Decay Timescales of MHD Turbulence in Molecular Clouds

Summary

We compute 3D models of supersonic, sub-Alfvénic, and super-Alfvénic decaying turbulence, with initial rms Alfvénic and Mach numbers ranging up to five, and an isothermal equation of state appropriate for star-forming interstellar clouds of molecular gas. We find that in 3D the kinetic energy decays as t^−η, with 0.85 < η < 1.2. In 1D magnetized turbulence actually decays faster than unmagnetized turbulence. We compared different algorithms, and performed resolution studies reaching 256³ zones or 70³ particles. External driving must produce the observed long lifetimes and supersonic motions in molecular clouds, as undriven turbulence decays too fast.

Introduction

Molecular cloud lifetimes are of order 3 × 10⁷ yr (Blitz & Shu 1980), while free-fall gravitational collapse times are only t_ff = (1.4 × 10⁶ yr) (n/10³ cm⁻³)^−½. In the absence of non-thermal support, these clouds should collapse and form stars in a small fraction of their observed lifetime. Supersonic hydrodynamical (HD) turbulence is suggested as a support mechanism by the observed broad lines, but was dismissed because it would decay in times of order t_ff. A popular alternative has been sub- or trans-Alfvénic magnetohydrodynamical (MHD) turbulence, which was first suggested by Arons & Max (1975) to decay an order of magnitude more slowly. (Also see Gammie & Ostriker 1996).

However, analytic estimates and computational models suggest that incompressible MHD turbulence decays as t^−η, with a decay rate 2/3 < η < 1.0 (Biskamp 1994; Hossain et al. 1995; Politano, Pouquet, & Sulem 1995; Galtier, Politano, & Pouquet 1997), while incompressible HD turbulence has been experimentally measured to decay with 1.2 < η < 2 (Comte-Bellot & Corrsin 1966; Smith et al. 1993; Warhaft & Lumley 1978).