Here's another thing that stars do. some stars vary.
We talked about eclipsing binaries, that's one way for the brightness of a
star to vary periodically. But it turns out that some stars vary
intrinsically. And the most famous one by far is Myra.
we talked about it later. Myra, we talked about it earlier.
Myra was discovered to be variable, probably earlier, but at least as early
as the 16th century. and that is because as you can see in the
two pictures on the right, its luminosity changes dramatically by a factor of 100
with a period that averages to about 332 days but is variable and
It was discovered by this, early astronomer, Fabrizius, and, variable
stars, are traditionally a regime where what I think someone called,
citizen-scientists have great contributions to make.
I will post in the resources links, and if you want to get involved in measuring
variable stars. There are lots of interesting challenges
and astronomers are looking to amateurs for data on variable stars.
the long period 332 days and the luminosity make Mira something called a
long period variable the physics and the modeling of these variable stars is
difficult and Mira, this is the best-known variable star, but
not the best-understood one. I want to talk about the ones that we
understand better, and those are located in something called the instability
strip. That's this region on the HR diagram over
here, which is almost vertical. It's almost determined by temperature.
And most massive stars, the sun will sneak under the instability strip for
population one stars. there are three types of variables in the
instability strip. Classic Cepheids, W Virginis variables, which is a fancy way
of saying population two Cepheid variables, and RR Lyrae variables, which
sit in this very narrow region over here. So let's start with.
and most stars will cross it as massive stars as part of their horizontal branch
evolution. So RR Lyrae variables are very
interesting. they have periods of hours, and you can
detect them by their spectral signature and by their light curve.
By the shape of their light curve. And if you find an arar lire, that's
brilliant because notice that the luminosities of arar lire variables vary
by. Perhaps a factor of two and so two within
a factor of route two you can know the lum to you can know the luminosity of a
star just by knowing that its an rr variable by measuring its brightness you
can now have two of the three variables that go into our cardinal equation b
equals l over four pie d squared. So, if you measure the brightness and you
know the luminosity from the fact that it's an RR Lyrae.
You can figure out the distance so things who's luminosity is known are very useful
they're called standard candles and RR Lyrae are not the best standard candles,
but they'll serve and so if you find an RR Lyrae variable in a cluster,
you can use that to improve your distance measurement of the whole entire cluster
by using the luminosity of the RR Lyrae variable.
To conclude, this is, sort of, spectrum improved version and spectroscopic
paradox. it has the advantage that variable stars
live very high, so RR Lyrae variables are quite luminous objects.
They're way more luminous, than say the sun.
cepheids and their population two cousins have periods of days, and modeling those
is an interesting problem in physics and it's worth paying attention to them
because they will come in they will turn into something very useful later.
So why is it that stars pulse at least these that we understand, it was
understood rather early that. They were not eclipsing binaries, the
shape of the light curve. This is from a famous 1931 paper.
This is the shape of the light curve of a Cepheid variable.
It does not match well onto an eclipsing binary.
in fact if you combine it with this measurement of Doppler shift.
So, this is roughly the radial velocity. Of the, part of the star that is facing
us, you see that what this star is doing is it is, not moving towards us and away
from us. It's not orbiting.
The star's actually pulsing its size. It's growing bigger, when the radial
velocity is negative. Here, the star is expanding, and the side
near us is approaching us, and then, the star contracts, and the side near us,
moves away from us, and then it expands again.
And so negative, radio velocity here corresponds to expansion, and positive
radio velocity to contraction. And what we see is that the star is most
luminous right after it's done contracting.
And periods of measurement. From the spectrum of the effective
temperature and we see that in the star is most luminous its surface temperature
is also highest okay so these are our tips and the idea for how a star could
pulsate, could have a hard time figuring out what
size it wants to be. So it bounces back and forth, hence
instability. was put forth by Eddington, and the idea
is if you could have roughly a situation where compression increases opacity in
some layer of the star makes it more opaque.
Then when the star is compressed that layer will trap energy.
And be pushed out by the radiation pressure until it, the star expands, the
layer releases its energy, and then. The star will contract again because the
layer will be transparent, the energy will be able to escape, so you have this
mechanism for trapping energy. The problem in general is that
compression typically in stars both compresses material, which increases
opacity, but also heats it and temperature reduces opacity.
So the problem was how to find a way to have compression.
Not heat material, so that it's opacity would increase.
And the solution is that under suitable condition, compression ionizes in this
case helium. And what that means is, that some its
energy is spent on heating the, ionizing helium.
Less of it goes to heating the material. This allows the net opacity to increase
under compression. Expansion reduces ionization.
This is called the Kappa Mechanism, and it is this mechanism that drives the
pulsations of sulfiate variables. And this determines the boundaries of
this instability strip as its models tell us that it is stars in this region that
have helium at the suitable temperature for
partial ionization where compression and expansion will change its ionization
state deep enough in the star, that it can push a significant amount of the star
up when it traps energy. And not so deep in the core that core
convection will completely destroy the effect.
And so we think we understand cepheid variables,
and we care. The reason we care is a discovery by an
American astronomer, Henrietta Leavitt in 1908.
And this is actually her data. This is a plot of again, magnitude is a
logarithmic version of luminosity increasing this way or the, not
temperature, luminosity. Logarhythmically, so this is the log of l
plotted versus the logrhythm of the period, remember the periods of the
accepted variables are days, they vary from.
A day to 50, or 60, or 90 days. And what she noticed is that the longer
period variables had, were the more luminous ones.
And she was plotting this for stars in the Small Magellanic Cloud.
Again, all of the stars she saw were approximately the same distance, so she
could use brightness, relative brightness as a surrogate for relative luminosity.
So she couldn't scale this plot, but she saw that luminosity grew with period.
And if you only knew the luminosity of. Some of these stars you could calibrate
this and this was calibrated by measuring against globular clusters, which by
methods of cluster fitting and spectroscopic parallax and other cluster
dynamical ways of measuring distance, the distances to globular clusters were quite
well known. There globular clusters have lots of
stars they had lots of cepheid variables and using that you could use measurement
of the period. To measure the luminosity to predict the
luminosity of this afied and again once you have the luminosity you measure the
brightness your using this as a standard candle suffieds become a great tool for
distance measurement again if you know the luminosity and the brightness you can
compute a distance. Now it turns out a little bit later that,
these are Population one Cepheids in the large Magellanic cloud.
In globular clusters, we find Population two Cepheids, or W Virginis variables,
Those have a period luminosity relation, but at the same period, the, globular
cluster, population two Cepheids are less luminous
so what we have here is a recent paper which made this comparison.
We have here the scatter plot here. These are the small Magellanic Cloud
Cepheids. The same ones that Levick measured.
And down here are globular cluster Cepheids or population two Cepheids.
And we see that there is a relative between
Luminosity and And a period.
But, at the same period, a lobular cluster appear type population two
sephiate variable, is less luminous than the corresponding population one sephiate
variable. Like two will play a role in what's to
come. What we've discovered is another
important step on our cosmic distance ladder.
We'll use that, and we are in Levitt's debt forever.