On the turbulent velocity dispersion in molecular clouds

P. C. Myers, C. F. Gammie

Research output: Contribution to journalArticlepeer-review


We model the "line width-size relation" σ-Lα by averaging a power-law spectrum of turbulent motions over a region of size L. This model reproduces the index α = 0-1 of most line width-size relations observed in molecular clouds, provided that L lies within the range of component wavelengths, the turbulent energy spectrum has power-law index p = 1-2, and the spectral components have random relative phases. The relation between p and α is independent of the dimensionality of the turbulence. As p increases beyond ∼3, α approaches unity, departing from the value (p - 1)/2 expected in a simpler model, because the velocity profile approaches that of its longest wavelength spectral component. Fixed relative phases, expected for excitation by coherent sources, also yield a power-law line width-size relation but require a much steeper energy spectrum to match observations. If the turbulent spectrum has sharp cutoffs, the slope α changes sharply as L goes beyond the range of component wavelengths, approaching α = 1 for L < λmin and α = 0 for L > λmax, independent of p. These changes in slope are due to simple properties of sinusoids and offer observational signatures of the extreme turbulent wavelengths in a cloud.

Original languageEnglish (US)
Pages (from-to)L141-L144
JournalAstrophysical Journal
Issue number2 PART 2
StatePublished - Sep 10 1999


  • ISM: Clouds
  • MHD
  • Turbulence

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science


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