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

The relationship between magnetic field strength B and gas density n in the interstellar medium is of fundamental importance. We present and compare Bayesian analyses of the B-n relation for two comprehensive observational data sets: A Zeeman data set and 700 observations using the Davis-Chandrasekhar-Fermi (DCF) method. Using a hierarchical Bayesian analysis we present a general, multiscale broken power-law relation,, with for, and with the field strength at and for For the Zeeman data, we find: for diffuse gas and for dense gas with cm. For the DCF data, we find: And, with cm, where the uncertainties give 68 per cent credible intervals. We perform a similar analysis on nineteen numerical magnetohydrodynamic simulations covering a wide range of physical conditions from protostellar discs to dwarf and Milky Way-like galaxies, computed with the arepo, flash, pencil, and ramses codes. The resulting exponents depend on several physical factors such as dynamo effects and their time-scales, turbulence, and initial seed field strength. We find that the dwarf and Milky Way-like galaxy simulations produce results closest to the observations.