The Density Distribution in Turbulent Bistable Flows

We numerically study the volume density probability distribution function ( n –PDF) and the column density probability distribution function (Σ–PDF) resulting from thermally bistable turbulent flows. We analyze three-dimensional hydrodynamic models in periodic boxes of 100 pc by side, where turbulence is driven in the Fourier space at a wavenumber corresponding to 50 pc. At low densities ( n ≲ 0.6 cm −3 ), the n –PDF is well described by a lognormal distribution for an average local Mach number ranging from ∼0.2 to ∼5.5. As a consequence of the nonlinear development of thermal instability (TI), the logarithmic variance of the distribution of the diffuse gas increases with M faster than in the well-known isothermal case. The average local Mach number for the dense gas ( n ≳ 7.1 cm −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 Σ–PDF is well described by a lognormal for all of 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 from those of the isothermal case.