Star Formation

Intergalactic space is filled with clouds of gas (mostly H₂ + He) and dust known as molecular clouds. Within these clouds there are also dense lumps known as molecular cores:

Clouds	Cores
R ~ 100 light years	R ~ 100,000 AU
10⁶ M_sun	10-1000 M_sun
20K	100K
10⁸ atoms/m³	10¹³-10¹⁵ atoms/m³

These clouds are often supported against gravitational collapse by their thermal pressure, but if they become too massive, gravity wins and they can start to collapse. This critical mass is referred to as the Jeans mass:

Why does it depend on temperature?
Why does it depend on density?
Here is a derivation of the Jeans mass.

Plugging in typical numbers, we find that while Giant Molecular Clouds are generally stable against collapse, the dense molecular cloud cores are not. Here gas clouds collapse to form stars.

Once started, how does the collapse form a star and the disk of material surrounding it?

Gravity is a central force -- it draws material in radially. So why doesn't it all collapse into a ball?

Angular Momentum

All clouds rotate, at least a little, due to gravitational shearing in the galaxy's disk. And if a cloud rotates, it has angular momentum:

And remember that angular momentum is conserved. So if a rotating cloud collapses (r gets smaller) than it must spin faster (v gets bigger). Even a little pre-collapse spin goes a long way!

How does rotation affect collapse? It adds a centripetal force term to the collapse. For a particle of mass m on the edge of the cloud, the force on it depends whether it is on the rotation pole or the equator:

So as the cloud collapses, material along the spin axis can collapse onto the star, but material in the spin plane has collapse halted by centripetal force. A disk is formed!

What about the central mass -- the protostar itself?

Remember from our discussion of the Sun that as a ball of gas collapses, it radiates away half of the gravitational energy. What happens to the other half? It heats up the collapsing cloud.

So the very central portions of the cloud are getting denser and hotter. Eventually the density and temperature will become high enough that nuclear reactions will begin to take place. A star is born!

The high central density and temperature also create sufficient pressure (via the ideal gas law) inside the star to halt gravitational collapse. The young star is now in hydrostatic equilibrium.

Nice theory. Does it have anything to do with reality?

Yes! We see these stars and young disks in nearby star forming regions:

The Orion Nebula