The Density Probability Distribution Function in Turbulent, Isothermal, Magnetized Flows in Slab Geometry

Abstract

We investigate the behavior of the magnetic pressure, $b^2$, in fully turbulent MHD flows in ``1+2/3'' dimensions by means of its effect on the probability density function (PDF) of the density field. We start by reviewing our previous results for general polytropic flows, according to which the value of the polytropic exponent $γ$ determines the functional shape of the PDF. A lognormal density PDF appears in the isothermal ($γ=1$) case, but a power-law tail at either large or small densities appears for large Mach numbers when $γ>1$ and $γ< 1$, respectively. In the isothermal magnetic case, the relevant parameter is the field fluctuation amplitude, $\dbb$. A lognormal PDF still appears for small field fluctuations (generally the case for {\it large mean fields}), but a significant low-density excess appears at large fluctuation amplitudes ({\it weak mean fields}), similar to the behavior at $γ> 1$ of polytropic flows. We interpret these results in terms of simple nonlinear MHD waves, for which the magnetic pressure behaves linearly with the density in the case of the slow mode, and quadratically in the case of the fast wave. Finally, we discuss some implications of these results, in particular the fact that the effect of the magnetic field in modifying the PDF is strongest when the mean field is weak.