Misc,
The Razor's Edge of Collapse: The Transition Point from Lognormal to Powerlaw in Molecular Cloud PDFs
(Sep 14, 2016)
Abstract
We derive an analytic expression for the transitional column density value
(\$s\_t\$) between the lognormal and power-law form of the probability
distribution function (PDF) in star-forming molecular clouds. Our expression
for \$s\_t\$ depends on the mean column density, the variance of the lognormal
portion of the PDF, and the slope of the power-law portion of the PDF. We show
that \$s\_t\$ can be related to physical quantities such as the sonic Mach number
of the flow and the power-law index for a self-gravitating isothermal sphere.
This implies that the transition point between the lognormal and power-law
density/column density PDF represents the critical density where turbulent and
thermal pressure balance, the so-called "post-shock density." We test our
analytic prediction for the transition column density using dust PDF
observations reported in the literature as well as numerical MHD simulations of
self-gravitating supersonic turbulence with the Enzo code. We find excellent
agreement between the analytic \$s\_t\$ and the measured values from the numerical
simulations and observations (to within 1.5 A\$\_V\$). We discuss the utility of
our expression for determining the properties of the PDF from unresolved low
density material in dust observations, for estimating the post-shock density,
and for determining the HI-H\$\_2\$ transition in clouds.
