Runaway core collapse and cluster survival: where are the parent clusters of ULXs?

Accreting intermediate-mass black holes (IMBHs) have been proposed as an explanation for ultraluminous X-ray sources (ULXs). Runaway core collapse inside a massive cluster is a possible mechanism for IMBH formation. But if so, why are ULXs only rarely found associated with a cluster? We use a simple analytical approximation to show that rapid core collapse can occur in two physical regimes. For cluster masses ~ 10^6 M_sun, an IMBH may be formed if the collapse timescale is <~ 3 Myr, as already well known; the parent cluster is expected to survive. For cluster masses ~ 10^5 M_sun, an IMBH may result from a core collapse on even shorter timescales (~ 0.5 Myr), when the protocluster is still embedded in optically thick gas. Most clusters in this latter regime are disrupted ``explosively'' as soon as the gas is ionized by the OB stars. We speculate that this process may produce isolated ULXs with masses up to a few 10^2 M_sun, surrounded by a loose OB association, and perhaps by a nebula, remnant of the expanding gas from the disrupted protocluster.