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Optical counterpart of HLX-1 during the 2010 outburst

We studied the optical counterpart of the intermediate-mass black hole candidate HLX-1 in ESO 243-49. We used a set of Very Large Telescope imaging observations from 2010 November, integrated by Swift X-ray data from the same epoch. We measured standard Vega brightnesses U = 23.89 +/- 0.18 mag, B = 25.19 +/- 0.30 mag, V = 24.79 +/- 0.34 mag and R = 24.71 +/- 0.40 mag. Therefore, the source was ~1 mag fainter in each band than in a set of Hubble Space Telescope images taken a couple of months earlier, when the X-ray flux was a factor of 2 higher. We conclude that during the 2010 September observations, the optical counterpart was dominated by emission from an irradiated disk (which responds to the varying X-ray luminosity), rather than by a star cluster around the black hole (which would not change). We modelled the Comptonized, irradiated X-ray spectrum of the disk, and found that the optical luminosity and colours in the 2010 November data are still consistent with emission from the irradiated disk, with a characteristic outer radius r_{out} ~ 2800 r_{in} ~ 10^{13} cm and a reprocessing fraction ~ 2 x 10^{-3}. The optical colours are also consistent with a stellar population with age <~ 6 Myr (at solar metallicity) and mass ~ 10^4 M_{sun}; this is only an upper limit to the mass, if there is also a significant contribution from an irradiated disk. We strongly rule out the presence of a young super-star-cluster, which would be too bright. An old globular cluster might be associated with HLX-1, as long as its mass <~ 2 x 10^6 M_{sun} for an age of 10 Gyr, but it cannot significantly contribute to the observed very blue and variable optical/UV emission.