Aspect Ratio Dependence of the Freefall Time for Nonspherical Symmetries
Abstract
We investigate the collapse of nonspherical substructures, such as sheets and filaments, which are ubiquitous in molecular clouds. Such nonspherical substructures collapse homologously in their interiors but are influenced by an edge effect that causes their edges to be preferentially accelerated. We analytically compute the homologous collapse timescales of the interiors of uniformdensity, selfgravitating filaments and find that the homologous collapse timescale scales linearly with the aspect ratio. The characteristic timescale for an edgedriven collapse mode in a filament, however, is shown to have a squareroot dependence on the aspect ratio. For both filaments and circular sheets, we find that selective edge acceleration becomes more important with increasing aspect ratio. In general, we find that lower dimensional objects and objects with larger aspect ratios have longer collapse timescales. We show that estimates for star formation rates, based upon gas densities, can be overestimated by an order of magnitude if the geometry of a cloud is not taken into account.
 Publication:

The Astrophysical Journal
 Pub Date:
 September 2012
 DOI:
 10.1088/0004637X/756/2/145
 arXiv:
 arXiv:1207.3078
 Bibcode:
 2012ApJ...756..145P
 Keywords:

 ISM: clouds;
 ISM: structure;
 stars: formation;
 Astrophysics  Galaxy Astrophysics;
 Astrophysics  Solar and Stellar Astrophysics
 EPrint:
 10 pages, 2 figures, accepted by ApJ, minor grammatical errors fixed