A comparison of cloud formation rates in the gravitational instability and random collisional buildup models

Abstract

The cloud collision time scale and the overall cloud formation time scale in the random collisional buildup model of molecular cloud formation are compared to the cloud formation time scale in the gravitational instability model. Observed values of the molecular cloud space density, gravitationally enhanced collision cross section, and velocity dispersion are used. Because the column density of a virialized cloud is proportional to the square root of the ambient pressure, the collision rate for molecular clouds depends only on the square root of the average interstellar density and is independent of velocity dispersion. This density dependence is the same for gravitational instabilities, so the ratio of cloud formation rates in the two models is independent of density and velocity dispersion. Two Monte Carlo simulations for random collisions are discussed. One determines the total time for a lowest mass cloud to grow into a largest mass cloud in a field of other clouds with a M-15 spectrum; the other calculates the time for a cloud ensemble to increase the mass of its largest clouds. The results suggest that gravitational instabilities generally form large clouds faster than random collisions by a factor of ∼ 3.