THE COLUMN DENSITY VARIANCE-Mₛ RELATIONSHIP

Although there is a wealth of column density tracers for both the molecular and diffuse interstellar medium, there are few observational studies investigating the relationship between the density variance (σ 2 ) and the sonic Mach number ( ). This is in part due to the fact that the σ 2 – relationship is derived, via MHD simulations, for the three-dimensional (3D) density variance only, which is not a direct observable. We investigate the utility of a 2D column density – relationship using solenoidally driven isothermal MHD simulations and find that the best fit follows closely the form of the 3D density – trend but includes a scaling parameter A such that , 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 probability distribution function (PDF) variance in addition to existing PDF sonic Mach number relations.