Velocity Dispersion and Magnetic Energy Distribution in a Turbulent Interstellar Medium driven by Supernova

The rapid decay of turbulence shown in recent magnetohydrodynamic simulations tells us that turbulence in interstellar molecular clouds must be driven by external energy sources. Taking supernovae (SNe) as a source, we investigate the properties of driven interstellar turbulence through numerical simulations using a total variation diminishing MHD code. In a uniform medium threaded by magnetic field, we explode SNe one at a time at randomly chosen positions with two different SN explosion rates, which are higher than, and equal to the Galactic value. Simplified radiative cooling and heating processes are also included. We follow the simulations to the point where the total energy of our system has a converged value (The input energy rate of SN explosions is balanced by the output energy rate by cooling.). Even though our model is simple, the two essential ingredients, SN explosions and cooling, form a rich turbulent interstellar medium (ISM). The velocity dispersion of the warm phase is consistent with the observational value, 10 km/sec. Most magnetic energy resides in dense regions and the power index of the B-n relation is 0.4. M-MML was partially supported by an NSF CAREER grant AST99-85392.