The correlation between magnetic pressure and density in compressible MHD turbulence

¹ CNRS, Observatoire de la Côte d'Azur, BP 4229, 06304 Nice Cedex 4, France e-mail: passot@obs-nice.fr
² Instituto de Astronomía, UNAM, Unidad Morelia, Apdo. Postal 7-32, Morelia, Michoacán 58089, Mexico e-mail: e.vazquez@astrosmo.unam.mx

Corresponding author: E. Vázquez-Semadeni, e.vazquez@astrosmo.unam.mx

Received: 7 August 2002
Accepted: 15 October 2002

Abstract

We study, both analytically and numerically, the behavior of magnetic pressure and density fluctuations in turbulent isothermal magnetohydrodynamic (MHD) flows in a slab geometry. We first consider “simple” MHD waves, which are the nonlinear analogue of the slow, fast and Alfvén linear waves, and show that the dependence of magnetic field strength B on density ρ in a simple wave depends on the mode which is considered: for the slow mode, , while for the fast mode, . We also perform a perturbative analysis about a circularly-polarized plane Alfvén wave to investigate Alfvén wave pressure, recovering the results of McKee and Zweibel that , with at large M_a, at moderate M_a and long wavelengths, and at low M_a. This wide variety of behaviors implies that a single polytropic description of magnetic pressure is not possible in general, but instead depends on which mode dominates the density fluctuation production. This in turn depends on the angle θ between the magnetic field and the direction of wave propagation and on the Alfvénic Mach number M_a. Typically, at small M_a, the slow mode dominates, and B is anticorrelated with ρ . At large M_a, both modes contribute to density fluctuation production, and the magnetic pressure decorrelates from density, exhibiting a large scatter, which however decreases towards higher densities. In this case, magnetic “pressure” does not act as a restoring force, but rather as a random forcing. These results have implications for the probability density function (PDF) of mass density. The non-systematic behavior of the magnetic pressure causes the PDF to maintain the log-normal shape corresponding to non-magnetic isothermal turbulence, except in cases where the slow mode dominates, in which the PDF develops an excess at low densities because the magnetic “random forcing” becomes density-dependent. Our results are consistent with the low values and apparent lack of correlation between the magnetic field strength and density in surveys of the lower-density molecular gas, and also with the recorrelation apparently seen at higher densities, if the Alfvénic Mach number is relatively large there.