A multi-shock model for the density variance of anisotropic, highly-magnetised, supersonic turbulence

TL;DR

This paper develops an anisotropic model for the density variance in magnetized, supersonic turbulence, accounting for magnetic field effects, and validates it with high-resolution simulations, advancing star formation theories in the interstellar medium.

Contribution

The paper introduces a novel anisotropic model for density variance in magnetized turbulence, incorporating shock contributions and magnetic field effects, extending previous isotropic models.

Findings

Model predicts an upper bound for density variance at high Mach numbers.

Good agreement between the model and 12 high-resolution MHD simulations.

Implications for star formation and observed density structures in molecular clouds.

Abstract

Shocks form the basis of our understanding for the density and velocity statistics of supersonic turbulent flows, such as those found in the cool interstellar medium (ISM). The variance of the density field, $\sigma^2_{\rho/\rho_0}$, is of particular interest for molecular clouds (MCs), the birthplaces of stars in the Universe. The density variance may be used to infer underlying physical processes in an MC, and parameterises the star formation (SF) rate of a cloud. However, models for $\sigma^2_{\rho/\rho_0}$ all share a common feature -- the variance is assumed to be isotropic. This assumption does not hold when a trans/sub-Alfv\'enic mean magnetic field, $\vec{B}_0$, is present in the cloud, which observations suggest is relevant for some MCs. We develop an anisotropic model for $\sigma_{\rho/\rho_0}^2$, using contributions from hydrodynamical and fast magnetosonic shocks that propagate orthogonal to each other. Our model predicts an upper bound for $\sigma_{\rho/\rho_0}^2$ in the high Mach number $(\mathcal{M})$ limit as small-scale density fluctuations become suppressed by the strong $\vec{B}_0$. The model reduces to the isotropic $\sigma_{\rho/\rho_0}^2-\mathcal{M}$ relation in the hydrodynamical limit. To validate our model, we calculate $\sigma_{\rho/\rho_0}^2$ from 12~high-resolution, three-dimensional, supersonic, sub-Alfv\'enic magnetohydrodynamical (MHD) turbulence simulations and find good agreement with our theory. We discuss how the two MHD shocks may be the bimodally oriented over-densities observed in some MCs and the implications for SF theory in the presence of a sub-Alfv\'enic $\vec{B}_0$. By creating an anisotropic, supersonic density fluctuation model, this study paves the way for SF theory in the highly anisotropic regime of interstellar turbulence.