On the relation between magnetic field strength and gas density in the interstellar medium: a multiscale analysis - Whitworth, David J.; Srinivasan, S; Pudritz, R E; Mac Low, M -M; Eadie, G; Palau, A; Soler, J D; Smith, R J; Pattle, K; Robinson, H; Pillsworth, R; Wadsley, J; et al. (Monthly notices of the Royal Astronomical Society, 2025)
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, $B=B_0(n/n_0)^{α }$, with $α =α _1$ for $n< n_0$ and $α _2$ for $n>n_0$, and with $B_0$ the field strength at $n_0$. For the Zeeman data, we find: $α _1={0.15^{+0.06}_{-0.09}}$ for diffuse gas and $α _2 = {0.53^{+0.09}_{-0.07}}$ for dense gas with $n_0 = 0.40^{+1.30}_{-0.30}× 10^4$ cm$^{-3}$. For the DCF data, we find: $α _1={0.26^{+0.01}_{-0.01}}$ and $α _2={0.77_{-0.15}^{+0.14}}$, with $n_0=14.00^{+10.00}_{-7.00}× 10^4$ cm$^{-3}$, 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.