So as promised, let's start our story by figuring out what the sun had to do to
become a main sequence star. we're going to follow the models.
The models are going to start with a spherical cloud with say, one solar mass
of gas and dust in it. and this is already fragmented possibly
from an even a bigger cloud. We'll talk about that when we talk about
the formation of clusters. We're now big building a star,
this cloud is collasping under the influence of gravity.
And what the model tell us is that within a few thousand years, the interior of
this cloud becomes dense enough that there is an optically thick opaque region
there. this is great.
this means that we can define the interior of this region as the protostar.
The protostar has a surface. It communicates with the rest of the
world through black body radiation. We can plot it on a HR diagram at this
point, we've produced if you want, an accent photo star.
This photospere will start out at about size of about five astronomical units and
a comfortable temperature of 300 Kelvin. And now but the models tells us is that
this thing is contracting and of course heating.
And you compute the luminosity remains the approximately constant over a
contraction from five astronomical units all the way down to about twice the
current solar radius. again, what's contracting is the surface
at which the, the protostar is opaque. Some material, of course, is penetrating
but it's still accreating. The protostar is still growing in mass
and the energy to heat for this heat is to some extent kelvin held hold seating
conversion of gravitational potential energy yo
heat. But also at these temperatures, we begin
to get fusion of deuterium. Whatever amounts of deuterium are
present, the deuterium fuses at a lower
temperature than hydrogen, that's why we use it in terrestrial fusion reactors.
And over the next 600,000 years or so we get this collapse down the twice as to
the radius and the temperature stabilizes at around 4,000 kelvin.
these early stages are built on models. We can try to verify them by looking for
these very young, very cool protostars. This used to be a very difficult
proposition because when a protostar starts forming, around it is the
leftovers of the big cloud, the parts that did not collapse yet. So there's
this gaseous dusty cocoon that hides the protostar to look through the dust, we
use radio and infrared radiation. And in recent years, we have had
detections of these early stages of protostars.
you can learn a lot from the intensity and various wave lengths, the shapes of
the absorption and emission lines. Too much detail for us, but here's a nice
direct imaging of these three nascent infrared sources
luminosities one and 1,000 and 1,000 solar luminosities and 100,000 solar
luminosities. These may be as young as 100,000 years
since they started collapsing so they are fueled by Kelvin-Helmholtz heating and by
the beginnings of deuterium burning, and these photospheres are the dusty hot
opaque regions that we were talking about.
this is a magnified image and it shows you that the IRS9A, the 100,000th solar
luminosity protostar is 5,000 astronomical units
across. It's a very large object,
still it's just beginning to collapse. another interesting object is this one,
L1527 in Taurus. And here we're seeing edge on the disk which the star is
forming. So, if we had a proto planetary disk it
would extend this way. And what were seeing is these bipolar
flows of gas leaving, this is an infrared image from the Spitzer telescope.
And here, we have a mangified Spitzer image which shows you that actually we're
not seeing the protostar in the infrared. And the infrared we're seeing reflected
light off the disk, and the center where the star would be, the disk is so
optically thick that it actually obscures the star.
the contours that are actually showing us the position of the protostar inside this
few hundred astronomical unit disk are, radio emissions.
So, superposing radio along with infrared, we can see both these bipolar
flows that we'll talk about later and the protostar itself.
So, we have now actually seen protostars, we know that they exist.
And at, at, when the protostar has reached the point at which, it's size is
about twice the solar radius. It's temperature is about 4,000 degrees
and deuterium is burning. We now call this a pre-main sequence
star. There is fusion that is fueling the star.
And so we begin to plot the trajectory of the sun as a pre-main sequence star on
the HR diagram. the protostar phase was this horizontal
trajectory that the sun followed. And what we see initially is that having
become a star, it's burning deuterium.
So it's sustained at least partly by fusion.
It's still contracting, and the contraction is along almost a vertical
line. This vertical line is called a Hayashi
Track. The temperature is determined by the fact
that the photosphere is no longer made of dust.
Dust has long since evaporated where it's 4,000 degrees.
What makes the photosphere optically opaque is the presence of negative
hydrogen ions. Negative hydrogen ions, that's a proton
with two electrons. The extra electron would have come from
ionizing metals, calcium, silicone, carbon.
They have outside electrons that are more weakly bound than the one electron of
hydrogen. They become ionized at lower temperatures
as positive ions. Some of these electrons will be captured
to produce negative hydrogen ions. Negative hydrogen ions are excellent
absorbers of radiation at all wavelengths because the second electron is rather
weakly bound and infrared visible and, certainly ultra-violet radiation will
ionize. So,
or deionize. And so, hydrogen, negatively charged
hydrogen ions are great light valve. A layer of those absorbs all colors of
light. This is now our photosphere and then
remix it as, as black body radiation. And so, this photosphere contracts and
it's temperatures controlled by it's ionization state of
of hydrogen. And so, it contracts essentially a longer
line of constant temperature. And this continues you notice at constant
temperature, that star is contracting therefore its luminosity is decreasing,
until the ionization in the center becomes as the center heats, the
ionization in the core increases. This makes the core less opaque.
This allows a radiative zone to be produced.
This makes the efficiency of transporting heat out of the core into the envelope
higher. And that increases the luminosity and
that is this knee in the track that we see around here,
this is this increased ionization. And this continues to proceed until
temperatures in the core reach sufficient temperatures and densities are such that
hydrogen fusion starts. What happens when hydrogen fusion starts?
Well, what happens is that the core ceases to expand, to contract.
in fact, under the increased radiation pressure, it expands slightly.
The expansion of the core absorbs the, some of the energy that's produced by
fusion and so the initial response, this is one of those, expansion by contraction
in reverse. When when the
fusion is initiated in the core, the reaction of the envelope is that the
luminosity decreases. And that's this final segment of the
track, so this turn here is the initiation of efficient hydrogen fusion
in the core. And the star now settles down by a loss
of luminosity down to the main sequence. It would have taken the sun models tell
us about 40 million years remember this was a few hundred thousand. Then, this
track takes about 40 million years and the sun settles down into main sequence
equilibrium. That time scale is familiar,
ten million years was the Kelvin-Helmholtz Timescale.
That is how long the sun would have produced its current luminosity
from gravitational potential energy. And ten million years is the time scale
on which gravitational energy is converted to heat,
and we'll come back to that time scale. Embolden by our understanding of the sun,
we can repeat the models with stars of different masses and we find these
tracks. They all, if you notice, start though
it's not obvious in all of them, with approximately the same Hayashi track
where negative ionized hydrogen controls the temperature.
And then move over to the left heating up and contracting for more massive stars at
almost fixed luminosity, all kinds of details they settle down to the main
sequence as we saw with main sequence lifetime.
the models tell us here that bigger stars go faster so the sun took 40 million
years to achieve its current main sequence, or to arrive on
the main sequence. A star with a mass of about five solar
masses would take a million. Star with a mass of fifteen solar masses
would take 100,000 years, and stars with 30 solar masses would get to the main
sequence in tens of thousands of years. So that when a cloud forms the first
stars to reach main sequence are going to be the hot O and B stars, and the slow,
the lightest stars will be the smallest, slowest ones to go.
So, we have seen how a cloud collapses down to a star.
we spoke of the lightest and the heaviest.
What makes these the lightest and those the heaviest?
What happens if you start with a cloud that is too small?
What happen what happens if you start with a cloud that is too big?
Why does the main sequence end? The mechanisms of star formation should
tell us, and they do. first,
below about 1.3% of a solar mass deuterium fusion never initiates.
If an object never initiates deuterium fusion, its collapse mechanisms are
different, we do not call that a star. It's also true that the fragmentation
processes that break the clouds up seem to stop at about 1% of the solar mass.
So, we do not expect stars to attempt to form, much below 1%..
But below 7.2% of the solar mass, efficient hydrogen fusion never takes
off. And so, these stars do not achieve
hydrostatic equilibrium under hydrogen burning conditions.
So, they do not become main sequence stars, they take their time contracting
and burning deuterium. They run out of deuterium earlier, these
are brown dwarfs type L, T and Y. These are the extra spectral types below
K that were added. they were added by models.
the first actual discovery of a brown dwarf is relatively recent, since 1994,
95, when this object Gliese 229-B was actually discovered both by, by Palomar
and by the Hubble Space Telescope. And after that, infrared surveys started
showing that there were brown dwarfs in the solar neighborhood.
People started extrapolating those surveys to imagine how many brown dwarfs
there were in the milky way and the going rate about a decade ago was that there
was one brown dwarf for each main sequence star.
So, at that point, the number, estimate of the number of stars in the milky way
essentially doubled because there was going to be as many brown dwarfs
previously undiscovered as there were main sequence stars.
more recent data has cast doubt on this. We found sort of a collection of brown
dwarfs. We've gotten rather good with these
infrared servers at discovering them. And a recent survey by the wise detector
of the solar neighborhood. A tally of these, the calculation of the
efficiency at detecting them suggests that it's more like one brown dwarf for
each five main sequence stars. The number of stars in the Milky Way has
again decreased. Science is an succession of
approximations to truth. this is what cuts off the main sequence
at the bottom end objects lighter than 7% of the solar mass will never actually
manage to heat and be hot and dense up in the core to initiate efficient hydrogen
fusion. What cuts you off at the top end? Well,
if you start with the cloud that is too big, it will not actually manage to make
a star as it collapses, radiation pressure will break it up.
We might talk about the Eddington limit that its involved here later. But again a
few years ago I would have said masses bigger than 100 or 150 solar masses
cannot possibly form a star. that is what models suggested, and indeed
stars with masses as high as 100 solar masses are exceeding rare.
But, it turns out that again observations come to the rescue in the Tarantula
Nebula, a Large Magellanic Cloud. 2010 discovery shows, well here's a
visible image of the Tarantula Nebula and an magnified visible image of the
Tarantula Nebula and over here on the right.
And infrared image which gets rid of all the scattered, light from dust and sees
through the dust. And among these stars that we're
discovering, these main sequence stars is this monster
object R136A, and R136A has a mass estimated about 250 solar mass's.
And, for a size comparison, we see here the sun O-type star perhaps, and then
this new monster. So the current limits are that stars can
form with masses up to about 250 solar masses.
This is still very, very, rare above that radiation pressure will
fragment the cloud. So, we understand what the solar, what
the main sequence is and where these stars come from.
We'll pick it up at the end of the main sequence lifetime in the next.