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We model the intermediate-mass black hole HLX-1, using the Hubble SpaceTelescope, XMM-Newton and Swift. We quantify the relative contributions of abluer component, function of X-ray irradiation, and a redder component,constant and likely coming from an old stellar population. We estimate a blackhole mass of about (2^{+2}_{-1}) x 10^4 M_{sun}, a spin parameter a/M ~ 0.9 formoderately face-on view, and a peak outburst luminosity of about 0.3 times theEddington luminosity. We discuss the discrepancy between the characteristicsizes inferred from the short X-ray timescale (R ~ a few 10^{11} cm) and fromthe optical emitter (R sqrt[cos theta] ~ 2.2 x 10^{13} cm). One possibility isthat the optical emitter is a circumbinary disk; however, we disfavour thisscenario because it would require a very small donor star. A more plausiblescenario is that the disk is large but only the inner annuli are involved inthe X-ray outburst. We propose that the recurrent outbursts are caused by anaccretion-rate oscillation driven by wind instability in the inner disk. Weargue that the system has a long-term-average accretion rate of a few percentEddington, just below the upper limit of the low/hard state; a wind-drivenoscillation can trigger transitions to the high/soft state, with a recurrenceperiod of ~1 year (much longer than the binary period, which we estimate as ~10days). The oscillation that dominated the system in the last decade is nowdamped such that the accretion rate no longer reaches the level required totrigger a transition. Finally, we highlight similarities between disk winds inHLX-1 and in the Galactic black hole V404 Cyg.

Outbursts of the intermediate-mass black hole HLX-1: a wind instability scenario