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The ultra-luminous intermediate-mass black-hole system HLX-1 in the ESO243-49 galaxy exhibits variability with a possible recurrence time of a fewhundred days. Finding the origin of this variability would constrain the stilllargely unknown properties of this extraordinary object. Since it exhibits anintensity-hardness behavior characteristic of black-hole X-ray transients, wehave analyzed the variability of HLX-1 in the framework of the disk instabilitymodel that explains outbursts of such systems. We find that the long-termvariability of HLX-1 is unlikely to be explained by a model in which outburstsare triggered by thermal-viscous instabilities in an accretion disc. Possiblealternatives include the instability in a radiation-pressure dominated disk butwe argue that a more likely explanation is a modulated mass-transfer due totidal stripping of a star on an eccentric orbit around the intermediate-massblack hole. We consider an evolutionary scenario leading to the creation ofsuch a system and estimate the probability of its observation. We conclude,using a simplified dynamical model of the post-collapse cluster, that no morethan 1/100 to 1/10 of Mbh < 10^4 Msun IMBHs - formed by run-away stellarmergers in the dense collapsed cores of young clusters - could have a few times1 Msun Main-Sequence star evolve to an AGB on an orbit eccentric enough formass transfer at periapse, while avoiding collisional destruction or beingscattered into the IMBH by 2-body encounters. The finite but low probability ofthis configuration is consistent with the uniqueness of HLX-1. We note,however, that the actual response of a standard accretion disk to bursts ofmass transfer may be too slow to explain the observations unless the orbit isclose to parabolic (and hence even rarer) and/or additional heating, presumablylinked to the highly time-dependent gravitational potential, are invoked.

The origin of variability of the intermediate-mass black-hole ULX system HLX-1 in ESO 243-49