The Column Density Variance in Turbulent Interstellar Media: A Fractal Model Approach

TL;DR

This paper uses fractal models to relate observable column density variance to the unobservable 3D density variance in turbulent interstellar media, providing new quantitative tools and exploring effects of turbulence forcing and magnetic fields.

Contribution

It introduces a fractal model approach to connect column density variance with 3D density variance and sonic Mach number, including effects of turbulence forcing and magnetic fields.

Findings

Derived quantitative expressions for 3D density variance from column density observations.

Established the relationship between column density variance and sonic Mach number in HD turbulence.

Showed how turbulence forcing and magnetic fields influence the proportional constant A.

Abstract

Fractional Brownian motion (fBm) structures are used to investigate the dependency of column density variance ({\sigma}_{\ln N}^2) in the turbulent interstellar medium on the variance of three-dimensional density ({\sigma}_{\ln\rho}^2) and the power-law slope of the density power spectrum. We provide quantitative expressions to infer the three-dimensional density variance, which is not directly observable, from the observable column density variance and spectral slope. We also investigate the relationship between the column density variance and sonic Mach number (Ms) in the hydrodynamic (HD) regime by assuming the spectral slope and density variance as functions of sonic Mach number, as obtained from the HD turbulence simulations. They are related by the expression {\sigma}_{\ln N}^2 = A{\sigma}_{\ln\rho}^2 = Aln(1+b^2M^2), suggested by Burkhart & Lazarian for the magnetohydrodynamic (MHD) case. The proportional constant A varies from ~ 0.2 to ~ 0.4 in the HD regime as the turbulence forcing parameter b increases from 1/3 (purely solenoidal forcing) to 1 (purely compressive forcing). It is also discussed that the parameter A is lowered in the presence of a magnetic field.