What regulates the velocity distribution of interstellar clouds?

Kinetic energy stored in ISM bulk/turbulent motions is a crucial ingredient to properly describe most properties of observed galaxies. By using Monte Carlo simulations, we investigate how this energy is injected by supernovae and dissipated via cloud collisions and derive the corresponding ISM velocity probability distribution function (PDF). The functional form of the PDF for the modulus of the velocity dispersion is $$p(v) \propto v^2 \exp[-(v/\sigma)^\beta].$$ The power-law index of the PDF depends only on the value of the average cloud collision elasticity < \epsilon > as \beta = 2\exp(<\epsilon > -1). If \beta and the gas velocity dispersion \sigma are known, the specific kinetic energy dissipated by collisions is found to be \propto \sigma^2 \ln (2 / \beta)/(\beta-0.947); in steady state, this is equal to the energy input from SNe. We predict that in a multiphase, low metallicity (Z \approx 5 \times 10^{-3} Z_\odot) ISM the PDF should be close to a Maxwellian (\beta = 2) with velocity dispersion \sigma \simgt 11$ km s\m; in more metal rich systems (Z \simgt 5 \times 10^{-2} Z_\odot), instead, we expect to observe almost exponential PDFs. This is in good agreement with a number of observations that we review and might explain the different star formation modes seen in dwarfs and spiral galaxies.