We now know how to characterize our 
population of stars. 
We use their luminosity and we use their 
spectra to determine what type of stars 
they are. 
We give their spectral type that gives us 
our, their surface temperature, and we 
can now try to find correlations between 
luminosity and temperature and so on, and 
do population studies. 
what do the statistics tell us? 
Well first of all we notice that 
luminosity varies over huge ranges. 
We find stars with luminosities less than 
1,000 times less than the sun and stars 
with luminosities more than 100,000 times 
more than the sun. 
At the same time the temperatures are 
ranging from 1000 or so Kelvin all the 
way to 50,000 Kelvin and more. 
And stellar radius, which we can compute 
if we know luminosity and temperature 
varies considerably less. 
how to organize the data was the subject 
of much speculation. 
And the successful presentation that we 
used to this day, and will accompany us 
for much of this class, is in the form of 
something called Herzsprung-Russell 
diagram. 
And was invented by Hertzsprung and 
Russell in 1910. 
And here is a Herzsprung-Russell diagram. 
It's a scatter plot of the stars. 
Each dot here represents a star. 
And in some sample, this is some part of 
the [INAUDIBLE] sample, and what do we 
have here? 
Well, the horizontal access is 
temperature with by convention, 
temperature increasing to the left. 
So the hottest O type stars are over here 
on the left. 
the temperature scale is at the top of 
the diagram. 
And the coolest M type stars are here on 
the right. 
The vertical axis is luminosity, so we're 
plotting, if you will, luminosity against 
temperature. 
the most luminous stars with luminosities 
of over 100,000 solar luminosities are at 
the top, the dimmer stars are at the 
bottom. 
And notice that the luminosity scale is 
logarithmic so that the sun is about in 
the center of this diagram. 
one solar lumnosity over here and above 
the next tag above it corresponds to ten 
solar luminosities. 
Similar distance above is 100 solar 
lumonisities and so on. 
And so what do we discern? 
Well we certainly discern that stars are 
not distributed randomly in the spot. 
We have a pattern. 
Good, that's the beginning of 
understanding. 
Now we try to understand it. 
What is the pattern? 
Well about 85% of all the stars lay along 
this one diagonal strip called the main 
sequence because that's where all the 
stars are. 
And this runs from cool, dense stars over 
here in the lower right, to hot, bright 
stars or hot very luminous stars in the 
upper left. 
And that means that if a star's a main 
sequence star, you know it's temperature 
you can predict its luminosity. 
We see a collection of stars scattered 
above the main sequence. 
What does it mean to be above the main 
sequence? 
That means that if you pick a temperature 
by in other words a vertical line, these 
stars lie above the main sequence, they 
are more luminous than our main sequence 
star with a same temperature. 
How do you get more luminous maintaining 
the same temperature that means they are 
radius, their radiating area is bigger. 
These stars are bigger than main sequence 
stars suitably they are called giants, we 
have this collected population of giants 
and still higher above the main sequence 
are various super giants and bright 
giants and even larger stars especially 
at the high temperatures. 
We see the very bright hyper giants and 
bright giants. 
And then there is the, below the main 
sequence, stars smaller than main 
sequence star. 
It just don't seem to be there except for 
this one arc towards the bottom. 
These are stars that, because they're way 
lower than the main sequence, are less 
luminous even though their temperature is 
quite high. 
And so suitably they're called white 
dwarfs. 
These are very small hot objects. 
We'll discuss where they come from later 
but other than that, the plot is 
relatively empty. 
we should we've talked about the way that 
radius plays into this. 
We can compute radius, of course, given 
temperature and luminosity, let's see how 
the radii of stars end up plotting on 
this diagram. 
This animation is designed to allow you 
to explore the HR diagram. 
Again, we have luminosity, 
logarithmically on the left where you can 
sort of pick a luminosity and a 
temperature and move your little cursor 
along the main sequence. 
Note that fixed, changing the temperature 
at fixed luminosity is a horizontal 
motion, changing the luminosity at fixed 
temperature is a vertical motion and the 
red line gives us the main sequence. 
And what we see is that, for the most 
part, stars on the main sequence have 
radii between one solar radius, this is 
where approximately the sun lies, and ten 
solar radii. 
So temperatures of 100,000 
illuminosities, 100,000 times the 
luminosity of the sun, are achieved with 
a modest factor of ten increase, or less 
increase, in radius. 
And the, the, the, 
main sequence sort of follows a slow 
increase in radius with luminosity 
except, a little bit below the sun's 
radius. It suddenly dips below the stars 
over here on the lower right of the main 
sequence are cooled and smaller than you 
would get by just extending the main 
sequence they go by the name red dwarfs, 
and we see that over here where the 
giants were are stars with radii of a 
hundred and even a thousand solar radii 
way over here in the upper right hand 
side of the plot. 
So. 
This is a useful demonstration. 
You can plot here some of our nearest 
stars to us. 
We note that most of the nearest stars 
are, in fact the sun-like or dimmer. 
On the other hand, if we plot the 
brightest stars, we see that most of the 
stars we actually see are going to be 
giants. 
This is clear. 
We can see giants farther out, where 
there is more of an opportunity for there 
to be more of them. 
And we'll come back. 
We'll be talking about HR diagrams a lot. 
For now, we have one more investigation 
to make. 
So what we saw is that if you know that a 
star, if a star happens to be on the main 
sequence all you need to do is measure 
its spectrum and you can tell its 
luminosity because being on the main 
sequence implies a relation between 
temperature and luminosity. 
But not all stars are on the main 
sequence. 
how do we tell? 
Is there a way just by looking at a star 
to tell if it's a hyper giant, a white 
dwarf, or a main sequence star? 
this was a very interesting 
A, a question and it was eventually 
understood in the 40s by Morgan, Keenan 
and Kellerman and the result of their 
investigations was the following 
Smaller stars at a given temperature tend 
to have denser higher pressure 
atmospheres. 
It's in the atmosphere that we're 
observing the line, absorption line 
spectrum. 
A denser, higher-pressure atmosphere 
exhibits broader spectral lines. 
As you condense matter more and more the 
spectral lines broaden. 
Of course if you condense it all the way 
to a solid you get a black body spectrum. 
That's sort of the extreme case. 
And so you find that you can divide stars 
into sort of classes by their luminosity 
at a given temperature. 
and these classes range from zero for 
hypergiants, way over here in at the top 
through type one for supergiants, 
type two for the bright giants, 
three are the giants, etcetera. 
Five importantly, type V is luminosity 
class V is the main sequence and down to 
luminosity class seven where the white 
dwarfs lie way below the main sequence. 
In this language, we can now say that our 
sun which had temperature that made it a 
G2 star 
somewhat in the middle of the type G 
temperature range since it is a main 
sequence star is a G25 star. 
So that's the spectral class, a 
combination of three 
designations one for spectral type one 
for the sub type within the type and one 
with luminosity class gives you a three 
parameter two dimensional position of a 
star. 
Roughly the first two letters tell you 
where it is horizontally along the the, 
HR diagram and the last one tells you 
where it is. 
In the vertical direction you can locate 
a star based on that. 
So now that we know how to distinguish 
just by looking at the spectrum 
the position of the star in a joint 
diagram, we now have a great idea. 
Something called spectroscopic parallax. 
I warn you it has nothing to do with 
parallax. 
What is spectroscopic parallax? 
It's a way of determining a star's 
distance. 
Just from looking at the spectrum. 
If a star is too far to make parallax 
measurements can you still give me an 
estimate of its distance? 
The answer is yes, the reason is if I 
look at the spectrum and I recognize the 
presence of a particular set of 
absorption lines that gives me a spectral 
type. 
That gives me an estimate of the surface 
temperature. 
Moreover, if I can look at the breadth of 
those lines, I can figure out which 
luminosity class the star belongs to. 
Is it a main sequence star? 
Or is it a hypergiant? 
And once I do that I can go back to my HR 
diagram and pick out the intersection of 
the corresponding curve with the 
corresponding vertical line for the 
temperature. 
And I can obtain a luminosity. 
So now I can read a star's luminosity 
with some accuracy right off of its 
spectrum. 
Now if I know the luminosity I can 
measure the brightness and of course use 
our expression for luminosity bright, 
brightness and distance to figure out the 
distance. 
So, I can measure a distance to a star 
with some accuracy, even if it was too 
far for parallex. 
Note that this is another one of those 
ladders on the cosmic distanct ladder. 
We know the calibration of the HR diagram 
because we've measured the actual 
luminosity of stars to which we knew the 
distance. 
Now we used that to extend the distances 
to things that are too far for parallex 
measurements that will be very useful for 
us, in the 
sequel when we need to know the distances 
to things that are too far for parallax. 
There are many other methods, all 
calibrated from parallax. 
But this is a good example of one and I 
think we need a little more of a, 
calculational example. 
Let's try to understand the star 
Alphecca. 
This is Alpha Coronae Borealis. 
And it's a whitish star. 
It's not the brightest star in the sky 
but it's a bright one. 
In fact, we can measure its la, photo 
measurement tells us that the brightness 
of, Alphecca is 2.6 times 10 to the -12 
times the solar luminosity. 
we look at its spectral lines, and we can 
measure its temperature. 
Its temperature is 9700 kelvin. 
It's star of type A. 
It's hotter than the sun, a zero, in 
fact. 
And Alphecca is a main sequence star as 
determined by the breadth of its spectral 
lines. 
So, we go over to our HR diagram we look 
at the main sequenc. 
We look at the luminosity of an A0 type 
this is the hottest of the type A stars 
and you can estimate a luminosity of 74 
solar luminosities. 
Alphecca is 74 times as luminous as the 
sun, and from this if I want, I can 
figure out a distance because I have the 
brightness and the luminosity. 
I can also figure out Alphecca's radius. 
Remember we had a relation between radii, 
luminosity and temperature. 
This is the scaling relation, and I 
predict a radius of about three solar 
luminosities for Alphecca. 
Remember we said that this main spectra, 
the main sequence goes from one solar 
radius at the sun all the way up to ten. 
Alphecca is a part of the way up there. 
Three solar radii is pretty reasonable 
and we can as I said predict a distance 
to Alphecca based on using the luminosity 
and the brightness, brightness is 
measured luminosity is predicted from HR. 
I plug in 74 solar luminosities here I 
plug in ten to the minus twelve or 
whatever for Alphecca's brightness. 
And I find five and a half million AU. 
I can convert that to parsec with our 
206, 265 astronomical unit per parsec 
conversion, and I predict Alphecca's 
distance to be 25.7 parsecs. 
Now with that range, we do have parallax 
measurements. 
And so I can look up the Alphecca's 
database, Alphecca's database read off 
the parallax angle of of Alphecca. 
And, of course I remember that the 
distance in units of parsec is just one 
arc second divided by the parallax angle 
plugging that in I know that we have 
measured the actual distance to Alphecca 
of 22.9 Parsecs. 
We have an error of an on the order of 
10%.. 
This is typical of spectroscopic parallax 
system its our under there is some 
breadth to the main sequence and we'll 
talk about where that breadth comes from, 
stars are not exactly on the line. 
So the luminosity is not absolutely 
precisely determined by spectro-class 
that being able to measure distances just 
from looking at the spectrum of the start 
within 10% is not that.