The Supernova Rate–Velocity Dispersion Relation in the Interstellar Medium

Abstract

We investigate the relationship between the velocity dispersion of the gas and the supernova (SN) rate and feedbackefficiencywiththree-dimensionalnumericalsimulationsof SN-driventurbulenceintheinterstellarmedium (ISM). Our simulations aim to explore the constancy of the velocity dispersion profiles in the outer parts of galactic disks at � 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., � ¼ 0:25, corresponding to an injectedenergyperSNof 0:25 ;10 51 ergs),ourresultsshowthat(1)SNdrivingleadstoconstantvelocitydispersions of � � 6k m s � 1 for the total gas andH i � 3k m s � 1 for the H igas, independent of the SN rate, for values of the rate between 0.01 and 0.5 the Galactic value (� G); (2) the position of the transition to the starburst regime (i.e., location of sharp increase in thevelocitydispersion)at around SFR/area ' 5 ;10 � 3 to 10 � 2 Myr � 1 kpc� 2observedinthe sim- ulations 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 (� /� G � 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 andthe observations; and (5) for � /� G < 0:5, � andH i fall below the observed values by a factor of � 2. However, a set of simulations with different values ofindicates that, for larger values of the SN feed- back 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 � /� G < 0:5, the H igas velocity dispersions are a factor of � 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. Subject headings: galaxies: ISM — galaxies: kinematics and dynamics — instabilities — ISM: kinematics and dynamics — supernova remnants — turbulence