1205.3792 (Blakesley Burkhart A. Lazarian)

The Column Density Variance-Sonic Mach Number Relationship    [PDF]

Blakesley Burkhart A. Lazarian

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 (\sigma^2) and the sonic Mach number (Ms). This is in part due to the fact that the \sigma^2-Ms 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 \sigma_{\Sigma/\Sigma_0}^2-Ms relationship using solenoidally driven isothermal MHD simulations and find that the best fit follows closely the form of the 3D density \sigma_{\rho/\rho_0}^2-Ms trend but includes a scaling parameter A such that: \sigma_{ln(\Sigma/\Sigma_0)}^2=Axln(1+b^2Ms^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=0.12. These results open up the possibility of using the 2D column density values of \sigma^2 for investigations of the relation between the the sonic Mach number and the PDF variance in addition to existing PDF sonic Mach number relations.

View original: http://arxiv.org/abs/1205.3792