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Decay Timescales of MHD Turbulence in Molecular Clouds

Published online by Cambridge University Press:  04 August 2010

Mordecai-Mark Mac Low
Affiliation:
Max-Planck-Institut für Astronomie, Königstuhl 17, Heidelberg, Germany
Ralf S. Klessen
Affiliation:
Max-Planck-Institut für Astronomie, Königstuhl 17, Heidelberg, Germany
Andreas Burkert
Affiliation:
Max-Planck-Institut für Astronomie, Königstuhl 17, Heidelberg, Germany
Michael D. Smith
Affiliation:
Astronomisches Institut der Universität Würzburg, Am Hubland, Würzburg, Germany
Jose Franco
Affiliation:
Universidad Nacional Autónoma de México
Alberto Carraminana
Affiliation:
Instituto Nacional de Astrofisica, Optica y Electronica, Tonantzintla, Mexico
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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 tff = (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 tff. 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).

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Publisher: Cambridge University Press
Print publication year: 1999

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