The nature of ultraluminous X-ray (ULX) sources is presently unknown. A possible explanation is that they are accreting intermediate-mass
black holes (IBHs) that are fed by Roche lobe overflow from a tidally captured stellar companion. We show that a star can
circularize around an IBH without being destroyed by tidal heating (in contrast to the case of MBH>106
Msolar massive black holes in galactic centers, where survival is unlikely). We find that the capture and circularization
rate is ~5¿10-8 yr-1, almost independently of the cluster's relaxation time. We follow the luminosity
evolution of the binary system during the main-sequence Roche lobe overflow phase and show it can maintain ULX source-like
luminosities for greater than 107 yr. In particular, we show that the ULX source in the young cluster MGG-11 in
starburst galaxy M82, which possibly harbors an IBH, is well explained by this mechanism, and we predict that >~10% of
similar clusters with IBHs have a tidally captured circularized star. The cluster can evaporate on a timescale shorter than
the lifetime of the binary. This raises the possibility of a ULX source that outlives its host cluster, or even lights up
only after the cluster has evaporated, in agreement with observations of hostless ULX sources.
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