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Parameters of the Supernova-Driven Interstellar Turbulence

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 $\sim1$-$3\%$. 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.