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.