The supernova rate-velocity dispersion relation in the interstellar medium

We investigate the relationship between the velocity dispersion of the gas and the supernova (SN) rate and feedback efficiency with three-dimensional numerical simulations of SN-driven turbulence in the interstellar medium (ISM). Our simulations aim to explore the constancy of the velocity dispersion profiles in the outer parts of galactic disks at similar to 6-8 km s(-1) and the transition to the starburst regime, i.e., high star formation rates (SFRs) associated with high velocity dispersions. With our fiducial value of the SN feedback efficiency (i.e., is an element of = 0: 25, corresponding to an injected energy per SN of 0: 25; 1051 ergs), our results show that (1) SN driving leads to constant velocity dispersions of sigma similar to 6 km s(-1) for the total gas and sigma H I similar to 3 km s(-1) for the H I gas, independent of the SN rate, for values of the rate between 0.01 and 0.5 the Galactic value (eta G); (2) the position of the transition to the starburst regime (i.e., location of sharp increase in the velocity dispersion) at around SFR/area similar or equal to 5 x 10(-3) to 10(-2)M(circle dot) yr(-1) kpc(-2) 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); (3) 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; (4) at the intermediate SN rates (eta/eta(G) similar to 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; and (5) for eta/eta(G) < 0: 5, sigma and sigma H I fall below the observed values by a factor of similar to 2. However, a set of simulations with different values of is an element of indicates that, for the larger values of SN feedback efficiencies, velocity dispersions of the H I gas of the order of 5-6 km s(-1) can be obtained, in closer agreement with the observations. The fact that for eta/eta(G) < 0: 5, the H I gas velocity dispersions are a factor of similar to 2 smaller than the observed values could result from the fact that we might have underestimated the SN feedback efficiency. On the other hand, it might also be an indication that other physical processes couple to the stellar feedback in order to produce the observed level of turbulence in galactic disks.