= Solution
Galactic <star formation> is limited by how much gas becomes cold, shielded and self-gravitating, and by how long it remains in that state. A useful local estimate is
$$
\dot\rho_*\simeq\epsilon_{\rm ff}\frac{\rho_{\rm sf}}{t_{\rm ff}},\qquad
t_{\rm ff}=\sqrt{\frac{3\pi}{32G\rho_{\rm sf}}}.
$$
The <star-formation efficiency per free-fall time> $\epsilon_{\rm ff}$ absorbs the fact that <turbulence>, magnetic support and <stellar feedback> prevent all eligible gas from collapsing in one <free-fall time of a uniform sphere>. Rotation and disk stability influence the supply of dense clouds, while <gravitational collapse> and <gravitational fragmentation> operate inside them.
For galaxy-averaged measurements, the <Kennicutt–Schmidt law> has $\Sigma_{\rm SFR}\propto\Sigma_g^N$, with the classic mixed spiral/starburst sample giving $N\simeq1.4$. This empirical relation was obtained using <H-alpha> and far-infrared star-formation tracers together with atomic-hydrogen and CO gas measurements.<The Global Schmidt Law in Star Forming Galaxies by Robert C. Kennicutt Jr.>[Abstract: sample, tracer combination and fitted index 1.4 plus or minus 0.15]{ref} Dust attenuation, contamination by older stellar heating, the stellar <initial mass function> and the CO-to-molecular-gas conversion must be controlled. A disk-averaged total-gas exponent is not automatically a small-scale cloud law.
Young stars then photoionize gas, drive winds and eventually inject <supernova> <energy> and <momentum>. These processes can disrupt clouds, sustain random motions or expel gas; <radiative cooling> and fresh inflow rebuild the cold supply. \b[Large-scale <star formation> is a regulated conversion of gas, rather than unimpeded free fall of the entire disk.] A long <gas-depletion time> $\Sigma_g/\Sigma_{\rm SFR}$ is compatible with short <galactic dynamical times> in the dense fraction.
Back to article page
