The Freefall Time of Finite Sheets and Filaments
Abstract
Molecular clouds often exhibit filamentary or sheetlike shapes. We compute the freefall time (τ_{ff}) for finite, uniform, selfgravitating circular sheets and filamentary clouds of small but finite thickness, so that their volume density ρ can still be defined. We find that, for thin sheets, the freefall time is larger than that of a uniform sphere with the same volume density by a factor proportional to \sqrt{A}, where the aspect ratio A is given by A = R/h, R being the sheet's radius and h is its thickness. For filamentary clouds, the aspect ratio is defined as A=L/{\cal R}, where L is the filament's halflength and {\cal R} is its (small) radius, and the modification factor is more complicated, although in the limit of large A it again reduces to nearly \sqrt{A}. We propose that our result for filamentary shapes naturally explains the ubiquitous configuration of clumps fed by filaments observed in the densest structures of molecular clouds. Also, the longer freefall times for nonspherical geometries in general may contribute toward partially alleviating the "star formation conundrum," namely, the star formation rate in the Galaxy appears to be proceeding in a timescale much larger than the total molecular mass in the Galaxy divided by its typical freefall time. If molecular clouds are in general formed by thin sheets and long filaments, then their relevant freefall time may have been systematically underestimated, possibly by factors of up to one order of magnitude.
 Publication:

The Astrophysical Journal
 Pub Date:
 January 2012
 DOI:
 10.1088/0004637X/744/2/190
 arXiv:
 arXiv:1110.0917
 Bibcode:
 2012ApJ...744..190T
 Keywords:

 ISM: clouds;
 ISM: structure;
 Astrophysics  Solar and Stellar Astrophysics
 EPrint:
 To appear on The Astrophysical Journal