Star Forming Rate

Star formation rate

If gas cooling time is shorter than the infall time, all infalling gas can cool. If infall rate is greater, however, only cooled gas is accreted. The rate at which gas is available for star formation is determined by the smaller value of the infall rate and the cooling rate. These can be formally calculated by taking the time derivatives of the virial radius and the cooling radius. For isothermal halos:

dM_cool/dt=9f_g_bH₀(1+z)^3/2V_c²r_cool(V_c,z)/4G

dM_infall/dt=3f_g_bV_c³/20G,

where f_g is the fraction of the initial baryon density that remains in gaseous form, which weakly depends on time, but otherwise makes dM_infall/dt constant. The rate the gas is available for star formation is therefore min(dM_cool/dt, dM_infall/dt).

As soon as a pool of cooled gas is available, the star forming time is modeled to be a factor of the dynamic crossing time t_dyn of a galaxy. So the star forming rate is:

=M_cold/t_dyn.

is usually taken as a free parameter.

In a disk of cold gas, some critical surface density can be defined below which the star formation is halted, such as the empirical Kennicutt (1989) value.

Newly formed stars are put on the ZAMS according to a chosen IMF.

References page
Introduction page

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Fan Fang Last update: 26-July-99