The Density Distribution in Turbulent Bi-stable Flows

TL;DR

This study investigates how thermal bistability influences the density and column density probability distribution functions in turbulent flows, revealing deviations from isothermal behavior and the impact of Mach number on distribution shapes.

Contribution

It provides the first detailed analysis of n-PDF and Sigma-PDF in thermally bistable turbulent flows, highlighting differences from isothermal turbulence and the effects of thermal instability.

Findings

n-PDF is lognormal at low densities across Mach numbers.

High density n-PDF shape transitions from power-law to lognormal with increasing Mach.

Sigma-PDF remains lognormal, with width larger than in isothermal cases, and varies with Mach number.

Abstract

We numerically study the volume density probability distribution function (n-PDF) and the column density probability distribution function (Sigma-PDF) resulting from thermally bistable turbulent flows. We analyze three-dimensional hydrodynamic models in periodic boxes of 100pc by side, where turbulence is driven in the Fourier space at a wavenumber corresponding to 50pc. At low densities (n <= 0.6cm^-3) the n-PDF, is well described by a lognormal distribution for average local Mach number ranging from ~0.2 to ~5.5. As a consequence of the non linear development of thermal instability (TI), the logarithmic variance of the distribution for the diffuse gas increases with M faster than in the well known isothermal case. The average local Mach number for the dense gas (n >= 7.1cm^-3) goes from ~1.1 to ~16.9 and the shape of the high density zone of the n-PDF changes from a power-law at low Mach numbers to a lognormal at high M values. In the latter case the width of the distribution is smaller than in the isothermal case and grows slower with M. At high column densities the Sigma-PDF is well described by a lognormal for all the Mach numbers we consider and, due to the presence of TI, the width of the distribution is systematically larger than in the isothermal case but follows a qualitatively similar behavior as M increases. Although a relationship between the width of the distribution and M can be found for each one of the cases mentioned above, these relations are different form those of the isothermal case.