Inverse Hubble Flows in Molecular Clouds

Abstract

Motivated by recent numerical simulations of molecular cloud (MC)evolution, in which the clouds engage in global gravitational contraction, and local collapse events culminate significantly earlier than the global collapse, we investigate the growth of density perturbations embedded in a collapsing background, to which we refer as an Inverse Hubble Flow (IHF). We use the standard procedure for the growth of perturbations in a universe that first expands (the usual Hubble Flow) and then recollapses (the IHF). We find that linear density perturbations immersed in an IHF grow faster than perturbations evolving in a static background (the standard Jeans analysis). A fundamental distinction between the two regimes is that, in the Jeans case, the time ${\tau }_{\mathrm{nl}}$ for a density fluctuation to become nonlinear increases without limit as its initial value approaches zero, while in the IHF case ${\tau }_{\mathrm{nl}}\le {\tau }_{\mathrm{ff}}$ always, where ${\tau }_{\mathrm{ff}}$ is the free-fall time of the background density. We suggest that this effect, although moderate, implies that small-scale density fluctuations embedded in globally-collapsing clouds must collapse earlier than their parent cloud, regardless of whether the initial amplitude of the fluctuations is moderate or strongly nonlinear, thus allowing the classical mechanism of Hoyle fragmentation to operate in multi-Jeans-mass MCs. More fundamentally, our results show that, contrary to the standard paradigm that fluctuations of all scales grow at the same rate in the linear regime, the hierarchical nesting of the fluctuations of different scales does affect their growth even in the linear stage.

7 pages, 3 figures; published in MNRAS

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