On the relation between magnetic field strength and gas density in the interstellar medium: A multiscale analysis

The relation between magnetic field strength B and gas density n in the interstellar medium is of fundamental importance to many areas of astrophysics, from protostellar disks to galaxy evolution. We present and compare Bayesian analyses of the B - n relation for a comprehensive observational data set, as well as a large body of numerical MHD simulations. We extend the original Zeeman relation of Crutcher et al. (2010) with a large body of magnetic data that includes 700 observations with the Davis-Chandrasekhar-Fermi method. By using a new multiparameter Bayesian analysis we present a new, more general, time-averaged observational relation: B \propto n^{0.27 \pm 0.017} for n \leq n_0 and B \propto n^{0.54 \pm 0.18} for n \geq n_0, with n_0 = 924^(+145-144) cm^-3. We perform a separate analysis on 19 numerical magnetohydrodynamics simulations that cover a wide range of scales, resolutions, initial conditions, and completed with a variety of codes: arepo, flash, pencil, and ramses. The power law exponents derived from the simulations depend on several physical factors including: dynamo effects, time scales, turbulence, and the initial seed field strength. In particular, early-time simulations where the density, velocity and magnetic fields are unevolved do not match the observational scalings. The simulations that trace the observed density range best, the evolved dwarf galaxy and Milky Way like galaxy simulations, settle into a near consistent exponent of = 0.5 in the dense gas, with variability in the diffuse gas exponent.