Star formation rates in disk galaxies and circumnuclear starbursts from cloud collisions

We invoke star formation triggered by cloud-cloud collisions to explain global star formation rates of disk galaxies and circumnuclear starbursts. Previous theories based on the growth rate of gravitational perturbations ignore the dynamically important presence of magnetic fields. Theories based on triggering by spiral density waves fail to explain star formation in systems without such waves. Furthermore, observations suggest gas and stellar disk instabilities are decoupled. Following Gammie, Ostriker, & Jog, the cloud collision rate is set by the shear velocity of encounters with initial impact parameters of a few tidal radii, due to differential rotation in the disk. This, together with the effective confinement of cloud orbits to a two-dimensional plane, enhances the collision rate above that for particles in a three-dimensional box. We predict Sigma(SF)(R) proportional to Sigma(gas) Omega(1 - 0.7 beta). For constant circular velocity (beta = 0), this is in agreement with recent observations by Kennicutt. Our estimates for the normalization of this star formation law, while uncertain, are consistent with the observed star formation in the Milky Way and starburst galaxies. We predict a B-band Tully-Fisher relation: L-B proportional to nu(circ)(7/3), also consistent with observations. As additional tests, we predict enhanced/reduced star formation in regions with relatively high/low shear rates, and lower star formation efficiencies in clouds of higher mass.