On the relation between magnetic field strength and gas density in the interstellar medium. II. Density uncertainties and diffuse gas constraints
Abstract
The relationship between magnetic field strength and gas density is essential to understand the interstellar medium and star formation. Zeeman measurements in dense atomic and molecular gas phases have traditionally been used to directly probe magnetic field strengths in the Milky Way. This allowed derivation of a relationship between magnetic field strength B and gas number density n . We recently generalized this relation as a two-part power-law with non-zero slopes and a transition density given as B / B 0 ∝ ( n / n 0 ) α 1 for n ≤ n 0 and ( n / n 0 ) α 2 for n > n 0 . Here, we extend our previous hierarchical Bayesian framework by incorporating a large body of pulsar observations that probe the diffuse interstellar medium and explicitly modelling density uncertainties through a log-density intrinsic scatter R n applied to all densities. We also account for magnetic field geometry and measurement uncertainties through a magnetic hyperparameter to estimate B . This results in a stronger constraint on the diffuse gas part of the B – n relation. Our results confirm a non-zero exponent in the diffuse gas and a broad transition density with our best model and data set yielding maximum a posteriori results of α 1 = 0.20 − 0.03 + 0.01 , α 2 = 0.65 − 0.07 + 0.06 , n 0 = 3330 − 3220 + 270 cm − 3 , and B 0 = 10.11 − 5.97 + 0.71 μ G .
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BibTeX
@article{whitworth2026relation,
title = {{On the relation between magnetic field strength and gas density in the interstellar medium. II. Density uncertainties and diffuse gas constraints}},
author = {David Whitworth and Amit Seta and Ralph E. Pudritz and Mordecai-Mark Mac Low and Juan D. Soler and Aina Palau and Ralf S. Klessen},
journal = {The Open Journal of Astrophysics},
year = {2026},
month = oct,
doi = {10.33232/001c.173229},
url = {https://astro.theoj.org/article/173229-on-the-relation-between-magnetic-field-strength-and-gas-density-in-the-interstellar-medium-ii-density-uncertainties-and-diffuse-gas-constraints},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - On the relation between magnetic field strength and gas density in the interstellar medium. II. Density uncertainties and diffuse gas constraints
AU - David Whitworth
AU - Amit Seta
AU - Ralph E. Pudritz
AU - Mordecai-Mark Mac Low
AU - Juan D. Soler
AU - Aina Palau
AU - Ralf S. Klessen
PY - 2026
DA - 2026/10/27
JO - The Open Journal of Astrophysics
DO - 10.33232/001c.173229
UR - https://astro.theoj.org/article/173229-on-the-relation-between-magnetic-field-strength-and-gas-density-in-the-interstellar-medium-ii-density-uncertainties-and-diffuse-gas-constraints
AB - The relationship between magnetic field strength and gas density is essential to understand the interstellar medium and star formation. Zeeman measurements in dense atomic and molecular gas phases have traditionally been used to directly probe magnetic field strengths in the Milky Way. This allowed derivation of a relationship between magnetic field strength B and gas number density n . We recently generalized this relation as a two-part power-law with non-zero slopes and a transition density given as B / B 0 ∝ ( n / n 0 ) α 1 for n ≤ n 0 and ( n / n 0 ) α 2 for n > n 0 . Here, we extend our previous hierarchical Bayesian framework by incorporating a large body of pulsar observations that probe the diffuse interstellar medium and explicitly modelling density uncertainties through a log-density intrinsic scatter R n applied to all densities. We also account for magnetic field geometry and measurement uncertainties through a magnetic hyperparameter to estimate B . This results in a stronger constraint on the diffuse gas part of the B – n relation. Our results confirm a non-zero exponent in the diffuse gas and a broad transition density with our best model and data set yielding maximum a posteriori results of α 1 = 0.20 − 0.03 + 0.01 , α 2 = 0.65 − 0.07 + 0.06 , n 0 = 3330 − 3220 + 270 cm − 3 , and B 0 = 10.11 − 5.97 + 0.71 μ G .
SN - 2565-6120
ER -