Parameters of the Supernova-Driven Interstellar Turbulence

Luke Chamandy,Anvar Shukurov

doi:10.3390/galaxies8030056

Abstract

Galactic dynamo models take as input certain parameters of the interstellar turbulence, most essentially the correlation time τ, root-mean-square turbulent speed u, and correlation scale l. However, these quantities are difficult, or, in the case of τ, impossible, to directly observe, and theorists have mostly relied on order of magnitude estimates. Here we present an analytic model to derive these quantities in terms of a small set of more accessible parameters. In our model, turbulence is assumed to be driven concurrently by isolated supernovae (SNe) and superbubbles (SBs), but clustering of SNe to form SBs can be turned off if desired, which reduces the number of model parameters by about half. In general, we find that isolated SNe and SBs can inject comparable amounts of turbulent energy into the interstellar medium, but SBs do so less efficiently. This results in rather low overall conversion rates of SN energy into turbulent energy of ∼1–3%. The results obtained for l, u and τ for model parameter values representative of the Solar neighbourhood are consistent with those determined from direct numerical simulations. Our analytic model can be combined with existing dynamo models to predict more directly the magnetic field properties for nearby galaxies or for statistical populations of galaxies in cosmological models.

Highlights

Turbulence affects a wide range of physical processes in the interstellar medium (ISM) of spiral galaxies, including the turbulent dynamo
Our approach is similar to that of Schober et al [28], but we calculate the fraction of SN energy converted into turbulence, rather than treating it as a parameter, and we model the turbulent correlation scale using the similarity solutions of supernova remnant (SNR) and SBs
As with turbulence driven by isolated SNe, we identify the injection scale of turbulence with the final radius reached by an SB near the midplane, h i lSB = min RSB

Summary

Introduction

Turbulence affects a wide range of physical processes in the interstellar medium (ISM) of spiral galaxies, including the turbulent dynamo. Turbulent flows are characterized by certain physical parameters, which are defined through some sort of averaging. These include the velocity correlation scale (or integral scale) l, which is similar to, but smaller than, the scale of the force driving the turbulence, the root-mean-square (RMS) turbulent speed u, and the turbulent correlation time τ. Our aim is to obtain scaling relations for the turbulence parameters l, u and τ in terms of other quantities like gas density, sound speed, and supernova rate density. The latter parameters are often readily computed from observations or models, so such relations can provide a missing link

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Conclusion