The Pressure Distribution in Thermally Bistable Turbulent Flows

We present a systematic numerical study of the effect of turbulent velocity fluctuations on the thermal pressure distribution in thermally bistable flows. The turbulent fluctuations are characterized by their rms Mach number M (with respect to the warm medium) and the energy injection (forcing) wavenumber k_for = 1/l, where l is the injection size scale in units of the box size L = 100 pc. The numerical simulations employ random turbulent driving generated in Fourier space rather than starlike heating, in order to allow for precise control of the parameters. Our range of parameters is 0.5 ≤ M ≤ 1.25 and 2 ≤ k_for ≤ 16. Our results are consistent with the picture that as either of these parameters is increased, the local ratio of turbulent crossing time to cooling time decreases, causing transient structures in which the effective behavior is intermediate between the thermal-equilibrium and adiabatic regimes. As a result, the effective polytropic exponent γ_e of the simulations ranges between ~0.2 and ~1.1, and the mean pressure of the diffuse gas is generally reduced below the thermal equilibrium pressure P_eq, while that of the dense gas is increased with respect to P_eq. The fraction of high-density zones (n > 7.1 cm^-3) with P > 10⁴ cm^-3 K increases from roughly 0.1% at k_for = 2 and M = 0.5 to roughly 70% for k_for = 16 and M = 1.25. A preliminary comparison with the recent pressure measurements of Jenkins in C I favors our case with M = 0.5 and k_for = 2. In all cases, the dynamic range of the pressure in any given density interval is larger than one order of magnitude, and the total dynamic range, summed over the entire density range, typically spans 3-4 orders of magnitude. The total pressure histogram widens as the Mach number is increased, and moreover develops near-power-law tails at high (low) pressures when γ_e ≲ 0.5 (γ_e ≳ 1), which occurs at k_for = 2 (k_for = 16) in our simulations. The opposite side of the pressure histogram decays rapidly, in an approximately lognormal form. This behavior resembles that of the corresponding density histograms, in spite of the large scatter of the pressure in any given density interval. Our results show that turbulent advection alone can generate large pressure scatters, with power-law high-P tails for large-scale driving, and provide validation for approaches attempting to derive the shape of the pressure histogram through a change of variable from the known form of the density histogram, such as that performed by Mac Low et al.