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.