STAR FORMATION

Most stars form in GIANT MOLECULAR CLOUDS

GMCs have masses from 10^5 to above 10^6 solar masses

typical densities above 1000 cm^{-3}

initial temperatures < 10 K, since their cores are well
shielded from external starlight and other heat sources

typical size of a GMC: > 5 pc

if triggered to collapse, these clouds yield entire STAR CLUSTERS

In both GMCs and regular Molecular clouds the most abundant molecules are:
H_2, He, CO, C0_2, OH, H_2O, but many others are detected.

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THE ENTIRE LIFE OF A STAR CAN BE CONSIDERED
TO BE A BATTLE BETWEEN PRESSURE, PUSHING IT OUTWARDS,
AND GRAVITY, PULLING IT INWARDS.

There are several types of pressure:

Thermal or Gas pressure (most common)

Radiation pressure

Degeneracy pressure (we'll talk about it later -- White Dwarfs)

Magnetic pressure

Turbulent pressure

Gas pressure is proportional to the product of density and temperature:

P ~ n T

compressing a cloud always increases n

compressing a cloud sometimes increases T

so P always goes up with compression.

BUT self-gravity also goes up with compression

and gravity is independent of T.

The force of gravity is given by

F_g = G m_1 m_2 / d^2

and for a gas cloud this is very roughly

F_g ~ n^2 .

So F_g rises faster with density than does P

If a cloud is squeezed it can either

collapse, with F_g >> P , OR

contract, with F_g just barely winning over P.

GMCs (Giant Molecular Clouds) are also supported by rotation, magnetic fields
and turbulence, so a small squeeze usually isn't enough to trigger star formation.

Once collapse is started, the cloud typically FRAGMENTS many times;
the original GMC yields hundreds, thousands or even millions of stars in CLUSTERS.

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TRIGGERS OF STAR FORMATION

compression of a GMC by a supernova remnant:
the shock wraps around the cloud and compresses it.

compression of a GMC by the ionization front at the edge
of a H II region.

BOTH of the above rely on the nearby existence of massive, hot (O and B) stars.

ALSO, density waves can cause compression:

these are usually due to non-symmetric gravitational distributions near the centers of galaxies
and produce SPIRAL ARMS; sometimes triggered by passage of a smaller galaxy.

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THE ROAD TO A STAR FROM A CLOUD

When a GMC is triggered to collapse, it will fragment and re-fragment.

The original 10^5 -- 3x10^6 M_sun cloud will typically form 1000's of stars,
but only somewhere between 5 and 25 % of the mass of the cloud eventually winds up in stars;
the rest is re-dispersed into the ISM.

The first stage is ISOTHERMAL COLLAPSE.

the fragment is at first of sufficiently low density that the heat generated
by compression of the cloud can escape as microwave radiation,

thus keeping the Temperature around only 10 K -- thus ISO(equal)THERMAL(temperature).

Since gravity wins over pressure by a large margin if only n and not T
too goes up, this is a COLLAPSE.

(We can make an economic analogy to Reagonomics: the denser regions at the center
collapse faster (the rich get richer quickly), the medium density regions collapse slower and might become
part of the star (the middle classes get a little richer, if they are lucky);
the lower density outskirts get blown away and dispersed (the lower middle class and the poor get poorer).
Basically what happens to newly forming stars is what happened to the American
economy in the 1980s and again in the 2000s.)

Once the density at the center of the cloudlet gets high enough, it becomes
OPAQUE and the photons are scattered or absorbed and reradiated many times before
their descendents escape.

Then the temperature as well as the density rises.

So, P ~ n T, rises faster and can nearly stave off gravity.

We call this a KELVIN-HELMHOLTZ CONTRACTION: a slower reduction in size,
accompanied by heat generation.

Actually, just about 1/2 of the generated heat is radiated in the microwave and
IR bands, while 1/2 is trapped and raises the temperature of the gas.

So the inner core contracts slowly, but the outer layers are in free-fall
onto that core.

This produces a STANDING SHOCK which generates much additional heat and light.

Note that this simple description of a spherical clouds collapse is a good
place to start in understanding star formation, and is all you need to worry
about for the exam, but it ignores some key features:

dissociation of H_2 molecules into H atoms yields an inner isothermal core within the
contracting outer core until that core too becomes opaque;

rotation and magnetic fields will prevent the collapse from being spherical --
they spread the outer parts into a disk, part of which accretes onto the
forming star, part of which is launched into winds and jets (bipolar nebulae, Herbig-Haro objects),
part of which can form smaller companion star(s) or planets.

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FINAL STAGES OF STAR FORMATION

The core of the contracting cloudlet heats up and gets denser -- but still not
hot enough to begin nuclear fusion.

Typically this protostellar period lasts for a few percent of the star's total life on the
Main Sequence (i.e. a few hundred million years for the Sun, whose total lifespan
would be around 10 billion yr.)

Much luminosity is generated in the collapse of the outer layers onto the opaque core:

this accretion generated heat makes the protostar some 10's or 100's of times
as luminous as it will be when it gets to the Main Sequence;

the protostars are 10's to 100's of times as large as they will be when on the MS;

the surface temperature of these protostars will be ~5000 K
(higher for higher masses, lower for lower masses, than the Sun).

On the H-R diagram the protostars move from the (way off usual plots) very lower right
-- T = 10K, L <<< L_sun to moderate T's and high L's -- above the MS.

BUT the observed T is often much less than protostellar surface T, since the visible
radiation is absorbed and reemitted by dust in the surrounding cloud --
the protostar looks much cooler for a long time.

Eventually, all the nearby gas has fallen onto the core and the
protostar's accretion generated luminosity falls.

The star then enters the HAYASHI TRACK, a nearly vertical decline in the
H-R diagram and gets very close to the MS -- such protostars are fully convective.

Often the outer layers of gas are dispersed by winds or bi-polar
outflows while the inner layers are accreted.

When the core temperature reaches about 1 x 10^6 K, it is hot enough
for deuterium, tritium and lithium to fuse.

But these are rare isotopes and are used up quickly.

However they can cause the L to rise while T_s also goes up and the
protostar gets a little brighter for a while.

T Tauri stars are found in this final stage of protostellar evolution,
just above the MS.

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A STAR IS BORN

When the center of the contracting protostar reaches T > 6 x 10^6 K
then ordinary H fusion can begin.

This is official definition of stellar birth -- the star is on the
Zero Age MS (ZAMS) now.

The star's location on the ZAMS is determined almost completely by its MASS
(there are lesser effects from composition and rotation that you should know exist,
but needn't worry about).

During the majority of its life on the MS, the star does not
move very much at all on the H-R diagram --

the particular place on the ZAMS is very close to the H-R diagram location where an
old MS star is found.

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LIMITS TO STELLAR MASSES

If the protostar's mass is less than about 8% of the Sun's mass it is
insufficient to compress the center to temperatures and densities adequate to allow ordinary fusion --
THE LOWER MASS LIMIT

Such failed stars are called brown dwarfs.

Most astronomers make a further distinction between brown dwarfs and even lower mass objects,
with less than about 1.3% of M_sun (or about 13 times Jupiter's mass):

these can't even trigger deuterium/tritium fission and are classified as giant planets.

over the past decade several brown dwarfs and over 100 giant planets have
been found, most through very careful spectroscopic studies of single-line spectroscopic binaries
with tiny (meters/sec) velocities.

At the other end of the spectrum, very few cloudlets with masses above about
60 M_sun are likely to survive intact.

Of those that do collapse at the very high mass end they are unlikely to ever be in
the state of hydrostatic equilibrium that characterizes true stars.

Such massive stars are likely to collapse/contract and then explode, so we've never
seen a convincing case of a star of more than 60 M_sun and the UPPER MASS LIMIT
is almost certainly less than 100 M_sun.

The most massive star with a carefully measured mass is R136-8 in the Large Magellenic Cloud,
with 56.9 +-0.6 M_sun.