Friday, January 25, 2008

Star formation 101. Part 1

The time has come to pay one of the old debts of this blog: A mini-course on star formation. The night sky is full of little twinkling stars, but despite their obvious abundance its formation is still far from being a closed case.

Gravitational collapse (a cloud of interstellar gas collapses and produces stars) is the obvious way to produce stars , but it leaves us with a startling question, we can estimate the time of this collapse using the expression:

$t_{ff} \sim \frac{1}{\sqrt{G \rho}}$

which is called the free fall time and as you can see it only depends on the density of the cloud and not of its size, for a typical cold cloud this time is around one million years, this is obviously problematic because we know galaxies are much older than that and we can observe star formation in practically every spiral or irregular galaxy.

This indicates us that other forces are acting on molecular clouds, slowing the process of gravitational collapse. There are four hurdles that star formation has to overcome, as we will see in this star formation series it is surprising that even a single star can overcome this hurdles! This hurdles are:

• The pressure hurdle: A homogeneous, spherical gas cloud is stabilized against collapse by its own pressure gradient. This means that the temperature of the cloud despite being small still implies enough energy for the particles in the cloud to overcome their own gravitational attraction. We can estimate the size at which the cloud is doomed to collapse, this is called the Jeans radius and is given by

$r_J=\sqrt{3kT/4 \pi G m^2 n}$

where k is Boltzmann's constant, T the temperature of the cloud, m the mass of the particles and n the numerical density of particles. The Jeans mass is simply $m_J=(4\pi/3)\rho r_J^3$ , when we plug numbers into it we realize that stars similar to our Sun require cooler and/or denser regions than the average of the interstellar medium. This regions are the molecular clouds.
• The dynamical hurdle: As the cloud collapses it is heated, the energy required to heat the cloud comes from its own gravitational potential and it eventually reaches an equilibrium state when

$2K+V=0$

where K is the kinetic energy and V the potential energy, when this condition is satisfied we say that the cloud is virialized. So we can see that star formation requires cooling, otherwise the cloud will get virialized and reach a stable configuration halting the collapse. Thermal conduction and convection are remarkably ineffective in this regions and most of the cooling is radiative.
• The angular momentum hurdle: As gravitational collapse shrinks the cloud, angular momentum conservation amplifies any initial angular momentum (which is usually of the same magnitude of galactic rotation) by an enormous amount, the spin frequency is amplified by around 10¹⁶, this is such an spectacular increase in the spin that the cloud should be teared apart by the centrifugal effects. Dissipation is required to get rid of this excess of angular momentum, it is thought that this excess leads to proto-stellar disks.
• The magnetic flux hurdle: Lorentz force implies that charged particles are free to move in the direction of the magnetic field but have a hard time moving perpendicularly to it, so the magnetic field behaves as a spring refusing to compression. Collisions between the charged particles and the neutral ones eventually transfer this "springy behavior" to the rest of the cloud. A process known as ambipolar diffusion eventually allows the neutral component to fall through the ionized component.
The current state of star formation is centered around two paradigms: The "standard model" based on the collapse of isothermal clouds under ambipolar diffusion and the "turbulent model" based on the redistribution of energy at diverse scales of the cloud, making some "lumps" where star formation takes place.

In future post I expect to explain you how each of this hurdles can be overcome and give an overview of this two paradigms.

1 comment:

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