Collisional buildup of molecular clouds: Mass and velocity spectra

We have studied the evolution of a local region of molecular clouds, moving in the mean gravitational potential of the Galactic disk. The clouds interact gravitationally with one another and undergo inelastic collisions. The clouds have been modeled as spheres, and a collision is assumed to take place when two clouds overlap. The outcome of a collision depends on the relative mass and velocity of the clouds and can result in the fragmentation or coalescence of the clouds. We find that the initial random mass distribution of the clouds evolves into a power-law distribution of the form N(m) proportional to m(alpha), where alpha = -1.7 to -1.9, and is flatter toward the low-mass end. The mean one-dimensional random velocity of the molecular clouds is similar to 8-10 km s(-1) and is found to be independent of cloud mass. These results agree well with the observed mass and velocity distribution of molecular clouds. We also conclude that cloud collisions in a sheared galactic disk, rather than local gravitional interactions, are important in determining the mass and random velocity distribution of molecular clouds. Cloud collisions thus play a dominant role in the formation of molecular clouds.