maximum of white dwarfs lies in the ultraviolet region. The
spectrum of a white dwarf is well-described in the blackbody approximation. There
are, however, some differences, such as, e.g., spectral lines, caused by a thin layer
of hydrogen atoms on the white dwarf’s surface. In the optical region of the spec­
trum, we can find ’Balmer’ lines, caused by electrons from the second-lowest orbit
and in the UV region, the more energetic ’Lyman’ lines are present, caused by the
13
electrons from the lowest orbit. Due to 'pressure broadening’, white dwarfs have
broader spectral lines than normaJ stars.
The much cooler red dwarf has a maximum of its radiated energy in the
infrared. Its spectrum is more pronounced thanks to its larger surface area, because
blackbody emission increases in proportion to the area. If it were not so, it would
be lost in the white dwarf spectrum. The differences from a typical blackbody spec­
trum are caused by the molecules which can survive in the lower temperatures of
the red dwarf. Due to the many energetic features of these molecules, the spectral
characteristic is a complex set of broad dips. The most common molecule there is
the otherwise rare titanium oxide.
The spectral characteristics of accretion disks are not well understood. It is
because the disks are quite cool at their outer edge, but they are heating up in their
inner regions due to gravitational energy to about (~ 30 000A"). We can therefore
assume that each annulus in the disc emits as a blackbody of the given temperature,
but this cannot explain the emission lines in its spectra. Another way is to assume
that each annulus emits the same spectrum as a star of that temperature, and we
can then explain the emission lines. However both of these approaches work only
approximatively. The problem is that moet spectral lines in stars are in absorption,
but here we often see lines both in emission and in absorption.
The next phenomenon that we can find in spectra of cataclysmic variable
are the S-waves. They are caused by the orbital motion of the emitter. When the
emitter is coming closer to us, there is blue Doppler shift, and a half orbit later we
can see red-shifted lines. If the orbit is circular the shift will change sinusoidally.
This can be seen in the bright spot.
The disk can be considered as a collection of small regions emitting Swaves. This will result in a double-peaked profile in which peaks are shifted due to
the velocity of the outer regions of the disk, reduced by the sin(i) projection factor.
The disk is bound to the white dwarf, so the double-peaked profile will follow the
S-waves caused by the orbital motion of the white dwarf.
14
3
3.1
Novae
Classical Novae
The word nova is used for a star that suddenly increases its brightness. The Latin
word norms means new. Classical novae are novae where only one outburst is known.
Novae were known by ancient cultures already. The earliest reports of a new star,
which were recorded by many ancient cultures, go back to a nova that emerged in
134 BC. Before 1900 there were 161 novae discovered (as stated in D.Hoffleit (1986)).
In the last hundred years this number has grown considerably.
A crucial step in the understanding of why novae erupt were the obser­
vations made by Walker (1954) and Kraft (1959, 1964). Novae are a subclass of
CV stars, so they are very close binary systems with a white-dwarf and a low-mass
main-sequence star.
The white dwarf has no thermonuclear fusion fuel of its own (H, He), it is
only a burned core enriched with inactive C,N,0. The hydrogen rich material from
the secondary accumulates on the white dwarf’s surface and forms a layer there.
This layer is compressed and heated due to the gravity of the primary until the crit­
ical temperature for one of the relevant thermonuclear reactions is achieved. The
mass transfer rate must be sufficiently low ~ IO- 1 0 —10- 9 M© yr_1. The thermonu­
clear burning of hydrogen synthesizes some unstable ß + nuclei with short lifetimes
which are transported to the outer envelope. Their decay leads to a huge energy re­
lease in the outer shells and causes the nova outburst accompanied by mass ejection
~ 102 —103 km/s. Nova eruptions have typical amplitudes of 8 - 15 mags and there
are only a few novae that seem to be recurrent, but Shara (1989) supposes that all
novae must be recurrent, so that we could see the number of novae we are observ­
ing nowadays. The bolometric luminosity of novae remains remarkably constant at
the Eddington luminosity for months after the visual luminosity decreases (Shara,
1989). The resulting release of energy is ~ 1037 —1039 J and the corresponding mass
loss is 10- 4 — 10- 5 M© .
According to their optical light curves, novae can be classified based on the
15
speed of their rise to maximum and fall to minimum light, but this classification is
ambiguous. To describe the rate at which novae change their brightness, we often
use í 2 (£3 ); it is the number o f days a nova takes to fade by two (three) magni­
tudes below the maximum light or the rates of decline υ&,
v<a =
3
where v& =
/Í 3 . We can also use the mass-loss time (ťm_j) instead of
*3
2/i2
and
to distinguish
between different classes of novae (Kovetz & Prialnik, 1995).
Very fast novae
Fast novae
have tm_< < 10 days
have a very rapid rise to maximum and maintain it for only few days;
10 days < £m_i <50 days. The decline is steep at first and slows down later. The
brightness drops from its maximum by three magnitudes within
Moderate novae
110
days.
are somewhere between the fast and the slow novae. Their tm-i
is greater than 50 but lower than 100 days.
Slow novae
have a gradual rise to maximum and may remain there for several
weeks or months. The decline is at first slow with fluctuations then it quickens.
A secondary maximum can be observed, followed by a return to the minimum
state. The overall three-magnitude decrease may take about 150 days, 100 days
< ťTO_í
<1
year.
Very slow novae
are similar to the previous varieties but the maximum extends
over years and the decline is extremely slow as well.
Symbiotic novae
are such novae that the time necessary for the brightness to
drop by three magnitudes from its maximum is longer than
10
years and whose
amplitude is moderate, from 4 to 10 mag. If the amplitude exceeds
10
mag., star
belongs to the very slow novae class.
There are at least three important physical parameters affecting the speed
of novae (Shara, 1989). These are the white-dwarf mass, the mass accretion rate
16
Sketch of Novae-dasses
Figuro 4: The sketch of light curves of diverse types of novae: very fast novae, fast
novae, moderate novae, slow novae and very slow novae.
onto the white dwarf, and the white-dwarf luminosity (core temperature).
On the surface of the white dwarf, the accreted hydrogen is mixed with
the white dwarf’s mass and so all novae show some degree of C-N-0 enhancement.
Wliite dwarfs of different masses and luminosities undergoing accretion at different
rates require very different times to reach thermonuclear runaway. The thermonu­
clear runaway usually begins locally rather than globally because of temperature
inhomogenities. It starts in the hottest region of the white dwarf's envelope. It
is not certain which energy transport mechanism is dominant, so it is not sure for
how long can localized runaways remain local. A months- or years-long brightening
before a dramatic rise to maximum light is often observed in classical novae. The
accreted material is mixed by diffusion induced convection or shear mixing or con­
vection induced shear mixing with the core material during the accretion process.
That is why we observe various combinations of large abundances of helium, carbon,
nitrogen, oxygen, neon, magnesium or iron compared to the Sun. From these abun­
dances we estimate the populations of Ο-Ne (with tract's of Mg, Na) white dwarfs
and C -0 white dwarfs.
All novae near peak brightness display the Eddington luminosity of a ~
1 - 2 M© object approximately (Shara, 1989). The luminosity in the plateau phase
(constant bolometric luminosity) is given by Iben & Tutukov (1989)
L/Lq ~ 4.6 x 10\ M w d /Mq - 0.26),
(4)
where L© is the luminosity of the Sun, M w d is the mass of the white dwarf in the
binary star and Ar© is the mass of the Sun.
The mass outflow rates from classical novae have been determined by Bath
& Shaviv (1976) as ~ 1021 - 1022 g s-1 . The visual brightness of a classical nova
begins to decline once mass ejection declines, after most of the envelope has been
ejected. The remnant of the envelope collapses back onto the white dwarf and most
of the energy from the white dwarf is radiated in the EUV in the X-ray band. There
is no difference in a nova’s brightness before and after its eruption. There is, how­
ever, a significant increase in luminosity between 1 to 15 years before the eruption
(Robinson, 1975). A while after the nova’s outburst, a nebulosity can be seen sur­
rounding the binary.
Between the nova’s eruptions there might be a period of hibernation; a few
centuries after the outburst from the red dwarf the mass transfer decreases. The
system might undergo a dwarf-nova eruption. The mass transfer can be very low
or it can stop and start again after a long interval. This is well described in Shara
(1989).
Livio (1992a) supposes that dwarf novae and classical novae are the same physical
systems, where only the accretion rates vary and thus a hibernation phase occurs
after the nova’s outburst.
There are two distinct nova populations: disk and bulge novae. Disk novae
are in general fast and bright (M V(max) — -9 mag, ť2 ^ 13d or Í3 < 20**) and bulge
novae are dimmer and slower, often display double maxima, and are related with
dust formation (Mv(max) — -7.2 mag, > 13d or t3 > 20**). With respect to post­
outburst spectra, there are Fell-type novae (evolving slowly with lower ionization
18
level), He/N-type novae (higher expansion velocities and lower ionization levels) and
Fellb-type novae, which are close to the previous type (Williams, 1992). Faster and
brighter nova events are associated with more massive white dwarfs. Disk novae
are close to the galactic plane (< 150 pc) and are often related to white dwarfs
A/wd
1 Mq , whereas bulge (or thick disk) novae are up to lOOOpc away from the
galactic plane and MWD <
1
M© .
The spatial distribution and population of novae depends on the Hubble
type of their parent galaxy and in the case of spiral galaxies generally follows the
background galactic light. However, after decomposing the background light into
bulge and disk components, it appears that the nova distribution follows the bulge
light better than the overall light (Shafter & Irby, 2001a).
3.2
Recurrent novae
If the white dwarf’s mass is near the Chandrasekhar limit, the CV star will probably
be a recurrent nova (Nariai & Nomoto, 1979). This is a group of novae consisting
of 7 confirmed and very heterogenous members. Recurrent novae are believed to be
related to dwarf novae because of their recurrence and to classical novae for their
outburst amplitude. During outburst, these stars typically brighten by 7-11 mag
by Shara (1989), they can reach peak luminosities of M y ~ —9 mag mid have ΙΟ­
Ι 00 days periods. The typical member of this class is RS Ophiuchi, whose light
curve is shown in Fig 5. FYom the photometric and spectroscopic data it seems that
the physical mechanism of novae and recurrent novae is the same, only in recurrent
novae, the companion of the white dwarf could be a red giant. It is thought that all
novae are recurrent given enough time.
Presently, the characteristics which distinguish a variable star as a recurrent
nova are provided by Webbink et al.(1987) and are given by two parameters:
( 1 ) the star must exhibit two or more nova-amplitude outbursts with an absolute
visual magnitude (Mv) ^ -5.5, and
(2) the ejection of a shell must have an expansion velocity of ^ 300 km s“1
It has been thought that there are two types of recurrent novae, one, where the
19
AAVSO DATA FOR RS ΟΡΗ - WWW.AAVSO ORG
Figure 5: The light curve of RS Ophiuchi, from h t t p : / / a s v s o .o r g .
outbursts arc caused by thermonuclear runaway from the white dwarf’s surface and
the other, where the disk instability or the instability of the cold companion are the
reasons for the outburst.
3.3
Novae as standard candles
Novae could be excellent standard candles; they are extremely luminous at max­
imum light, and their rates of decline are tightly correlated with their absolute
magnitudes at maximum Arp (1956). The problem is, that we do not know all
other influences (like absorption) and it is difficult to identify the prccisc moment
of maximum brightness and the moment when it drops by 3 magnitudes as well.
The problem of the proper calibration of the maximum magnitude versus the de­
cline rate relationship is still subject to discussion. The equation relating these two
parameters was first proposed by Zwicky (193G) and later adjusted to:
where Ci, C2 depends on the nova’s place of origin and
is t2 or r3 as defined
above. Other empirical relations between the absolute visual magnitude at maxi­
mum and the time of decline follow:
20
Schmidt-Kaler (1957):
Mvmax = —11-5 + 2.5log[t3)
(6)
M b = (-10.67 ± 0.30) + (1.80 ± 0.20)log t3
(7)
Pfau (1976):
Cohen (1985)
M v = (-10.70 ± 0.30) + (2.41 ± 0.23)log í2
(8)
Capaccioli et al. (1990):
(9)
Della Valle & Livio (1995):
( 10 )
Downes & Duerbcck (2000):
(11)
According to the della Valle & Livio (1995), a linear equation is good enough
for extragalactic novae but not for galactic novae where a nonlinear equation must
be used to describe this relation.
3.4
Supernovae type la
It is likely that novae with the white dwarf near the Chandrasekhar limit can be the
progenitors of supernovae type la. When the total mass of the white dwarf and the
accreted material exceeds the Chandrasekhar limit, the white dwarf collapses into
a neutron star. The nuclear explosion releases a huge amount of energy which we
observe as a supernova type la.
21
Figure 6:
And,
The Andromeda galaxy.
The bright star in ·the left is v
the galaxy in the left-down is M32,
and right-up MllO.
From
http://www.skyfactory.org/m31/m31_it.htm.
4
4.1
Novae in M31
M31
M31 or the Andromeda galaxy is our nearest large neighbour spiral galaxy, belonging
to the Local Group of galaxies together with its companions (including M32 and
MllO, two bright dwarf elliptical galaxies), our Milky \Vay and others. This object
is visible to the naked eye. It was known to the Persian astronomer Abd-al-Rahman
Al-Suti as the "little cloud". He described it in 964 AD in his Book oj Fixed Stars.
First telescopic description was gíven by Simon Marius in 1612. Charles Messier
catalogued it on August 3, 1764.
It was long believed that the "Great Andromeda Ne bula" was one of the
nearest nebulae. In 1864 William Huggins, the pioneer of spectroscopy, noted the
difference between gaseous nebulae with their line spectra and the "nebulae" with
star-like, continuous spcctra. In 1887, Isaac Roberts obtained the first photographs
22
of the Andromeda ” Nebula” , which showed the basic features of its spiral structure
for the first time. V.M.Slipher of Lowell Observatory measured the radial velocity
of the Andromeda ’’ Nebula” about 300 km/s in approach in 1912.
It was the highest velocity ever measured and pointed to the extra-galactic
nature of this object. In 1923 Edwin Hubble found the first Cepheid variable in
the Andromeda galaxy and thus established the intergalactic distance and the true
nature of M31 as a galaxy. The distance was incorrect by a factor of more than two
and this error wasn’t discovered until 1953 (Messier 31, 2007). Hubble published
his study of the Andromeda ’’ Nebula” as an extragalactic stellar system (galaxy) in
1929.
In modern times, the M31 is the most studied ’’ external” galaxy. It allows
studies of all the features of a galaxy from outside. At present the radial velocity is
301 km/s. The visual magnitude is 3.4 mag and the distance is ~ 770 kpc.
4.2
Novae in M31
Novae have been observed in M31 for a long time. The first ’’ nova” in this galaxy
was discovered in 1885. Actually, it wasn’t a nova, but a supernova, nevertheless,
since tills time, observers have been looking for novae. The first group that focused
on more or less systematic hunting for novae at the beginning of the
20
th century
(started at 1909) was from Mount Wilson observatory. Since.1932, about 108 novae
were found in the M31.
The first systematic survey was made between 1909 and 1927 and referred
by Edwin Powell Hubble. He recorded 85 M31’s novae using the Mount Wilson 1.5 m
and 2.5 m telescopes. These same telescopes were used by Arp between 1953 and
1955 and he found 30 novae. The next survey was made by Rosino between 1955 and
1963 using the 122 cm telescope on Asiago, photographs were taken on blue sensitive
plates, and he found 46 novae. During the next 20 years he found 142 novae in total.
In the years 1955 through 1970 Rosino discovered 90 novae. In these days there are
many discoverers in this field - both by amateurs and professional astronomers.
Each year many new novae are discovered in M31. All principal surveys are shown
in Table 1 , partly from Damley et al. (2004).
23
Table 1: Principal M31 surveys.
Author (s)
Epoch
Detector
Novar
Annual rate
„
Hubble
1909 - 1929
plates
85
~ 30
y
Mayall
1927 - 1928
plates
10
-
Arp
1953 - 1954
plates
30
24 ± 4
Rosino et al.
1955 - 1963
plates
46
29
• Börngen et al.
1960 - 1967
plates
27
-
v Rosino et al.
1963 - 1970
plates
44
-
Meinunger
1975
plates
13
-
Ciardullo et al.
1982 - 1986
CCD
40
-
·, Rosino et al.
1971 - 1986
plates
52
-
^ Sharov & Alksins
1969 - 1999
plates
64
31
JTomaney & Shafter
1987 - 1989
CCD
9
-
^ Shafter h Irby
1990 - 1997
CCD
72
y
Rector et al.
1995 - 1999
CCD
44
-
v.
Damley et al.
1999 - 2002
CCD
20
-
Henze et al.
1962 - 1996
plates
19
-
j
y
24
The M31 novae are primarily associated with the bulge. It seems that about
70% of novae arise from the bulge. Ciardullo et al. (1987) supposes that novae in
M31 belong overwhelmingly to the bulge population. However, there is an article
contradicting this Hatano et al. (1997a) according to which the majority novae in
M31 comes from disk population.
At the beginning of this research no novae were discovered further than 4
or 5 kpc from the centre of the Galaxy because photographs of more distant areas
were not taken. In Sharov (1972b) an opinion is expressed that the density of nova
subsystems depends very strongly on the distance from the centre of the galaxy.
The existence of a nova hole in the central region of M31 with a radius ~ 2’ is
mentioned in Vader et al. (1982). The authors suggest that this nova hole exist as
an age effect: the central region of M31 should be so old that its novae have evolved
beyond the nova stage. In Ford et al. (1986) we can find that using CCD cameras,
there is no longer a ’nova hole’ in the central region of M31, and that the ’nova hole’
existed only because of the used equipment. The rate of appearance of new novae
is approximately 30 novae per year. Due to observational bias we are finding about
20
novae per year.
The importance of M31’s novae is that through this we can understand
novae generally; their spatial distribution, populations. The Galactic data are heav­
ily biased by selection effects (interstellar absorption). In M31, all novae are at
essentially the same distance, the rate of observed novae is high and the spatial
distribution can be measured.
25
5
5.1
Observations and R esults
Review of novae
I collected position-data of known novae from the beginning of the last century. My
data begins with Hubble’s novae; the last nova is from November 2007. I found
704 novae which were detected in M31, 402 of these were observed using plates, 312
with CCD detectors. I’m using X,Y scale established by Hubble and Arp, where X
is along the major axis of M31, positive to northeast and Y is along the secondary
axis of M31 positive to southeast:
( 12)
(13)
where P A = 37.7° is the position angle of M31, α, δ are the nova equatorial cöordinates, αο, δο are the equatorial coordinates of the M31 nucleus for a given equinox.
The M31 centre coordinates are listed in Table 2 for various equinoxes.
The error in measurement was not presented in the articles I used for col­
lecting data. The error in calculation of position X,Y with regard to previous articles
could be caused by the ambiguity in position angle, which varies from 35° to 38°,
37.7° is the most frequently used value in articles, so my estimation of error is about
5%.
In the very beginning of M31 observations, there was a ’nova hole’ discovered
in the centre of the galaxy. It appeared th at there are no novae near the nucleus of
M31. The ’nova hole’ is evident if we plot the oldest data, from Hubble (1929) Arp
(1956) as we can see in Figure 7.
With better measuring methods the ’nova hole’ disappears, in Figure 9 or
Figure 8 there is no evident ’nova hole’ in the centre. Figure 10 clearly shows that
there is no ’nova hole’ in the centre of M31.
I have compared the data obtained on plates versus the data obtained with
CCDs. Most novae on both are near the centre of M31. On plates we have found
that there are few novae in the proximity of the nucleus. This lack of novae in the
centre of M31 becomes more evident if we compare nova rates on Figure 12 and
26
Figure 7: The novae observed by Hubble (1909-1927) and Arp (1953-1954). There
is an evident ’nova hole’ around the centre in 0,0.
Figure 8: The detail view on novae observed on plates near the centre of M31. These
novae were observed during the last century (1909-1999). There is no significant lark
of novae in the centre.
27
Figure 9: All novae found on plates during the last century. There are 6 novae out
of the depicted interval.
Figure 10: Novae found with the aid of CCDs.
28
Figure 11: The number of novae found on plates versus the interval of proximity to
the centre.
Figure 12: The number of novae found using CCDs versus the interval of proximity
to the centre.
29
Table 2: The coordinates of M31 nucleus
RA
equinox
Dec
1900
0/‘37m16*.9
+40°43’24”
1950
0*40m24i
+40°59’43.6”
1975
0A41m22*.2
+41°8’5”
2000
0/*42m44*.31
+41°16’09.4”
Figuře 11. This phenomenon is caused by the observation method, with the same
cause as the mentioned ’nova hole’.
If we compare Figure 12 and Figure 11 we can see, that more novae are
found near the centre using the CCDs, but there are less novae further from the
centre. This is probably due to the selection effect and the narrow area observed in
M31, because most telescopes are focused on the centre of M31. T h at’s why it is
difficult to arrive at any conclusion about the spatial distribution of novae in M31
from these data. It is obvious th at most novae are in the bulge and near the disk,
not in the halo of M31. On plates, 270 of the 402 novae found (67.2%) are more
them 5’ far from the centre. On CCDs, 153 of the 312 novae found (49%) are more
than 5’ far from centre. In Table 3 you can see this relation for selected values. In
Figure 13 there are all novae which were observed in M31.
5.2
Spectrum of nova 2005-01a
I have analyzed a spectrum of ’nova 29’ discovered on 6th January 2005 by Kamil
Hornoch (nova 2005-0la). In figure 14 you can see the image of this nova around its
maximum light made by Kamil Hornoch. This nova was located at o= 00,*42m28*, 40
6 = +41°16’36.8”. This spectrum was acquired at Lick observatory using a Kast
Double-Beam Spectrograph1.
In table 5 you can find the emission and absorption lines I have identified
in this spectrum. I have had to assess most of these Unes myself because of the
background noise which prevents reliable fitting. This nova belongs to PJe class
in Tololo Nova Spectral Classification System (Williams et al. (1991)). This nova
has a very bright maximum, but a nonconforming rate of dedine. I have also tried
l http://www .ucolick.org/public/telescopes/8hane.html
30
NovaelnM31
,., . . .
""
.
·'
.
...
X CA<Cmhlles)
Figure
November
13:
AU
2007.
novae
The
found
picture
M31
m
of
M31
between
is
1909
taken
and
from
http://www.astronomie . de/technik/ccd-technik/projekt_m31/leistung/
mosaik/2003_2004...kmpl_grau....hoch.jpg.
Figure 14: The image of nova 2005-0la in maximum light made by Kamil Hornoch
in Lelekovice with an SBIG ST-6V CCD camera with 18' x 13' FOV in the Newtonian
focus, on 2005 January 13.
31
distance
number of
number of
from nucleus (r)
novae closer
novae closer
in arcsec
than r on CCDs
than r on plates
0.5
6
1
% on CCDs
% on plates
1
1.9
0.2
16
4
5.3
1
1.5
36
13
11.5
3.23
2
63
26
20.2
6.5
2.5
78
41
25
10.2
3
94
67
30.1
16.7
5
159
132
51
32.8
7
191
180
61.2
44.8
10
217
233
69.6
58
15
244
285
78.2
70.9
20
260
320
83.3
79.6
60
308
385
98.7
95.8
170
312
402
100
100
Table 3: Number of novae with respect to the distance from the nucleus for selected
values. See Figure 11,12 for comparison.
equation
Mv
distance (kpc)
8
-7 .8 0 ± 0.82
368.1 ± 35
6
-8 .3 0 ± 0 .8
463.4 ± 46.3
10
-8 .3 0 ± 0.8
463.4 ± 46.3
11
-8 .2 9 ± 0.88
461.3 ± 49
Table 4: The distance of M31 computed using various equations. It does not agree
with the known distance of M31, which is 770 kpc.
32
nova 2005-01•
14
l•ltkoVJe11
Ondrejov
.
KPHO
15
o
LePalae
~'
VATT
16
17
~
i
18
>-
19
20
21
D
D
'ilo
22
sseo
3400
3420
3440
3460
34lro
julhn date - 2450000
3500
3520
3540
Figure 15: The light curve of nova 2005-0la. The data were obtained by Kamil
Hornoch-Lelekovice, P.Kušnirák, L.Šarounová, M.Wolf - Ondřejov, P.Garnavich.
N.Samarasinha-KPNO, P.Garnavich, C.Kennedy, J. Gallagher, B.Tucker - VATT,
D.Mackey - La Palma
to derive its distance. From the nova light curve I have derived its rate class t 3 =
18.9 ± 1.9 days, t 2 =16 ± 1.6 days. The relative error was assumed to be 10%. I
have computed the Mv and distance of this nova using the equations mentioned in
Tahle 4.
I rneasured the radia! velocity frorn the rectified spectra using the SPLATVO prograrn2 . Only Ho: and Hf3 could be fitted dueto the background noise:
.A-.Ao
= C ---
(14)
Ao
where .A is the rneasured wavelength and .A 0 is the laboratory value, c is the speed
Vradíal
of light in vacuurn, c = 2.9979 · 108 ms- 1 .
From the Ho: and Ha lines I calculated the radial velocities
Vr
= -108 ±
17 km/s and -111 ± 17 km/s; for the emission lines and from absorption line O I
ca.lculated the radial velocity of the ejected envelope
2 http://star-www.dur.ac.uk/"'pdraper/splat/splat-vo/
33
Vr
= -1220± 240 km/s. The
ID
Ao (Ä)
Aoia (-Ä)
Ht
3970
3970
Ht
4101
4100
H,
4341
4344
Hß
4865
4864
Fe II (42)
4924
4926
Fe II (42)
5018
5022
F e ll
5529
5528
He I
5876
5880
Na I
5896
5866
Ne I
5906
A 5906
Fe II (74)
6148
6150
Ne I
6206
6204
Fe II (74)
6238
6240
0 I
6454
6452
Ha
6562
6561
0 I
7773
7776, A 7742
Mg II
8232
8230
8446
8442
Ne I
8484
8486
Ca II
8542
8544
Ne I
8704
8708
Ne I
8668
8668
Cl
9095,9112
9104
P9
9226
9224
P<
9543
9540
0 1
9265
9262
NI
9393
9392
0 1
9399
9400
0 1
Table 5: Suggested identification is followed by the inultiplet number in brackets.
Supposed error of measurement is
1
A.
absorption line.
34
” A ” before the measured value means
Figure 16: Spectrum Nova 2005-01a, splited iuto 5 parts. All identified emission
lines are denoted. Note different scale on vertical axis.
36
heliocentric correction was computed via the BarCor-program 3. The velocity of
envelope with respect to the nova-surface is 1177 ± 280 km/s. This velocity is lower
than expected. For line identification NIST Atomic Spectra Database Lines Form
(2007) and Brackett (1922) were used.
5.3
The Geom etry
I tried to compute the velocity of the envelope of this nova. M31 rotates counter­
clockwise in Figure 6. Milky Way rotates clockwise when we are watching it from
the North Galactic Pole. From the position of the nova in M31, we know that the
star is receding. The magnitude of this velocity is
where i is the inclination angle
where urot is taken from Carignan et al. (2006), P A is the position angle of M31 as
defined above, X is the coordinate along the major axis and Y' = Y/cos{i), Y is
the coordinate along the secondary axis.
M31 and Milky Way are approaching each other with the velocity υαρρ=310 km/s.
Our Sun is receding from M31 with the velocity ν$η„,
where I, b are the galactic coordinates of M31, Z=121.1742° 6=-21.57°. The final
velocity correction is
uTOr=-42.9km/s. The uncertainty of this correction is comparable in magnitude with
this correction, because I have only assumed the position of the nova in the disk of
M31. The sketch of M31 geometry is in Figure 17.
9This program was made by MarieH rudkové,bttp:/ / l a b t e .troja.m ff.cu ni.cz/~brudm O an/B arcor
37
Figuře 17: The sketch of the geometry of M31. PA is the position angle (PA=37.7°),
X, Y' are the axis of the M31, A'n, V'n are the axis angled of PA.
38
5.4
Photom etry and light curves
I participated in observations at the Ondrejov Observatory during three nights on
Octobrer/November 2007. Our data were obtained with a 650/2342mm telescope
equipped with an Apogee AP7p CCD camera, 197x 197FOV (with 2.11”/pixel) at the
primary focus, today it is equipped with G2CCD-3200, chip Kodak KAF-3200ME,
21.8' x 14.8' FOV (1.2” /pixel) with better image sampling then the previous one.
The standard reduction procedures for CCD images were applied (bias, dark-frame,
flat-field corrections). The total exposure time of the image was typically 15-30
minutes (partial exposure time is 90s). Gradient of the galaxy background of added
images is flattened by median-filter using SIMS 4. The last procedure is nearly
manual aperture photometry because it is necessary to determine the precise level
of background coming from the direction of the nova. The place, where the nova
appeared, can be found on some images taken before the nova explosion with a very
good signal-to-noise ratio. Then we calculate the background signal in the place
where the nova appeared. Using the same reference stars on both images (taken
before nova explosion as well as with the nova in the image) located at a place with
uniform background we are able to determine the precise background signal from
the nova’s direction using the following equation:
(19)
where T W S is the total signal of the reference star on the image without the nova,
B W S is the background signal around the reference star on the image without the
nova,
T S is the total signal of the reference star on the image with the nova,
B S is the background signal around the reference star on the image with the nova,
B W N is the background signal from the nova’s direction on the image without the
nova, A W B is the average level of the background signal of the image without the
nova,
B N is the background signal from the nova’s direction on the image with the nova,
A B is the average level of the background signal of the image with the nova.
4http://ccd.m ii.cz/
39
When we have determined the precise background level from the nova’s direction
we calculate the signal from the nova and from some reference stars with known
magnitudes (about R=16-18 mag) on the image where the nova is present. In the
next step we must subtract the determined background signal around each reference
star from the total signal of each reference star as well as background signal from
the nova’s direction (BN) from the total signal measured for the nova. To determine
the nova’s magnitude we use the Pogson equation:
In Figure 18 you can see the lightcurve of nova 2007-1 la, which was discovered
by W.Pietsch and V.Burwitz, Max-Planck-Institut für Extraterrestrische Physik,
Garching; A. Updike, Clemson University (CU); P. Milne and G. Williams, Univer­
sity of Arizona; and D. Hartmann, CU, on stacked R-band CCD images obtained
with the robotic 60-cm telescope (+ E2V 2000x2000 CCD) of the Livermore Opti­
cal Transient Imaging System (Super-LOTIS) located at Steward Observatory, K itt
Peak, on November 2nd, 2007(from M31 (Apparent) Novae Page, 2007).
This nova belongs to the class of fast novae, it dropped by three magnitudes
below its maximum in ~ 11 days.
40
Nova 2007-11a
...•
17
ic
i„
..
.
~·
1
19
-
-·
H ..__~~~~--''--~~~----''------------''------------'
Jullandm
Figure 18: CCD data obtained by Pietsch and Burwitz, Updike, Milne and Williams,
Hartmann and by Kamil Hornoch and Markéta Tukinská -
Ondřejov.
Figure 19: The negative image of nova 2007-lla, made by Kamil Hornoch, with
G2CCD-3200, chip Kodak KAF-3200ME, 21.8' x 14.8' FOV (1.2" /pixel), Ondřejov
November 5th, 2007.
41
6
Conclusions
I have collected coordinates for novae observed in M31 since the beginning of
2 0 th
century. From these data it is obvious that the majority of novae is in the central
bulge and in the disk. There are almost no novae in the halo. These data are
biased due to the selection effect caused by the measuring method. This bias is ev­
ident when comparing the data obtained using plates and data obtained with CCD
detectors. Nowadays, the centre of M31 is observed more often than the peripheries.
I have processed the spectrum of nova 2005-01a. This nova is classified as
Pfe. From the nova light curve I have derived its speed class - it is a fast nova.
There is still some doubt about the distance of this nova. From the light curve, and
the velocity of its envelope and wind it looks like this nova is not in M31.
I have obtained the photometric data of nova 2007-lla, using the 65-cm
telescope of the Ondrejov Observatory. I have always used supplementary photo­
metric observations from the robotic 60-cm telescope (+ E2V 2000x2000 CCD) of
the Livermore Optical Transient Imaging System (Super-LOTIS) located at Steward
Observatory, Kitt Peak. This nova belongs to the fast nova class.
Novae are unsuitable as standard candles. It is difficult to determine the
maximum and the exact time of decline precisely. Certain unpredictable influences,
like absorption, have to be considered as well. The Cepheids or supernovae are
therefore better standard candles than novae.
42
References
J
A rp , C. H a l t o N. 1956. Novae in Andromeda Nebula. The Astronomical Journal, 15-34.
B a e r n b a n t n e r , O ., &í R i f f e s e r , A. 2006:
Novae in M31.
The Astronomer's Telegram,
808(May), 1.
B a r k a t , Z., R e is s , Y ., & R a k a v y , G. 1974. Stars in the mass ratio range from 7 to 10 as
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