Download Measuring Stars

Measuring Stars
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Type Ia Supernova
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The type of supernova discussed are called core collapse supernova.
Supernovas are classified into various classes, type I, type II etc.,
according to features of their spectrums.
One particular type called type Ia, has interesting and important
properties.
Starts as a ordinary binary pair
more massive star evolves faster
When the companion goes through the red giant
phase it spills matter into the white dwarf
and becomes a white dwarf
White dwarf mass increase until it reaches the 1.4Mʘ
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Chandrasekhar limit and then explodes
SN SCP-0401
A supernova Ia in the pinwheel
galaxy (M101) 20 million ly away
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A supernova Ia in a galaxy
10 billion ly away
Since Type Ia Supernovae involve an explosion that occurs around a fixed
mass (1.4Mʘ ), they are a very homogeneous events, and have about the
same luminosity.
So they are like standard candles, wherever they occur, they have the
same intrinsic luminosity.
If we see a type Ia supernova somewhere (in another galaxy), by
comparing its observed brightness to intrinsic brightness we can estimate
the distance to it using the inverse square law.
(The inverse square law tells us that the brightness of an object falls off as
one over the distance squared)
Since supernova are very bright, they can be seen at large distances, in
galaxies billions of light years away. So provide a way to measure distance
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to far away galaxies.
Measuring the Stars: Distance
distant stars
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Nearby stars appear to move with respect to more
distant background stars due to the motion of the
Earth around the Sun
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the line of sight to the star when the Earth is at A
is different than at B, when the Earth is on the other
side of its orbit.
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As seen from the Earth, the nearby star appears to
move in the sky with respect to the distant stars.
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Half of this angle, is called the parallax of the star.
It is the angle subtend by a 1 AU distance at the
star.
nearby star
parallax
angle
B
A
Earth orbit
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Closer stars have a larger parallax
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Distant stars have a smaller parallax, if they are very far away parallax is
too small to observe.
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This gives a means to measure distances to nearby stars directly by
measuring their parallaxes.
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When the parallax is 1 arc second (1”), corresponding distance is called a
parsec (parallax of an arc second)
1 parsec is about 3.26 light years (or 3.086×1013 km)
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If a star has a parallax p its distance is parsecs is given by
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Parallax of Polaris (north star) is 0.0075” so its distance =
𝑫=
1
𝟏
𝒑
=133 parsecs
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0.0075
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In 1838 Friedrich Bessel measured the parallax of Cygni 61 to be 0.33”,
First time a parallax (distance) measured for an object outside the solar
system.
Soon after Henderson measured the parallax of alpha Centauri to be
0.76 arc seconds and Struve measured the parallax of Vega to be 0.12
arc seconds.
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Even for nearby stars parallax is very small.
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The smallest parallax measurable from the ground is about 0.01-arcsec
(100 parsec )
Better resolution can be obtain from space, thus smaller parallax
measurements.
Hipparcos Satellite, operated 1989-1993 had a resolution of 0.001”
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– Hipparcos measured parallaxes for over 100,000 stars
– Got 10% accuracy distances out to about 100 pc
– for bright stars out to 1000 pc.
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Cepheid Variables
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Most stars undergo an unstable oscillations at the end of the red giant
phase, later in their evolution. The star becomes a variable star, star with
changing brightness.
There are many types of variable stars, and many reason why they change
their luminosity periodically.
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One type of variable stars called Cepheid Variables, which have periods from
one to about 100 days show a direct relationship between their luminosity
and the period of variation.
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In 1912 Henrietta Leavitt working at the Harvard College Observatory was
looking for variable stars in the Small Magellanic Cloud.
She noticed that one type of variable stars, Cepheids (named after delta
Cepheus, first star of that type) had a longer period when they were brighter.
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apparent brightness
log(period)
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A Cepheid in the Andromeda galaxy.
Since all stars in the Small Magellanic Cloud are at about the same distance, the
brighter stars had longer periods suggested that period and luminosity
were related.
Thus if a its period is known, its luminosity can be estimated .
Cepheids are bright supergiant stars (~1000 times brighter than the
Sun), so they can be identified even in other galaxies.
In fact, in 1924 Edwin Hubble showed that Andromeda galaxy was an object
outside the Mikey way by identifying few Cepheid variables in the Andromeda
nebula (as it was called then) and estimating its distance.
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Steller Temperature and Classification
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In principal stellar temperature can be
estimated by its color and the peak of the
spectrum.
But due to absorption lines and bands in the
spectrum it could get complicated.
Spectral lines in the spectrum provide a
additional information about the
temperature of a star.
Absorption line strength in a stellar spectrum
is mostly controlled by the star temperature
– Above 25000K show absorption lines of ionized
helium and heavier elements appear, because
at high temperatures those elements ionize
– Hydrogen absorption lines of such stars is very
weak, because hydrogen is totally ionized and
there are no electrons to make transitions to
produce light
– At low temperatures (3000k) molecular
abortion lines visible, since at low temperatures
molecules can survive in the outer layers of the
star, which breakdown at higher temperatures.
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Stars were first classified according to the strength of hydrogen absorption lines
late 19th early 20th century. They used a scheme of classification A, B, C …
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But later on in 1920s, with better understanding of atomic structure and
spectra it was realized that original order of the scheme was not correct.
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They were rearranged according to the temperature as O,B,A,F,G,K,M in
descending order of the temperature.
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Each class is sub divided 1-10, like B2, G8…
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Hertzsprung–Russell Diagram
O
B
A
F
G
K
M
Blue giants
107years
Luminosity (solar)
10000
Red super giants
10M☉
108years
100 R☉
100
Red giants
A
1
1010years
Sun
10 R☉
main sequence
1011years
0.2M☉
0.01
white dwarfs
0.0001
25000
10000
1 R☉
red dwarfs
8000
6000
4500
surface temperature
3000
0.1 R☉
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When luminosity of stars is plotted versus their surface temperature, stars
appear to fall into few distinct groups, according to their stage of life cycle.
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Main Sequence: The majority of stars (~90%), including the Sun, are in a diagonal
band, going from upper left corner (hot, luminous, massive stars) to the lower right corner
(cool, dim, low mass stars). Those are the stars fusing hydrogen in their cores. Since
every star spend most of their life cycle in the hydrogen burning main sequence stage, it is
the mostly populated region of the plot.
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Evolutionary path of a star like Sun in the HR diagram
planetary nebula forms
supergiant stage
helium burning
100 R☉
red giant stage
10 R☉
main sequence
Sun
helium core
contracting
1 R☉
white dwarf
0.1 R☉
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Star Clusters
M92
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M13
Since a large interstellar cloud first fragments to smaller pieces when it
collapses under gravity, end result is a cluster of stars.
All stars in a cluster are of the same age and composition, an ideal place
to study the effect of mass on the stellar evolution.
There are two main types of star clusters:
– Globular clusters: A tight spherical collection of hundreds of thousands (or
millions) of very old (over 10 billion years) stars. Most of them are in a
spherical halo surrounding the galaxy, ~150
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M44
NGC 3603, A young open cluster, radiation
pressure from the stars has cleared the
cavity in the cloud, few light years across
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Pleiades
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Open clusters: A loose irregular group of stars up to few thousands, that
originated from the same gas cloud. They are found in the plane (disk) of
the galaxy where there is abundant gas and dust for new star formation.
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Evolution of Stars in a Cluster
Shortly after the formation, massive stars already in the
main sequence and burning hydrogen and with lower
mass just beginning to arrive on the main sequence.
After 10 million years, the most massive stars have already
evolved out the main sequence or exploded, while many of
the least massive have not even reached there yet.
After 100 million years, stars larger than 4-5 solar masses
have left the main sequence and there is a distinct mainsequence turnoff. Most of the low mass stars are now in the
main sequence.
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red
giants
After 1 billion years, main-sequence turnoff is now at
about 2 solar masses. Red giant branch associated with
low mass is evident. White dwarfs are beginning to appear.
white
dwarfs
After 10 billion years, solar mass stars are evolving away
from the main sequence. The red-giant, supergiant,
and horizontal branches are all clearly populated. White
dwarfs, indicating that solar-mass stars are in their last
phases, also appear.
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The double cluster in Perseus, H-R diagram shows that most
young stars has not reached the MS and only most massive
stars has left the MS, it is very young probably 10-15 million
years
Pleiades, H-R diagram shows lo mass stars in the main
sequence and more higher mass stars moved away from MS,
likely it is 100 million years old.
The Hyades cluster. Its H-R diagram shows that the MS cut off
progressed further down, and few white dwarfs. Probably it is
600 million years old.
Globular cluster 47 Tucana, MS turnoff has reached Sun like
stars well developed radiant and white dwarf branches. So it
has to be more than 10 billion years old.
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Binary Stars
CoM
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A binary star system consists of two stars which are gravitationally bound
and orbit around their center of mass.
About half of the stars are binary, some systems even have more than two.
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In some cases individual stars of the can be seen through a telescope,
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which are called Visual binaries. Many visual binaries have long orbital
periods of several centuries or millennia.
In many cases a binary system is too far away, or the stars are too
close, or one star is so much brighter than the other that we cannot
distinguish the two stars visually.
But still we can infer that the system is binary by several indirect methods.
– Eclipsing binaries: In some binary systems orbital plane of the stars is
oriented edgewise toward earth. So that one star passes directly in front of
the other eclipsing its light Most famous example is Algol:
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Algol:
• A star in the constellation Perseus known for centuries which change its
brightness.
• A blue spectral class B8 star with a diameter of 3 solar diameters and
red-yellow spectral class K2 star of about 3.5 solar diameters are in very
close orbit around each other.
• They are so close together that tidal forces are distorting the shape of
the K2 star, into a teardrop shape.
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Spectroscopic binaries are systems in which the stars are so close
together that they appear as a single star even in a telescope.
The only evidence of a binary star comes from the Doppler effect on its
emitted light.
As the stars move through their orbits around the center of mass, their
radial velocity toward Earth changes, which blue and red shift their
spectral lines.
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