Alfven Waves in Interstellar Gasdynamics
Abstract
Magnetohydrodynamic (MHD) waves contribute a significant pressure in both the diffuse interstellar medium and in molecular clouds. Alfvén waves are subject to less damping than compressive MHD waves and are therefore likely to be the dominant mode in astrophysical environments. Provided that the medium in which the waves are propagating is slowly varying, the dynamical effects of ideal MHD waves are governed by equations derived by Dewar. We show that these equations are similar in form to the equations of radiation hydrodynamics to order υ/c, provided that the radiation is nearly isotropic. For the case of Alfvén waves, the pressure due the waves, P_{w}, is isotropic. Furthermore, P_{w} is directly observable through the non thermal line width σ_{nt}; for a randomly oriented field, P_{w} = (3/2)ρσ^{2}_{nt}. In several simple cases, including that in which the Alfvén waves are isotropic, that in which the density is spatially uniform, and that in which the medium undergoes a selfsimilar contraction or expansion, undamped Alfvén waves behave like a gas with a ratio of specific heats of 3/2; i.e., pressure variations are related to density variations by Δ ln P_{w} = γ_{w}Δ ln ρ with γ_{w} = 3/2. In a spatially nonuniform cloud, γ_{w} generally depends on position; an explicit expression is given. In the opposite limit of rapid variations, such as in a strong shock, the wave magnetic field behaves like a static field and the wave pressure can increase as fast as ρ^{2}, depending on the orientation of the shock and the polarization of the waves. The jump conditions for a shock in a medium containing MHD waves are given. For strong nonradiative shocks, neither the wave pressure nor the static magnetic field pressure is significant downstream, but for radiative shocks these two pressures can become dominant.
Alfvén waves are essential in supporting molecular clouds against gravitational collapse. In a static cloud with a nonuniform density ρ(r), the spatial variation of the wave pressure is given by the polytropic relation P_{w}(r) ∝ ρ(r)^{γρ}) with γ_{ρ} = 1/2. This generalizes the result obtained by Fatuzzo & Adams and is consistent with observations showing that molecular clouds have velocity dispersions that increase outward. The polytropic index γ_{ρ} for Alfvén waves differs substantially from the adiabatic index γ_{w} which has implications for the gravitational stability of molecular clouds.
 Publication:

The Astrophysical Journal
 Pub Date:
 February 1995
 DOI:
 10.1086/175306
 Bibcode:
 1995ApJ...440..686M
 Keywords:

 ISM: KINEMATICS AND DYNAMICS;
 ISM: MAGNETIC FIELDS;
 MAGNETOHYDRODYNAMICS: MHD;
 TURBULENCE;
 WAVES