The Column Density Variance-Sonic Mach Number Relationship

Blakesley Burkhart; A. Lazarian

doi:10.1088/2041-8205/755/1/L19

paper

The Column Density Variance-Sonic Mach Number Relationship

arXiv:1205.3792 · doi:10.1088/2041-8205/755/1/L19

Abstract

Although there are a wealth of column density tracers for both the molecular and diffuse interstellar medium, there are very few observational studies investigating the relationship between the density variance ( $σ^{2}$ ) and the sonic Mach number ( $M_{s}$ ). This is in part due to the fact that the $σ^{2}$ - $M_{s}$ relationship is derived, via MHD simulations, for the 3D density variance only, which is not a direct observable. We investigate the utility of a 2D column density $σ_{Σ/ Σ_{0}}^{2}$ - $M_{s}$ relationship using solenoidally driven isothermal MHD simulations and find that the best fit follows closely the form of the 3D density $σ_{ρ / ρ_{0}}^{2}$ - $M_{s}$ trend but includes a scaling parameter $A$ such that: $σ_{l n (Σ/ Σ_{0})}^{2} = A \times l n (1 + b^{2} M_{s}^{2})$ , where $A = 0.11$ and $b = 1/3$ . This relation is consistent with the observational data reported for the Taurus and IC 5146 molecular clouds with $b = 0.5$ and $A = 0.16$ and $b = 0.5$ and $A = 0.12$ , respectively. These results open up the possibility of using the 2D column density values of $σ^{2}$ for investigations of the relation between the sonic Mach number and the PDF variance in addition to existing PDF sonic Mach number relations.

submitted to ApJ Letter

The Column Density Variance-Sonic Mach Number Relationship

Abstract

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