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Session 15 - Structure and Collapse of Molecular Clouds: Theory.
Display session, Monday, January 13
We present semi-analytical similarity solutions for the inside-out, expansion-wave collapse of initially virialized gas clouds with non-isothermal equations of state. Results are given for the family of negative-index polytropes (P\propto\rho^\gamma, \gamma\le1), but we focus especially on the so-called logotrope, P/P_c=1+A\ \hboxln(\rho/ \rho_c). In a separate paper, we have shown this to be the best available phenomenological description of the internal structure and average properties of molecular clouds and dense clumps of both high and low mass. The formalism and interpretation of the present collapse theory are quite similar to those in Shu's (1977) standard model for accretion in self-gravitating isothermal spheres: a collapse front moves outwards into a cloud at rest, and the gas behind it falls back to a collapsed core, or protostar. The infalling material eventually enters free-fall, such that the density profiles and velocity fields have the same structure at small radii in logotropic and isothermal spheres both. However, several differences arise from the introduction of a new equation of state. The accretion rate onto a protostar is not constant in a logotrope, but grows as \dotM\propto t^3. Thus, the formation timescales for stars of different masses M vary only as M^1/4; low-mass stars are accreted over longer times, and high-mass stars over shorter times, than expected in isothermal clouds. Densities behind the expansion wave increase with time in our theory, rather than decreasing. The infall velocities also grow, but at an initially much slower rate than found for isothermal collapse. These results apply to low- and high-mass star formation alike, and we briefly discuss how they could affect the ages of Class 0 protostars (including the collapsing globule B335) and the luminosity problem of young stellar objects.
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