Gravitational instability in turbulent, non-uniform media.

Details Gravitational instability in turbulent, non-uniform media. Gravitational instability in turbulent, non-uniform media.

Nov 1995

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995a%26a...303..204v&link_type=abstract

Astronomy and Astrophysics, v.303, p.204

Astronomy and Astrophysics

Astrophysics

29

Ism: Clouds, Instabilities, Turbulence

Scientific paper

We present a gravitational instability analysis for a non-uniform medium, with "microturbulence" characterized by a kinetic energy spectrum E(k)=Ak^-α^, and within which density condensations ("clouds") follow a density-size scaling law of the form ρ(k)=Bkbeta^, where k~1/l, and l is the scale size. Model terms are used for the turbulent pressure and for the scale dependence of the gravitational potential. Since the initial state is already non-uniform, this work bypasses the problem of cloud formation, and just focuses on the problem of cloud support against gravitational collapse. We find that a variety of regimes exist depending on the parameters α and β. The case β>2 implies a total inversion of the Jeans criterion, with small clouds being unstable and large clouds stabilized by turbulent pressure, regardless of the spectral index α. If β<2, then two possibilities exist: if α+β<3, then the original Jeans criterion is recovered, while if α+β>3 small clouds are stabilized by thermal pressure, and large clouds are stabilized by turbulent pressure, with the possible existence of an intermediate range of cloud sizes that are unstable. The special case α+β=3 is discussed. It corresponds to virial balance between gravity and turbulent pressure at all cloud sizes. This case includes the empirical scaling relations ρ~l^-1^ and {DELTA}v~l^1/2^, although a continuum of other possible combinations exist. More generally, however, a wide range of stable configurations exist that do not require precise balance between gravity and turbulence at all cloud sizes. Finally, we discuss the assumptions necessary to perform a linear instability analysis for this problem, in particular that of microturbulence. We conclude that this type of calculations can only provide crude guidelines for media with large-amplitude fluctuations such as the interstellar medium, a complete understanding of which most likely necessitates fully nonlinear calculations.

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