Implications of the delayed 2013 outburst of the ESO 243-49 HLX-1

After showing four outbursts spaced by $sim 1$ year from 2009 to 2012, the hyper luminous X-ray source ESO 243-49 HLX-1, currently the best intermediate mass black hole (IMBH) candidate, showed an outburst in 2013 delayed by more than a month. In Lasota et al. (2011), we proposed that the X-ray lightcurve is the result of enhanced mass transfer episodes at periapsis from a donor star orbiting the IMBH in a highly eccentric orbit. In this scenario, the delay can be explained only if the orbital parameters can change suddenly from orbit to orbit. To investigate this, we ran Newtonian smooth particle hydrodynamical simulations starting with an incoming donor approaching an IMBH on a parabolic orbit. We survey a large parameter space by varying the star-to-BH mass ratio ($10^{-5}-10^{-3}$) and the periapsis separation $r_p$ from 2.2 to $2.7~r_t$ with $r_t$, the tidal radius. To model the donor, we choose several polytropes ($Gamma = 5/2,~n=3/2$; $Gamma=3/2,~n=2$; $Gamma=5/3,~n=2$ & $n=3$). Once the system is formed, the orbital period decreases until reaching a minimum. Then, the period tends to increase over several periapsis passages due to tidal effects and increasing mass transfer, leading ultimately to the ejection of the donor. The development of stochastic fluctuations inside the donor could lead to sudden changes in the orbital period from orbit to orbit with the appropriate order of magnitude of what has been observed for HLX-1. Given the constraints on the BH mass ($M_{rm BH} > 10^4~M_odot$) and assuming that HLX-1 is currently near a minimum in period of $sim 1$ yr, the donor has to be a white dwarf or a stripped giant core. We predict that if HLX-1 is indeed emerging from a minimum in orbital period, then the period would generally increase with each passage, although substantial stochastic fluctuations can be superposed on this trend.