So, using closely looking at the stars and making some measurements and thinking
about it, we can actually measure the mass of stars.
And we can ask, we're almost ready to start modelling.
We need to know where do the masses of stars along the main sequence line up
with their masses. And so, we can add masses into our plot
for the main sequence. And here's what we learn, masses don't
vary very much. way down here, down where the red dwarves
reside, masses of stars, we discover, are as small as a tenth of a solar mass, but
not much smaller than that. And the biggest, most luminous, hottest,
main sequence stars top out at 50 solar masses.
We rarely find anything even up there. And so, by measuring a few stars along
the main sequence, we can figure out the mass of a point along the main sequence.
The main story is that the heaviest amounts stars are the hottest
and the most luminous. And now, we can fit it into the model.
Because when you're going model of star, basically, if you say a star is a ball of
hydrogen, I don't need to tell a good model or the luminosity of the radius. I
would tell them take a bottle of hydrogen,
held up on in hydrostatic equilibrium against its gravitational attraction by
hydrogen fusion, and then run your equation. Now, in practice, that's a
little bit difficult. But in principle, nature knows how to do
that. So, if you give nature a ball of hydrogen
of a given mass, it'll produce a star, and that star will lie somewhere along
the main sequence. And we can now attempt to study modeling.
We'll discuss the results of that in our next clip.
But first, let's note that there's a very reasonable approximation you can do
better but the luminosity along the main sequence scales with mass.
As I said, the heavier stars are more luminous and it scales like the three,
third, three and a half, or fourth power of mass.
It's not exactly fixed relation you can improve this, and go into the details,
but this is good enough. What this means is that a ma, a star that
is twice as massive as the sun has a luminosity between eight and sixteen
times the luminosity of the sun. It's way more luminous, this is how change from a
tenth of a solar mass, to ten solar masses, gives us this five orders of
magnitude or seven orders magnitude change in luminosity.
Now, this sort of makes and are models bear this out. A heavier star has more
pressure from the outer layers crushing down on its core, the pressure in the
center is higher, densities in the center are higher.
We said that fusion proceeds best at high temperatures and densities, and that
means the rate of fusion in a big star will be higher.
That's the way that mass is going to determine the rate of fusion.
And so, it makes sense that bigger stars will be more luminous.
But note, that if say, the core of a star like the
sun, we estimated how long the sun would last by saying, if it converted all of
it's hydrogen to helium, it would last 100 billion years.
But, the sun will actually stop converting hydrogen to helium when it has
converted a tenth of it's hydrogen because that's the amount that will be
available in the core. If all stars had a bout a tenth of their
hydrogen available in the core, what this would tell us is that big stars run out
of hydrogen much faster than slow stars, and indeed, appended to this table of the
main sequence is a list of main sequence lifetimes adjusted. Remember, right over
here, the sun has a main sequence lifetime of about ten billion years and
stars with te, luminosity ten times that of the sun, it turns out only last a
billion years. And up here, the really bright type O and B stars might last only
ten or a few million years, and the lightest red dwarfs last hundreds of
billions of years. What that tells us is that if we see a
type O main sequence star, since they only live, two, three, five, ten million
years, that star is brand new.
When the sun was formed five billion years ago, that star was nowhere near to
existing. So, when we see, say in Orions belt type
O stars, we know that very recently stars have been forming there.
And we'll see what modeling tells us and conclude the week and the last clip of
the week now.