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 $M_{\rm cl}\lesssim 5\times 10^{-2}$ of the GMC, radii $r_{\rm cl}
\sim 1$pc, and free-fall times $\tau_{\rm cl} \sim 2\times 10^5\yr$. We show
that clumps inside giant molecular clouds should accrete at a modified Bondi
accretion rate, which depends on clump mass as $\dot M_{\rm cl}\sim M_{\rm
cl}^{5/4}$. 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, $\dot M_*=\epsilon_{\rm ff} M_{\rm cl}/\tau_{\rm cl}$, with
$\epsilon_{\rm ff} \approx 0.017$). However, after $\sim 2$ GMC free-fall times
$\tau_{\rm GMC}$, the clump accretion rate accelerates rapidly; formally, the
clump can accrete the entire GMC in $\sim 3\tau_{\rm GMC}$. 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 $\taug$ 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 $\sim 0.001$ up to 0.1 or larger and
that the mass spectrum of star clusters is flatter than that of clumps,
consistent with observations.
