The correlation between magnetic pressure and density in compressible MHD turbulence

Free access article

Issue		A&A Volume 398, Number 3, February II 2003


Page(s)		845 - 855
Section		Cosmology
DOI		http://dx.doi.org/10.1051/0004-6361:20021665

A&A 398, 845-855 (2003)
DOI: 10.1051/0004-6361:20021665

The correlation between magnetic pressure and density in compressible MHD turbulence

T. Passot¹ and E. Vázquez-Semadeni²

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

(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 $\rho$ in a simple wave depends on the mode which is considered: for the slow mode, $B^2 \simeq c_1 - c_2 \rho$ , while for the fast mode, $B^2 \simeq \rho^2$ . 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 $B^2 \simeq \rho^{\gamma_{\rm e}}$ , with $\gamma_{\rm e} \simeq 2$ at large $M_{\rm a}$ , $\gamma_{\rm e} \simeq 3/2$ at moderate $M_{\rm a}$ and long wavelengths, and $\gamma_{\rm e} \simeq 1/2$ at low $M_{\rm a}$ . 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 $\theta$ between the magnetic field and the direction of wave propagation and on the Alfvénic Mach number $M_{\rm a}$ . Typically, at small $M_{\rm a}$ , the slow mode dominates, and B is anticorrelated with $\rho$ . At large $M_{\rm a}$ , 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.

Key words: magnetohydrodynamics -- turbulence

Offprint request: E. Vázquez-Semadeni, e.vazquez@astrosmo.unam.mx

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