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 (σ2) and the sonic Mach number (Ms). This is in part due to the fact that the σ2-Ms 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 σΣ/Σ02-Ms relationship using solenoidally driven isothermal MHD simulations and find that the best fit follows closely the form of the 3D density σρ/ρ02-Ms trend but includes a scaling parameter A such that σln(Σ/Σo) = A x ln(1+b2 Ms2), 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 σ2 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.