The Supernova Rate - Velocity dispersion Relation in the Interstellar Medium

We investigate with three-dimensional numerical simulations of supernova driven turbulence in the interstellar medium (ISM) the relationship between the velocity dispersion of the gas and the supernova rate and feedback efficiency. Our simulations aim to explore the constancy of the velocity dispersion profiles in the outer parts of galactic disk at ∼ 6 − 8 km s, and the transition to the starburst regime i.e., high star formation rates associated with high velocity dispersions. With our fiducial value of the supernova feedback efficiency (i.e., ǫ = 0.25 corresponding to an injected energy per supernova of 0.25× 10 ergs), our results show that (a) supernova driving leads to constant velocity dispersions of σ ∼ 6 km s for the total gas and σH i ∼ 3 km s for the H i gas, independent of the supernova rate, for values of the rate between 0.01 and 0.5 the Galactic value (ηG), (b) the position of the transition to the starburst regime (i.e., location of sharp increase in the velocity dispersion) at around SFR/Area ≃ 5× 10 − 10 M⊙ yr −1 kpc observed in the simulations, is in good agreement with the transition to the starburst regime in the observations (e.g., NGC 628 and NGC 6949), (c) for the high SN rates, no H i gas is present in the simulations box, however, for the total gas velocity dispersion, there is good agreement between the models and the observations, (d) at the intermediate SN rates (η/ηG ∼ 0.5− 1), taking into account the thermal broadening of the H i line helps reach a good agreement in that regime between the models and the observations, (e) for η/ηG < 0.5, σ and σH i fall below the observed values by a factor of ∼ 2. However, a set of simulation with different values of ǫ indicates that for larger values of the supernova feedback efficiencies, velocity dispersions of the H i gas of the order Max-Planck-Institut für Astronomie, Königstuhl 17, D-69117 Heidelberg, Germany; [email protected], [email protected] University Observatory Munich, Scheinerstrasse 1, D-81679 Munich, Germany; [email protected] Centro de Astronomía y Astrof́isica, UNAM, Apdo. 72-3 (Xangari), 58089 Morelia, Michoacán, Mexico