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

TL;DR

This study investigates the magnetic field strength and gas density relation in the interstellar medium using Bayesian analysis of observational data and simulations, revealing a multiscale broken power-law behavior influenced by physical conditions.

Contribution

It introduces a hierarchical Bayesian framework to model the B-n relation as a multiscale broken power-law and compares observational data with simulations, highlighting physical factors affecting the relation.

Findings

Different power-law indices for diffuse and dense gas phases.

Observational data favor a broken power-law model.

Simulations of galaxies align closely with observational results.

Abstract

The magnetic field strength to gas density relation 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, multi-scale broken power-law relation, $B=B_0(n/n_0)^{\alpha}$ , with $\alpha=\alpha_1$ for $n<n_0$ and $\alpha_2$ for $n>n_0$, and with $B_0$ the field strength at $n_0$. For the Zeeman data we find: $\alpha_1={0.15^{+0.06}_{-0.09}}$ for diffuse gas and $\alpha_2 = {0.53^{+0.09}_{-0.07}}$ for dense gas with $n_0 = 4.00^{+12.7}_{-2.90} \times 10^3$ cm$^{-3}$. For the DCF data we find: $\alpha_1={0.26^{+0.15}_{-0.15}}$ and $\alpha_2={0.77_{-0.15}^{+0.14}}$, with $n_0=13.9^{+10.1}_{-7.30} \times 10^4$ cm$^{-3}$, where the uncertainties give 68\% credible intervals. We perform a similar analysis on nineteen numerical magnetohydrodynamic simulations covering a wide range of physical conditions from protostellar disks to dwarf and Milky Way-like galaxies, completed 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. \textcolor{red}{We find that the dwarf and Milky Way-like galaxy simulations produce results closest to the observations.