STAR FORMATION IN MASSIVE CLUSTERS VIA BONDI ACCRETION

Essentially all stars form in giant molecular clouds (GMCs). However, inside GMCs, most of the gas does not participate in star formation; rather, denser gas accumulates in clumps in the GMC, with the bulk of the stars in a given GMC forming in a few of the most massive clumps. In the Milky Way, these clumps have masses M-cl less than or similar to 5 x 10(-2) of the GMC, radii r(cl) similar to 1 pc, and free-fall times tau(cl) similar to 2 x 10(5) yr. We show that clumps inside GMCs should accrete at a modified Bondi accretion rate, which depends on clump mass as (M) over dot(cl) similar to M-cl(5/4). This rate is initially rather slow, usually slower than the initial star formation rate inside the clump (we adopt the common assumption that inside the clump, (M) over dot(*) = epsilon M-ff(cl)/tau(cl), with epsilon(ff) approximate to 0.017). However, after similar to 2 GMC free-fall times tau(GMC), the clump accretion rate accelerates rapidly; formally, the clump can accrete the entire GMC in similar to 3 tau(GMC). At the same time, the star formation rate accelerates, tracking the Bondi accretion rate. If the GMC is disrupted by feedback from the largest clump, half the stars in that clump form in the final tau(GMC) before the GMC is disrupted. The theory predicts that the distribution of effective star formation rates, measured per GMC free-fall time, is broad, ranging from similar to 0.001 up to 0.1 or larger and that the mass spectrum of star clusters is flatter than that of clumps, consistent with observations.