Great. 
So now we have a catalog, a growing 
catalog of stars to which we know the 
distance. 
We have pulled those stars. 
We, some of them stars nearby, 
down off of the celestial sphere. We know 
the distance to them, we live, they live 
in our three-dimensional universe. 
And what does that tell us about them? 
Well, tells us a lot. 
Let's start by seeing what we can tell 
about a star just by looking at it, 
that's all we can do with stars. 
But, assuming that someone tells us 
because we measure carefully the distance 
to it. 
Well, one thing we can do is we can do a 
photometric measurement. 
We can measure the brightness of a star, 
literally aim a telescope with a known 
aperture area at the star and measure the 
rate at which the telescope gets energy 
from the star. 
You correct for dark sky. 
There's a process, 
it's not that difficult. 
But if we know the brightness, then we 
can remember, remind ourself that 
brightness is related to luminosity of 
the star by this expression. 
Right? 
And this is luminosity divided by four pi 
D^2, if we know the brightness because we 
measured it. 
We know the distance because we measured 
it. 
We can extract an expression by solving 
this for the luminosity. 
So we know the actual luminosity of the 
star. 
Now we can tell you, is this some very 
huge, very luminous star, or some very 
tiny star? 
this is norm way to write the equation, 
a more convenient form in which to write 
it is to scale it to something known. 
In other words, this same equation holds 
for any star in particular, 
it holds for the sum. 
And the advantage of writing it in this 
way is now whether this suggests is if I 
divide the left-hand sides and set that 
equal to the ratio of the right-hand 
sides, first of all the, four pis and 
whatever constants are sitting around 
cancel, but more usefully I now get a 
product of dimensionless quantities. 
I get an expression that says that this 
divided by that is this divided by that 
or this expression here, where I have 
plugged in that the value of the distance 
of the sun from earth is one astronomical 
unit and the sun's brightness is the 
solar constant. 
So we have rate of dimensionless object. 
the luminosity of the star in units of 
solar luminosity written as the product 
of two others. 
Whenever possible, we'll write it that 
way. 
Okay. 
Now we know the luminosity of the star. 
What else can I get just by looking at 
it? 
Well, if I'm careful I can measure the 
color, star's color. 
And the star's color as we know gives us 
information about its temperature. 
If I find the maximum of its black body 
spectrum, I can get an estimate from a 
temperature from Wien's law. 
So there is Wien's law. 
It relates the surface temperature of a 
star to the wavelength at which it emits 
its maximum emission, 
this is written in Kelvin. 
And now, if I know the temperature and I 
know the luminosity, I can remind myself 
that I have yet another expression for 
the luminosity of any star. 
L was equal to the sigma T^4, given by V 
Stefan-Boltzmann law for the rate at 
which each square meter of the star 
surface radiates times the surface area 
of the star, which in terms of the star's 
radius is given by four pi R^2, 
where R is the star's radius. 
And now, if I know T and I know L, I can 
extract an expression for R. 
you find that R^2 is L over four pi sigma 
T^4 or if I just want R, I simply take 
the square root of both sides. 
And I can rewrite that as the square root 
of L over four pi sigma times the square 
root of one over T^4 is T minus two, one 
over T^2. 
And in this form, again I can compare to 
the sun by dividing this expression for 
the star by the same expression for the 
sun. 
The radius of the sun is luminosity of 
the sun square root divided [INAUDIBLE] 
one over the temperature, solar 
temperatures square, 
and this gives me another one of those 
nice scaling expressions. 
But then, bottom line is if I know the 
temperature and luminosity, for which I 
needed observations and the distance, I 
can get the radius of the star. 
Now, 
now some stars, a few tens have actually 
been imaged and this is a recent 
development. 
There's a few tens of stars for which the 
radius has actually been measured 
particularly optically by imaging them 
and measuring the angular distance 
between the left and right side of the 
star. 
This is a new result, but most stars, 
when we say we know their radius, we know 
it from this. 
This is brilliant, we can know a lot from 
a star, about a star if we know it's 
distance. 
the problematic measure here is the 
temperature Remember we said the black 
body spectrum is very broad. 
If you have a very broad mountain, 
identifying exactly where the summit is 
can be a problem, in the same way, 
finding the precise maximum of a very 
broad black body spectrum is a difficult 
and imprecise task. 
We want a better thermometer, since 
measuring the stellar temperature is so 
important. 
And, it turns out that we have a better 
thermometer. 
it's also less subject to distortion, 
for example, if there is a cloud of gas 
or dust between us and the star, we know 
that we'll preferentially scatter blue 
light star viewed through dust or gas 
will appear redder than it is and that 
might mislead us into thinking it is 
cooler than it is. 
In fact, if you looked at the sun at 
sunset and tried to devise it's 
temperature from it's color or even in 
the middle of the day, you would conclude 
that it's yellow rather than green. 
Now something that is 
not distorted by interception intervening 
media is the star's absorption line 
spectrum. 
So, we can look and understand something 
about the chemical composition of the 
star's atmosphere. 
This was known and there was a big 
ongoing project late 1930, twentieth 
centure into the 20s to classify the 
forms that stellar absorption spectra 
take. 
It was clear that there was a lot of 
information there, but isn't clear until 
the 20s exactly what it is that we are 
classifying when we classify stellar 
spectrum. 
we now understand the classification. 
Here is a sort of 
compilation of representative stellar 
spectrum arranged in order of what is 
called spectral type. 
And spectral type runs from A through B, 
A, F, G, K, and M. 
And, within each category there are ten 
subdivisions, 
so B0 is on one end and then it goes all 
the way up to B10, 
and A0 up to A10 and so on. 
and, 
if you notice there are sort of 
properties, 
there are spectral lines that are very 
prominent, say in this region between the 
Bs and the As, but almost absent in the O 
type stars and then disappear in the F 
stars. 
This for example are the spectral lines 
of hydrogen, these are [INAUDIBLE] lines 
of hydrogen and the interpretation that 
is understood in the 20s is that this 
organization, and the reason B, B comes 
before A is because there was previously 
another organizing principle, and this 
is, this was understood later. 
this organization, this organization is 
in direction of decreasing temperature. 
So O stars are the hottest stars and M 
stars are the coolest stars. and for 
example if you look at the 
hydrogen in the stellar atmosphere, then 
O stars are so hot that the hydrogen is 
essentially ionized and in B stars much 
of the hydrogen is ionized. 
An ionized hydrogen atom is just a free 
proton and electron, there is no 
absorption line spectrum for a free 
proton. 
So, hydrogen lines are almost completely 
absent from the spectrum of O and they're 
really weak in the spectrum of B type 
stars. 
in the cooler Bs and in the A type stars, 
hydrogen lines are very permanent because 
hydrogen is now atomic. 
the ambient the, the light that the star 
is emitting is at high frequencies so the 
and the temperature is high enough that 
these hydrogen atoms get excited to their 
excited state in the observed 
this language is associated to a hydrogen 
atom in it's first excited state the 
hydrogen atom ground state excitations of 
the Hydrogen atom from the ground state 
are ultraviolet and they don't appear in 
the visible light spectrum. 
And indeed, as we proceed in lowering 
temperature, once we go from A to F type 
stars, the hydrogen lines weaken and 
eventually disappear, because hydrogen in 
the cooler atmosphere of F type stars is 
in the ground state. 
And if it absorbs anything, it absorbs 
ultraviolet light, 
very few of the atoms are in the first 
excited state where they can absorb 
visible light protons, 
so hydrogen lines disappear. 
What starts to appear is the spectral 
lines over here of ionized metals, 
heavier elements. 
You see these forests with many, many, 
many, many lines in them. 
and these are characteristics of more 
complex atoms, so these are the spectral 
lines of ionized metals, and in cooler 
stars, yeah, then cooler Gs and the Ks we 
find the spectrum of neutral metals. 
So now, it's, the temperature is cool 
enough that heavier atoms do not become 
ionized. 
And in the M types star the cooler M 
types stars, we actually find these 
bands, these ray broadened bands of 
absorption. 
This corresponds to the existence of 
molecules with eternal degrees of freedom 
and so they can absorb light at various 
wavelengths. 
And so, this progression is a progression 
in temperature, and once you understand 
that, we know that we can use this as a 
precise thermometer, 
here is the current list of spectral 
types. 
they are listed according to the color, 
the color the perception of stars is very 
subjective. 
Here are the temperatures. 
Note that the temperatures at stellar 
surfaces range from as hot as 50 or 
60,000 Kelvin in hot O type stars to 2000 
or 3000 Kelvin on the very cool, dark red 
M type stars. 
And, these are the sort of description of 
the spectral features that characterize 
them. 
This is the prevalence and I should be 
careful, this is our understanding of the 
prevalence of this type of star among all 
stars. 
I'll explain why this needs some 
qualification. 
And note that it is precisely increasing 
as you go to cooler stars. 
So, the coolest M type stars form three 
quarters of all known stars, whereas the 
O type stars form a tiny, tiny fraction 
and the cooler the star is the more 
likely it is to appear. 
And here's some examples of stars of each 
spectral type. 
And so dark red Betelgeuse and orange are 
Arcturus and Aldebaran are examples that 
you are familiar with. 
The sun is a G type star. 
In fact, G2 within the internal 
classification of G type stars and Sirius 
and Vega are A type stars and so on. 
The bright stars of Orion's Belt are O 
type stars. 
some of these stars are listed here in 
not in black type and in the next clip, 
we'll understand what we now have is a 
collection of data about stars. 
We now have a huge population of stars 
about which we know their luminosity, 
their radius, their temperature, 
and we can start trying to arrange this 
data as a sociologist would to do 
population study and try to draw 
conclusions. 
We'll figure out how to organize it in 
the next clip.