Abstract
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 language | English (US) |
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Pages (from-to) | L141-L144 |
Journal | Astrophysical Journal |
Volume | 522 |
Issue number | 2 PART 2 |
DOIs | |
State | Published - Sep 10 1999 |
Keywords
- ISM: Clouds
- MHD
- Turbulence
ASJC Scopus subject areas
- Astronomy and Astrophysics
- Space and Planetary Science