Post Main Sequence Evolution Continued
1. Helium Fusion
This fusion phase is a much shorter phase compared to hydrogen fusion stage on the
Main Sequence. Why? First of all, the energy output from helium fusion is much less
than that of hydrogen fusion. So the star has to fuse the helium faster to have a high
energy output. Also at this time the star is much more luminous compared to its
luminosity on the Main Sequence, so it is fusing at a much higher rate. Even though
helium fusion is the dominant energy source, there is still some small amount of
hydrogen fusion occurring though it contributes very little to the star’s energy output.
The descriptions described here are mainly for moderate to low mass stars (2 or less M).
We’ll also get to the higher mass stars eventually.
After the helium flash and the start of steady helium fusion, the star will adjust to the new
energy source. The core expansion caused by a helium flash will remove the degeneracy
and also drop the core temperature slightly, which causes a slight drop in the overall
fusion rate.
The drop in the fusion rate will drop the luminosity to a level that is below that just
before the helium flash. The star will contract as well. Gradually the star move down the
RGB, and slowly evolves to the left on the HR diagram since the star’s radius will also
decrease. This leads to an increase in density and a higher surface temperature – which
of course is what you get when you go left on an HR diagram.
This puts the star on the Horizontal Branch (HB) on the HR diagram.
Low mass stars are found on the HB, and are vertically distributed based upon mass.
Stars are on the HB for a fair amount of time, 100 million years or so for some stars,
Notes 6 - 1
since in a way this is another “Main Sequence”, in a way it is like a helium fusion Main
Sequence. Stars like the Sun spend about 10% of their lives here. That is why a
relatively large number of stars are observed here, and these are generally classified as
Giants (luminosity class III).
The HB tends to be found in a region of the HR diagram where the physical parameters
of stars behave in an unusual manner – it is basically a place where density, temperature,
and opacity all conspire to make the stars unstable to hydrostatic equilibrium. This is
where you would find low mass pulsating stars, such as RR Lyrae types.
What about the bigger stars? Of course stars that are 2-10 M don’t have a helium flash.
So when their helium ignites they don’t have as great a drop in their luminosity since
there is no major restructuring in the cores. They do get hotter (on the surface) though,
so they have a Blue Loop. This is where the luminosity classes for types III, II and Ia, Ib
would be found.
For the high mass stars the helium fusion is much more dominant so there is much less
hydrogen fusion going on at the same time. This decreases the heating of the outer layers
and causes the star to contract more (and makes it have a smaller radius), which causes
the outer layers to get hotter. That’s why the loops are “blue”.
Like the small mass stars, these stars also are unstable to hydrostatic equilibrium but
become Cepheids, another type of pulsating star. And of course Cepheids are the most
important of all types of stars!
Generally there are many more low mass stars in this phase of evolution (found in HB
and blue loops), since the low mass stars are longer lived even during this phase. So
generally speaking there are many more RR Lyrae stars out there than Cepheids.
Evolution models try to determine the characteristics of the pulsating stars based upon the
observed location of the Cepheids and RR Lyrae stars on the H-R diagram (based upon
observed values of L and surface T). This is one area where the computer models of stars
can be tested in a variety of ways since the observed characteristics of the pulsating stars
Notes 6 - 2
can be used to directly test computer models of not only the evolutionary paths of stars
but also stellar pulsation models. But not all stars in this phase are pulsating stars like
Cepheids or RR Lyre, so that also needs to be explained. The region of instability is
relatively narrow, and star will evolve into and out of this region over time, and tend to
become stable or unstable as they evolve.
2. End of Helium Fusion – Planetary Nebula
The second phase of major fusion doesn’t last forever of course and once helium fusion
stops, things get bad again for the star. The core becomes fully convective and that
means that the carbon-oxygen rich core gets thoroughly mixed, and this is just referred to
as the CO core. You now have a star with a CO core, with a shell of helium fusion
around the core, and further out, a shell of hydrogen fusion.
The next steps are similar to what happened after the Main Sequence phase. The core
will contract and heat up again. This causes the outer layers to expand and cool off, so
the star is seen to move again to lower temperatures on the HR diagram. And as before,
convection develops throughout most of the star. This can dredge up material from the
core to the surface, so these stars may have very unusual surface compositions. So the
path the star now takes is again to the upper right hand corner of the HR diagram along
what is called the asymptotic giant branch (AGB). This is really just an extension of the
RGB that goes to even higher luminosities and lower temperature than what happened
before. Typically the stars here are those with CO rich cores, while the ones on the RGB
have helium rich cores.
So the core gets hotter and hotter, and the radius gets bigger and bigger and the
luminosity goes way, way up. These would be considered cool supergiants.
Low mass stars that are in this phase will again become degenerate in the cores, with
fusion only occurring in shells around the core – one shell of hydrogen fusion, and one
of helium fusion. The helium fusion shell is particularly unstable, since the degenerate
nature of the material will cause the star to have shell flashes, which are sort of like mini
helium flashes. These outbursts are “only” about 100 million L . Technically these are
viewed as thermal pulses –high temperature eruptions that occur deep inside the stars.
Helium shell fusion isn’t very productive particularly since it has all of the hiccups
associated with the shell flashes. This causes the fusion to start and stop and start again
(though rather violently). The two fusion shells are separated by a layer of non-fusing
helium. If all things were simple this would remain nice and orderly – but that’s not how
it works.
Let’s say you have hydrogen shell fusion going on nicely, and that of course makes more
helium. Eventually the helium ignites (violently) in another helium shell flash. The
helium shell flash will cause the core to expand a bit and this will cause the hydrogen
fusion in the other shell to stop since the environment is now too cool due to the
expansion. So now only helium shell fusion is important and this eats through the helium
Notes 6 - 3
layer producing more carbon and oxygen. This goes on until the helium fusion layer
reaches the base of the old hydrogen fusion layer. The presence of the hot helium fusion
layer causes the hydrogen fusion to start up again, which has a stabilizing effect on the
core. Since hydrogen fusion produces more energy, it doesn’t have to be as hot or dense,
so the temperature drops a bit. As the core adjusts to the more stable hydrogen fusion,
the helium fusion diminishes since it can’t be sustained in that environment (since the
temperature went down). And so now you’ve got the hydrogen shell making a bunch of
helium and you are back at where you started….This is a thermal pulse cycle, and is a
normal property for an AGB star.
Another fun feature of an AGB star is the start of very strong winds. These stars are very
high up on the HR diagram so they are pretty luminous to begin with. This can put them
over the Eddington Luminosity briefly. The stellar winds are helped along when there
are particles that easily absorb energy, particularly large gas molecules and dust. Such
large molecules can exist in the outer layers of these cool stars, and have been observed.
The winds in these stars are actually best described as superwinds. These are the types of
winds we see when we see large scale mass loss from stars that produce very thick shells
of material around them. The previously given relation for mass loss (equation 5-2) is
valid but at these times the mass loss rate can be as much as 10-4 solar masses/year, which
is considered a very large amount. Mass loss will also mess up the star’s evolution later
on.
It is also possible that a pulsating star can help the mass loss process along. Stars like RR
Lyrae and Cepheids don’t really have the right conditions for major mass loss, since they
aren’t near the AGB, but there are a bunch of pulsating stars in the area of the AGB –
those with very low surface temperatures and very large radii. These are known as Miras
and LPV (long period variables). They are very slow pulsating stars with very extended
outer layers. It can take them a year to do a single pulsation.
For stars between about 1 and 8 M, superwinds and thermal pulses will get rid of the
material outside of the core and will leave behind a CO core that has a mass between 0.6
and 1.1 M This is when the star enters the Planetary Nebula phase. Here are the
characteristics of a typical planetary nebula:
 Size around one light year (or 1/3 pc)
 Very low density material in the nebula (1000 particles/cc)
 Central star ionizes the gas though this will eventually fade over time as
the star cools and the material gets further away
 Approximately 1500 planetary nebulae are observed in the Milky Way
 Gas cools down after about 10,000 years or so
 Shapes vary – tend to be symmetric either with bipolar outflow or
spherical forms
Initially the core of the star keeps the gas very ionized. The core stars are generally
30,000 K or hotter and give off significant amounts of UV light which easily ionizes
hydrogen and many other atoms in the show/outflow.
Notes 6 - 4
Spectra of planetary nebula show many emission features, since these nebula have the
conditions required to make an emission spectrum. There is a great variety of elements
apart from hydrogen and helium. There are also various features that are denoted as
“Forbidden” or “semi-Forbidden” spectral features. These are not really forbidden but
are very, very unlikely to occur under most circumstances. They are seen in astronomy
in a variety of situations, such as in planetary nebulae, since they occur in an incredibly
hot but very low density region. Forbidden features are denoted with brackets around the
ion, like [O II] or [S III], while semi-forbidden spectral features would be denoted by a
single bracket, like Ca III] or Fe IV].
The cores of the stars at the centers of the planetary nebula still have a very small layer of
hydrogen and helium on it that is technically the “atmosphere” of the star. There is really
no more fusion going on at this point, just a hot ember slowly cooling off. Finally the
core cools, and the material that was once the outer layers of the star gets further and
further away from the core, and it cools down and fades away. Now all that remains of
the star is the core, which is a White Dwarf.
The evolutionary path of stars during the planetary nebula phase is rather narrowly
confined. Even for stars of different masses, they tend to converge to a very narrow
location on the HR diagram to the left of the Main Sequence as is shown in the graph of
theoretical evolutionary paths.
5
1
1.5
2
2.5
5
4
Log (L/Lsun)
3
2
1
0
-1
-2
5.4
5.2
5
4.8
4.6
4.4
4.2
4
Log (Teff)
3. White dwarfs
This is the final state for low-medium mass stars, typically stars that have masses less
than 8 M.
Notes 6 - 5
3.8
Characteristics of a White Dwarf –
 Hot, surface temperatures ranging from 5000 – 80,000 K
 Core temperature of ~107 K.
 Temperature decreases as it ages
 Small radius, approximately the size of the Earth, around 6000 km.
 Masses are not too diverse, typically only 0.6 M
 Maximum mass defined by the Chandrasekhar limit (equation 3-10)
 Density on the order of 1 billion kg/cubic meter
 Magnetic field ranges from few – 100 Tesla (Sun’s magnetic field is
around 0.1 T at most)
A white dwarf isn’t entirely degenerate throughout since it still has an atmosphere
(surface layer) of hydrogen and helium, and this also means that will produce a spectrum
like a “normal” star in most cases. The atmosphere layer is very small in terms of mass
and radius compared to the rest of the star.
Since a white dwarf can produce a stellar spectrum, there is a special way that we classify
their spectra. Previously it was mentioned that the letter “D” was used to denote a white
dwarf, but there are various subdivisions of these –
 DA – has H absorption features. This is the most common spectral type
 DB – has He I absorption features, approximately 8% of all white dwarfs
 DO – has He II absorption features, rare
 DC – has no absorption features, but a continuum. 14% of white dwarfs
 DQ – has carbon features in the spectrum, very rare
 DZ – has metals in the spectrum, but no H, or He, very rare
Since they are very small it takes them a long time to cool off. It is possible that they
crystallize as they cool down, with a structure like a diamond resulting. There is
observational evidence that such stars actually exist. The star BPM 37093 is a DAV
white dwarf (“V”=variable) with a hydrogen atmosphere and mass of approximately 1.1
M. Since it is actually a pulsating object, the way in which it pulsates depends upon its
internal structure. Based upon the form of the pulsations, researchers estimate that a
good fraction of the interior of the star is in a crystalline form (the amount of the interior
that is crystalline varies with different assumptions). The star’s nickname is
appropriately “Lucy”. It is only about 16 pc away, which makes it a relatively nearby
object. Of course if you wanted to mine this diamond, you’d first have to get past the hot
surface (12,000 K), and the killer surface gravity (nearly one billion x Earth’s gravity).
Technically this would probably not be a diamond since the crystalline structure would
not be the same as a regular diamond.
Theoretically a white dwarf should cool down to a “black dwarf” but the time for that to
happen would be really long. How long? Here’s an approximation of the core
temperature for a white dwarf –
Tcore
L
4 10
M
2/ 7
7
6-1
Notes 6 - 6
with the luminosity and mass in solar values. If this relation is taken for the value of the
temperature, and you combine it with a typical value for a white dwarf’s luminosity, you
get a time scale for cooling as
M
2.5 10
L
5 7
6
cooling
6-2
with L, M in solar units, and time in years. This gives the time generally for only the
lowest luminosity white dwarfs (around 0.001 x sun’s luminosity).
Shown here are theoretical
cool-down curves for different
white dwarfs – one of carbon,
and the other a mix of helium
and carbon. Both models are
0.6 M. The rate is initially
very quick but once the object
become mainly crystallized the
rate of cooling slows down, so
the final cooling phase is very
long.
Even though the white dwarf cools down, it doesn’t change its radius. This is pretty
much the first time in the star’s life when a change in temperature doesn’t result in or
produce a change in radius. As white dwarfs cool down they travel along a line of
constant radius on the HR diagram, which lies nearly parallel to the Main Sequence.
There are slightly different paths for the different mass white dwarfs – remember, as a
degenerate object the mass and radius are linked.
White dwarfs will have different compositions depending upon the star’s initial mass
which determines how much fusion they will have and what ends up in the core at the
end of their fusion history
White dwarf mass
Mass < 1 M
M>1 M
M>1.5 M
Helium rich
C, O rich core
O, Ne, Mg, Na, etc
Generally most white dwarfs are C-O rich or Helium rich. And eventually they will
become a black dwarf, but so far the coolest white dwarf is one with a surface
temperature of around 3900 K. It is worth mentioning that white dwarfs are an important
tool for age dating the universe, and current estimates give ages of only 12-13 billion
years for the coolest white dwarfs observed.
4. High Mass Evolution after the Main Sequence
Notes 6 - 7
After the Main Sequence, the high mass stars don’t do anything exciting. They are pretty
steady in their fusion with no major or drastic events happening until the end. This
would be stars that are above 8 or 10 M.
After leaving the Main Sequence, what happens? Or in this case, what doesn’t happen?
 No degeneracy until the very end of all fusion stages
 No thermal pulses of any type
 No helium flash or helium shell flashes
 Smooth transitions between successive fusion cycles, helium, carbon,
etc…
 Mass loss can be significant or important in later stages
 The star could get close to the Eddington Luminosity
 Found in upper part of HR diagram, in Ia, Ib domain.
 Eventual fate – supernova
There has been work at linking massive stars to various fates based upon their masses as
well as the phases they go through on the way to a supernova. Below is a current
breakdown for the likely evolution of various mass ranges, and of course none of this is
entirely precise, but does seem to be in the right ball park.
10 to 20 M. On Main Sequence O type → Red Supergiant → Blue Supergiant →
Supernova
20 to 25 M. O type → Red SG → WN → Supernova
25 to 40 M. O type → Red SG → WN → WC → Supernova
40 to 85 M. O type → O with emission lines (Of) → WN → WC → Supernova
Above 85 M. O type → Of → LBV → WN → WC → Supernova
For Masses>40 M, there is a greater chance for mass loss to alter the star’s evolution –
these would be stars best classified as Hypergiants (beyond supergiants). These are the
stars that are also likely to become Wolf-Rayet stars (WN or WC). When we observe
these stars, they tend to be generally much less massive then their original mass at
formation. These are also the stars that have the chance to become LBV (Luminous Blue
Variables) and they can change their brightnesses relatively quickly.
Another feature of these hypergiants is their tendency to be self-destructive. Since their
luminosities can be very close to the Eddington Luminosity, they will lose mass more
often than lower mass stars. This will alter their evolution and also limits their evolution
to lower temperatures on the HR diagram. Stars of lower temperature, but of high
luminosity will be the most prone to mass lose, and this will often cause their evolution to
reverse, sending the stars to higher temperatures. There is an observed upper limit to the
HR diagram called the “Humphreys-Davidson” limit which can be mapped out based
upon the distribution of high mass stars. Stars tend not to be found above the H-D limit
since this is where the Eddington Luminosity will kick up quite a bit. And stars that do
happen to get into this region can be seen to evolve quickly as they have outbursts or
huge mass loss episodes.
Notes 6 - 8
The evolutionary
models shown here
(dashed lines) show
the effects of mass
loss, as well as
rotation, which
cause major changes
in evolution from
the standard path
that would be
expected.
The various dots are
the observed
characteristics of
various massive
stars.
Here are the characteristics of Hypergiants:
 Surface temperatures vary “quickly” from hot to cool
 Luminosity extremely high (millions of L)
 Highest possible Masses, perhaps up to 200 M
 Evolution – extremely fast, changes can be observed in decades or
centuries
You have to remember that most stars in the galaxy are small and boring, and about 10%
of all stars are close to the Sun’s mass. Only about 1 in a million stars will become
supergiants. And the number of stars that are hypergiants is an even smaller number
(very difficult to estimate how many). These are stars with masses well over 30 M, and
values can be as high as 120 M. It is possible that some of these stars initially had over
200 M worth of material but have lost a good amount of mass through their lives.
Masses that high are just not stable enough to maintain a high amount of material for very
long.
5. Extreme Supergiants/Hypergiants
Like all things extreme, hypergiants have come to prominence in a variety of ways over
the past few years. There are quite a few famous hypergiants, and I’ll describe some
here.
P Cygni – a star that is visible in the northern hemisphere (in the constellation of Cygnus
the swan). This star was not noted until it suddenly became bright enough to be visible to
the naked eye. The first recorded observation of the star was in 1600 when its apparent
magnitude was estimated to be V=3. This would make it a bit fainter than the North Star.
It then started to fade until it got to the point where it was not visible to the naked eye
Notes 6 - 9
(around V=6). In 1655 it again got brighter, this time reaching a value of V=3.5, and
then it faded again. And in 1665 again got brighter and since about 1715 it has had a
fairly steady but slowly increasing magnitude which is currently at around V=5.
While many stars have been known to change their brightness in rather unpredictable
ways, the really important feature about P Cygni is its spectrum. This is because if you
look at the spectrum, you’ll see an emission feature right next to an absorption feature.
That’s not what you are supposed to see in stars – they should all have absorption
spectrum. Why is it like this?
This spectral
feature, which
is called a P
Cygni Profile
when it is seen
in a star’s
spectrum, is
caused by an
expanding
envelope of
material and is
a dead
giveaway for
large scale
mass loss in a
star.
Here’s how it
works. If
someone views
a star that is losing mass, they will have various spectral features produced by the
different areas around the star. If in the diagram below the observer is to the far left of
the mass losing star, they would see different spectral features which originated from the
mass loss material found in areas “A” and “B”. The material in area “A” is coming
directly towards the observer and is in front of the star, so it would produce a blue shifted
Notes 6 - 10
absorption feature (it is absorbing the light of the star behind it). The areas that are not
directly in line with the star (areas “B”) are made up for material that is being blown off,
so they only see the light produced by the material (not the star), which would be
emission features in the spectrum. But the material in areas “B” are moving at a range of
velocities (Doppler shifts) due to
motions towards and away from the
observer. The end result is a spectra
which is a combination of a large
absorption feature at shorter wavelengths
(from the stuff in area “A”) and a large
emission feature at longer wavelengths
(stuff from area “B”). The P Cygni
profile is commonly seen in any object
that is experience a large scale mass loss
event. The higher the velocity of the
material that is being blown off, the
wider the spectral feature feature.
P Cygni has the following characteristics
 Classified as a LBV
 Spectral Type B1Ia
 V=4.8
 Effective temperature = 19,300 K
 Luminosity = 725,000 L
 Initial mass, likely 50 M
 Current mass, closer to 30 M
The changes in P Cygni that were observed over the centuries are not only due to
evolutionary changes. The overall energy output of P Cygni has remained fairly constant
during this time. What has changed is how the energy is given off by the star. This can
be linked to the surface temperature changes of the star. As the temperature goes up, the
light tends to be given off more in UV than visible wavelengths so the star may not
appear as bright to the eye. Also there is the likely effect of the mass loss blocking off
the light from the object as well, so that can also cause the star to fade.
Eta Car - Another weird star is Car (pronounced eta Car) which is located in the
Keyhole nebula and is only visible from southern locations. Like P Cygni, eta Car has a
long history of varying brightness. When it was first noted in 1603 by European
astronomers it was a V=4 star. Over the next few centuries it changed its brightness
erratically, and one day it sort of went nuts. In 1843 its brightness shot up to V=-1,
which made it the second brightest star in the night time sky, only fainter than Sirius (V=1.4).
To give you an idea of how crazy that is, you need to know that Sirius is about 3 pc away,
while eta Car is closer to 2300 pc away! Right away this tells you that something crazy is
going on with eta Car to make it nearly as bright as Sirius, yet it is 800 times further
away. Actually the energy output observed in 1843 from eta Car is around 600,000 times
Notes 6 - 11
what we measure from Sirius. If eta Car were moved to the distance of Sirius it would
have been as bright as the full moon during 1843! Between 1837 and 1856 the brightness
of eta Car was significantly enhanced. It is estimated during this time that it lost
somewhere between 1 and 3 M, and had a luminosity as high as perhaps 20 million L.
Once the outburst ended in 1856, eta Car has faded significantly, though it is currently
getting brighter again.
The spectrum of eta Car shows a strong P Cygni Profile, which right away tells us that
there is significant mass loss going on. When you look at it today with the Hubble Space
Telescope you can see expanding shells of material comprised of several solar masses,
maybe even upto 12 M. The speed and size of these shells indicate that this material
was blown off from the star in 1843. Currently the material is traveling outwards at
about 1000 km/s. In IR wavelengths, eta Car is the brightest object in the sky, which tells
us that there is a lot of cool material, likely dust rich material, around it. There has also
been x-ray flares (outbursts) observed from time to time.
What is going on with eta Car? Careful observations of its spectrum indicate that there is
a 5.5 year periodicity visible in the emission features. So every 5.5 the emission features
are seen to be at a minimum (low level). This minimum was observed in 2003, and early
2009. It is generally thought that eta Car is a binary system with an interaction between
the two stars causing the change in the emission lines every 5.5 years. The stars are
thought to be in very elliptical orbits so the effects are very pronounced for a short period
of time. In this scenario it is possible that there are two 70 M stars in orbit about one
another, about 15 AU apart on average. The brightness of the nebula implies that one of
the stars isn’t very bright, which is unusual for such high masses. Also there needs to be a
source for x-rays in the system which again is unusual. There is generally no consensus
about what is actually happening in eta Car or one simple solution for the observations.
This makes it a very well studied object.
Here are the current characteristics of eta Car:
Notes 6 - 12
 LBV
 V=6.21
 Total masses = 100-150 M
 Temperature 40,000 K
 Mass loss rates of close to 10-3 M/year
 Binary system
 Current Luminosity ~ 50 million L
It may be a while before we can figure eta Car out completely, since it is a very distant
object, and high resolution images of the system are not able to provide enough detail.
HR 8752 is another strange hypergiant. It has been observed since around 1840, and
oddly it wasn’t observed before that time. This would indicate that it was fainter than
V=6 before 1840, but since that time it has become visible and has had a rather well
studied history from the early 1970’s to 2000’s. During that time spectra were obtained
which helped to define the temperature and density of the star, which resulted in rather
interesting results.
But perhaps the most surprising aspect of HR 8752 is that it has changed temperature
rather dramatically over the last 30 years. Unfortunately the value for E(B-V) isn’t well
defined, but using the best estimates, the surface temperature was approximately 5000 K
in 1975 and close to 8000 K in 2005! During this time the radius also decreased, going
from 750 R to 400 R. The reason for the changes aren’t known, but it may have been
due to an outburst or eruption of some sort, though that is only speculation. We can
watch this star, since it is located in the constellation of Cassiopeia.
And what discussion of extremes could we have without including the current champion
of largest radius – VY CMa. This is currently the largest radius star known, with a radius
estimated to be about ~1400 R. It is a very cool M3-M5 type, so its mass may not be
very large – perhaps only 15-20 M.
And currently the largest mass star is R136a1, which isn’t even in our galaxy, but is
found in the nearby galaxy, the Large Magellanic Cloud. R136a1 is found in the
Tarantula Nebula star formation region of that galaxy, and there was some debate about
what this object actually is for some time. Early images showed a large “blob” of stars
and only recent high resolution images have revealed individual stars in this area. The
bizarre name is based upon the survey of the region and earlier designations before they
realized just how many stars were in R136! The mass is approximately 265 times that of
the Sun and has a surface temperature of around 53,000 K. The luminosity is around 8.7
million times that of the Sun. It is entirely possible that the star originally had a mass
closer to 400 M when it formed, but has since lost a good fraction of its mass.
6. Variable stars
We’ll cover the final fate of large mass stars in the next section, but before we get to that
let’s take a closer look at variable stars in general. Stars can be variable due to either
internal or external causes. The case of an external cause is an eclipsing binary system
Notes 6 - 13
which isn’t really all that exciting, so we’ll just stick with the internal/intrinsic variables.
These variables physically change (in radius, and/or temperature usually) which causes
them to also change their brightness. There are two main types of intrinsic variables,
pulsating and eruptive. Whatever causes the star to change its brightness doesn’t last
forever. Eventually the pulsation phase of the star’s life ends or the eruptions stop
happening, since stability is returned to the star. Generally the time scale for significant
variability is very short in a star’s life and doesn’t last forever.
The way that we name variable stars is rather strange, but that’s not surprising in
astronomy. Variables are named according to the constellation they are found in and a
letter based upon the order of their discovery. The first variable discovered in a
constellation is given the letter “R”. The next one is given the letter “S”, and so on to
“Z”. I’m not sure why we started with “R”, but that’s how it starts. After “Z” comes RR,
then RS, RT, RU…to RZ. Then SS, ST..SZ, and so on all the way to XX, XY, XZ, YY,
YZ, ZZ. What’s next? Well why not use the first part of the alphabet? That’s right, after
ZZ is AA, AB, AC, AD…to AZ, then BB, BC, BD…to BZ and so on until you have QQ,
QR, to QZ. By the time you get to QZ you’ve gone through 334 stars. So if you have
more than 334 variable stars in your constellation you would label the next one V335,
then V336, then V337….and fortunately the numbers can just keep getting bigger. I
should mention that in all of the alphabet stuff mentioned above, the letter “J” is never
used.
So stars like RR Lyrae, S Doradus, RU Lupi, V335 Sagittarii are all real star names.
Often we’ll just use the 3-letter constellation name, so that would be RR Lyr, P Cyg, S
Dor, RU Lup, V335 Sgr etc. Stars that were named before their variability was
discovered just have their regular name used, like delta Cepheid, Polaris, eta Aql, etc.
6.1 Pulsating Variables
Pulsating stars can be divided into various groups, those that regularly pulsate and those
that irregularly pulsate. The regular pulsators are much better behaved with their changes
in brightness much more predictable and steady. Over time the way that the stars pulsate
can change as the star evolves, but it is usually a very slow change often taking centuries.
Here are some well known pulsating variables
 Cepheids – relatively high mass, supergiant phase for a star. Comes in two main
types based upon composition
o Classical, metal rich (normal Z), also called Type I Cepheids
o W Vir, metal poor (low Z), also called Type II Cepheids
Generally the Type I Cepheids are brighter and more common than the Type
II Cepheids.
 RR Lyrae – low mass pulsators, short periods, red giants, also low Z values
 BL Her – similar to W Vir, but lower mass
 Anomalous Cepheids – sort of between Cepheids, RR Lyrae
 Scuti – very short period, multiple modes of pulsation, found close to main
sequence
Notes 6 - 14
 SX Phe – metal poor, like Scuti
 Dor – cooler version of Scuti, also close to main sequence
 RV Tauri – double amplitude pulsator
Cepheids and RR Lyrae variables are most commonly used for distance determine due to
the well defined relationship between their pulsation periods and their luminosity
(absolute magnitudes).
Irregular pulsators are also very common, and are sort of like irregular heartbeats – they
don’t have any specific period, or they change their pulsation periods or the amount that
their light varies. Many of these are very large radius stars which causes them to vary in
unusual ways.
 Mira – very long period, LPVs, very cool, very slow, lots of dust
 SRabcd – Semi-regulars type a, b, c, d, similar to Miras
 LBV – luminous blue variables, basically very massive stars like P Cygni or eta
Car that are pulsating
 Cyg – A high mass supergiant pulsator
 Cep – Btype giant pulsator, found close to the main sequence.
 R CrB – an eruptive type of variable, yellow supergiant
Notes 6 - 15
Careful observations of stars in planetary nebulae and white dwarfs indicated that these
stars also pulsate, often with a period of seconds to a few minutes. Many of these stars
pulsate at very low levels and in non-radial modes. This means they vibrate more than
pulsate.
 GW Vir – pre white dwarf – period of a few seconds
 ZZ Ceti – White dwarf pulsator, period of minutes
 DB – White dwarf, 100-1000 second period
Virtually all of the short to moderate period pulsating stars are unstable due to the
(opacity) mechanism. These stars are at a stage in their evolution where the temperature
and density values in their atmospheres result in a very large opacity. This is usually
seen in the area of the atmosphere where hydrogen is being ionized, often around
temperatures of 10,000 K or more in the atmosphere (below the surface). As stars
evolve, their internal structures change, and the temperature and density structure that
produced the high opacity is removed. If the star is evolving to higher temperatures, the
ionization region gets closer to the surface, and that disrupts the pulsations. If the star is
evolving to lower temperatures, convection will develop and that will also disrupt the
pulsations. So in the case of the main pulsating types, like Cepheids are RR Lyrae
variables, the Instability Strip is well defined both observationally and theoretically.
Cepheids are most notable for being used as one of the most reliable distance indicators,
particularly to distant galaxies. This is through the use of a relationship that was first
recognized by Henrietta Leavitt, one of the many women working as “calculators” at
Harvard University in the early 1900’s. While examining photographic plates she
discovered 2400 Cepheids with periods between 1 and 50 days, mainly in the nearby
galaxy, the Small Magellanic Cloud. She went one step further in determining that those
with a larger average brightness also had a longer pulsation period. Over the years this
relationship has been re-calibrated and is provided in many formats, but in general the
most common form of Leavitt’s Law is that of the relationship between the absolute
magnitude and the pulsation period.
Since Leavitt’s Law is primarily empirical (based on observations), there is no one single
definitive value for the variables in the relation –
Mv =
Log P +
6-3
where and have to be experimentally determined, and P is in days. Here are some
recently derived values for the B, V and I filters –
MB = -2.757 Log P + 0.472
6-4
MV= -3.141 Log P + 0.826
6-5
MI = -3.408 Log P + 1.325
6-6
Notes 6 - 16
Each of the above relations has uncertainties associated with the constants, so there is a
small amount of errors associated with using these values (about 0.2 magnitudes). And
they of course are open for debate in terms of just how accurate they are. In 2012 alone
there are about a dozen publications in which Leavitt’s Law is re-calibrated, often when it
was used in getting distances to galaxies.
For the longer period variables or those with unusual pulsations it is much more difficult
to explain why they pulsate. Very LPV, which are also very cool stars, tend to have lots
of dust in their outer layers. This dust as well as various gas molecules can play a role in
the pulsations, but it is difficult to determine how much dust forms and how effective it is
in blocking energy flow.
6.2 Eruptive and Cataclysmic Variables
There are quite a few different types of eruptive variables – those that alter their
brightness through a unexpected (usually), non-periodic outburst. Some get brighter due
to eruptions like flares, or due to major mass loss episodes. Some will change brightness
due to interactions with the material around them, or through strong winds. While
eruptive variables can be pretty bright, they are not as self-destructive as cataclysmic
variables (CVs). These include supernovae (which will be covered in the next set of
notes) and novae (singular nova).
A nova requires a binary system with a relatively close pair of stars, one of which is a
white dwarf. The closeness of the binary system allows mass to be exchanged from one
star to another. Material will tend to first build up on an accretion disk around the white
dwarf, and sometimes that is where the explosion occurs. But if a great deal of material
is being transferred, it will tend to make its way to the white dwarf and pile up on its
surface. The material on the surface of the degenerate white dwarf will increase in
temperature until it reaches the point of thermonuclear runaway (this is discussed way
back in the 3rd set of notes). At this point we don’t know when this will be triggered
precisely, sort of like how it is not possible to predict earthquakes, but there are some
stars that nova in a rather systematic manner, and it is possible to make “predictions” of
their eruptions. These are usually for
the smaller eruptions seen in dwarf
novae (also called U Gem stars).
About 250 dwarf novae are known to
exist in our galaxy. They will get
brighter by about 2-6 magnitudes, and
in this case it isn’t really the white
dwarf that is causing the eruption, but
the build-up of material on the
accretion disk around the white dwarf.
Dwarf novae eruptions are not
continuous. There are quiet periods
that can last from 30-300 days.
Notes 6 - 17
In general the rate of mass transfer for dwarf novae is not very large, since the eruption
occurs before the mass is deposited on the white dwarf. Rates are only about 10-11
M/year. For higher mass rates, there is more material that is deposited on the white
dwarf and that will lead to a classical novae. There should be dozens of these events
occurring in our galaxy each year, but we don’t always get a clear view of them. We
have a better chance of observing them in other galaxies. In general only a few are
observed in our galaxy each year. Novae have an increase in brightness of about 7 to 20
magnitudes, though typically they brighten by about 10 to12 magnitudes. Typically a
nova has a luminosity that is 105 times that of the sun. Nova do not all act in the same
manner. The best way to distinguish them is based upon how quickly they decline in
brightness. There are fast novae and slow novae. A fast nova can decrease from its
maximum brightness by 2 magnitudes in a few weeks. A slow nova will take nearly 100
days to decrease by 2 magnitudes.
Nova V2467 Cyg is an
example of a fast nova,
while V475 Sct is a slow
nova. In either case the
transfer of material that
triggers the eruption is on
the order of 10-8 to 10-9
M/year. It may take
only 10-4 to 10-5 M
worth of material to
trigger the thermonuclear
runaway event. While
the name of the explosion
implies a destruction of
the hydrogen that is
deposited on the surface
of the white dwarf, only a
small fraction of the
material is actually
destroyed (converted into
energy), and only about
10% of it is expelled into
space during the eruption.
So if during the novae
event the majority of the
hydrogen rich material
isn’t destroyed in the eruption, nor ejected into space, what happens to it? It actually
starts to fuse on the surface of the nova! This happens mainly in the slow nova, with
energy production at the rate of the Eddington Luminosity. The energy production will
also cause this layer of material to expand, and be eventually ejected from the surface,
Notes 6 - 18
leaving behind the carbon-oxygen rich white dwarf ready for a new batch of material to
begin accreting onto its surface.
Another group of novae are the recurrent novae, or those that repeatedly erupt with time
between eruptions of between 10 to 80 years. These novae also behave differently than
the fast and slow novae, with very fast declines in brightness, and orbital periods that are
relatively long. There is also evidence of material around the novae from previous mass
loss/outburst episodes. Material expelled from the star can have velocities in excess of
4000 to 10,000 km/s. While it is possible that novae events typically result in no net
mass increase of the white dwarf in the binary system, it is possible that for recurrent
novae the white dwarfs are increasing in mass, and these systems warrant further
attention in the event that they go over their Chandrasekhar mass limits.
A relatively famous recurrent novae is RS Oph, which had outbursts in 1898, 1933, 1958,
1967, 1985 and 2006. The outburst features at each event are very similar. The stars
involved are a red giant (M2III) and white dwarf in a 455 orbital period. During the most
recent eruption, a range of instruments measured how the eruption material interacted
with material that had been previously ejected via stellar winds. This interaction
produced x-ray emission.
While the concept of recurrent novae is very interesting, there are actually only a few
stars that fall into this category.
Notes 6 - 19