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Here's another thing that stars do. 
some stars vary. 

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We talked about eclipsing binaries, 
that's one way for the brightness of a 

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star to vary periodically. 
But it turns out that some stars vary 

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intrinsically. 
And the most famous one by far is Myra. 

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we talked about it later. 
Myra, we talked about it earlier. 

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Myra was discovered to be variable, 
probably earlier, but at least as early 

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as the 16th century. 
and that is because as you can see in the 

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two pictures on the right, its luminosity 
changes dramatically by a factor of 100 

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with a period that averages to about 332 
days but is variable and 

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It was discovered by this, early 
astronomer, Fabrizius, and, variable 

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stars, are traditionally a regime where 
what I think someone called, 

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citizen-scientists have great 
contributions to make. 

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I will post in the resources links, and 
if you want to get involved in measuring 

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variable stars. 
There are lots of interesting challenges 

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and astronomers are looking to amateurs 
for data on variable stars. 

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the long period 332 days and the 
luminosity make Mira something called a 

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long period variable the physics and the 
modeling of these variable stars is 

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difficult and Mira, 
this is the best-known variable star, but 

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not the best-understood one. 
I want to talk about the ones that we 

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understand better, and those are located 
in something called the instability 

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strip. 
That's this region on the HR diagram over 

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here, which is almost vertical. 
It's almost determined by temperature. 

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And most massive stars, the sun will 
sneak under the instability strip for 

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population one stars. 
there are three types of variables in the 

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instability strip. Classic Cepheids, W 
Virginis variables, which is a fancy way 

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of saying population two Cepheid 
variables, and RR Lyrae variables, which 

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sit in this very narrow region over here. 
So let's start with. 

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and most stars will cross it as massive 
stars as part of their horizontal branch 

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evolution. 
So RR Lyrae variables are very 

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interesting. 
they have periods of hours, and you can 

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detect them by their spectral signature 
and by their light curve. 

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By the shape of their light curve. 
And if you find an arar lire, that's 

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brilliant because notice that the 
luminosities of arar lire variables vary 

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by. 
Perhaps a factor of two and so two within 

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a factor of route two you can know the 
lum to you can know the luminosity of a 

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star just by knowing that its an rr 
variable by measuring its brightness you 

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can now have two of the three variables 
that go into our cardinal equation b 

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equals l over four pie d squared. 
So, if you measure the brightness and you 

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know the luminosity from the fact that 
it's an RR Lyrae. 

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You can figure out the distance so things 
who's luminosity is known are very useful 

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they're called standard candles and RR 
Lyrae are not the best standard candles, 

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but they'll serve and so if you find an 
RR Lyrae variable in a cluster, 

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you can use that to improve your distance 
measurement of the whole entire cluster 

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by using the luminosity of the RR Lyrae 
variable. 

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To conclude, this is, sort of, spectrum 
improved version and spectroscopic 

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paradox. 
it has the advantage that variable stars 

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live very high, so RR Lyrae variables are 
quite luminous objects. 

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They're way more luminous, than say the 
sun. 

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cepheids and their population two cousins 
have periods of days, and modeling those 

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is an interesting problem in physics and 
it's worth paying attention to them 

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because they will come in they will turn 
into something very useful later. 

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So why is it that stars pulse at least 
these that we understand, it was 

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understood rather early that. 
They were not eclipsing binaries, the 

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shape of the light curve. 
This is from a famous 1931 paper. 

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This is the shape of the light curve of a 
Cepheid variable. 

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It does not match well onto an eclipsing 
binary. 

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in fact if you combine it with this 
measurement of Doppler shift. 

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So, this is roughly the radial velocity. 
Of the, part of the star that is facing 

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us, you see that what this star is doing 
is it is, not moving towards us and away 

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from us. 
It's not orbiting. 

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The star's actually pulsing its size. 
It's growing bigger, when the radial 

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velocity is negative. 
Here, the star is expanding, and the side 

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near us is approaching us, and then, the 
star contracts, and the side near us, 

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moves away from us, and then it expands 
again. 

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And so negative, radio velocity here 
corresponds to expansion, and positive 

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radio velocity to contraction. 
And what we see is that the star is most 

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luminous right after it's done 
contracting. 

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And periods of measurement. 
From the spectrum of the effective 

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temperature and we see that in the star 
is most luminous its surface temperature 

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is also highest okay so these are our 
tips and the idea for how a star could 

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pulsate, 
could have a hard time figuring out what 

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size it wants to be. 
So it bounces back and forth, hence 

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instability. 
was put forth by Eddington, and the idea 

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is if you could have roughly a situation 
where compression increases opacity in 

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some layer of the star makes it more 
opaque. 

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Then when the star is compressed that 
layer will trap energy. 

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And be pushed out by the radiation 
pressure until it, the star expands, the 

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layer releases its energy, and then. 
The star will contract again because the 

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layer will be transparent, the energy 
will be able to escape, so you have this 

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mechanism for trapping energy. 
The problem in general is that 

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compression typically in stars both 
compresses material, which increases 

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opacity, but also heats it and 
temperature reduces opacity. 

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So the problem was how to find a way to 
have compression. 

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Not heat material, so that it's opacity 
would increase. 

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And the solution is that under suitable 
condition, compression ionizes in this 

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case helium. 
And what that means is, that some its 

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energy is spent on heating the, ionizing 
helium. 

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Less of it goes to heating the material. 
This allows the net opacity to increase 

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under compression. 
Expansion reduces ionization. 

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This is called the Kappa Mechanism, 
and it is this mechanism that drives the 

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pulsations of sulfiate variables. 
And this determines the boundaries of 

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this instability strip as its models tell 
us that it is stars in this region that 

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have helium at the suitable temperature 
for 

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partial ionization where compression and 
expansion will change its ionization 

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state deep enough in the star, that it 
can push a significant amount of the star 

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up when it traps energy. 
And not so deep in the core that core 

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convection will completely destroy the 
effect. 

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And so we think we understand cepheid 
variables, 

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and we care. 
The reason we care is a discovery by an 

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American astronomer, Henrietta Leavitt in 
1908. 

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And this is actually her data. 
This is a plot of again, magnitude is a 

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logarithmic version of luminosity 
increasing this way or the, not 

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temperature, luminosity. 
Logarhythmically, so this is the log of l 

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plotted versus the logrhythm of the 
period, remember the periods of the 

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accepted variables are days, they vary 
from. 

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A day to 50, or 60, or 90 days. 
And what she noticed is that the longer 

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period variables had, were the more 
luminous ones. 

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And she was plotting this for stars in 
the Small Magellanic Cloud. 

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Again, all of the stars she saw were 
approximately the same distance, so she 

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could use brightness, relative brightness 
as a surrogate for relative luminosity. 

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So she couldn't scale this plot, but she 
saw that luminosity grew with period. 

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And if you only knew the luminosity of. 
Some of these stars you could calibrate 

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this and this was calibrated by measuring 
against globular clusters, which by 

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methods of cluster fitting and 
spectroscopic parallax and other cluster 

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dynamical ways of measuring distance, the 
distances to globular clusters were quite 

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well known. 
There globular clusters have lots of 

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stars they had lots of cepheid variables 
and using that you could use measurement 

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of the period. 
To measure the luminosity to predict the 

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luminosity of this afied and again once 
you have the luminosity you measure the 

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brightness your using this as a standard 
candle suffieds become a great tool for 

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distance measurement again if you know 
the luminosity and the brightness you can 

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compute a distance. 
Now it turns out a little bit later that, 

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these are Population one Cepheids in the 
large Magellanic cloud. 

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In globular clusters, we find Population 
two Cepheids, or W Virginis variables, 

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Those have a period luminosity relation, 
but at the same period, the, globular 

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cluster, 
population two Cepheids are less luminous 

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so what we have here is a recent paper 
which made this comparison. 

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We have here the scatter plot here. 
These are the small Magellanic Cloud 

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Cepheids. 
The same ones that Levick measured. 

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And down here are globular cluster 
Cepheids or population two Cepheids. 

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And we see that there is a relative 
between 

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Luminosity and 
And a period. 

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But, at the same period, a lobular 
cluster appear type population two 

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sephiate variable, is less luminous than 
the corresponding population one sephiate 

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variable. 
Like two will play a role in what's to 

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come. 
What we've discovered is another 

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important step on our cosmic distance 
ladder. 

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We'll use that, and we are in Levitt's 
debt forever.