Irradiation models for ULXs and fits to optical data

We have constructed a model which describes the optical emission from ultra-luminous X-ray sources (ULXs), and have used it to constrain the parameters of seven ULX systems. Our model assumes a binary nature for ULXs, and accounts for optical emission from an X-ray irradiated companion star and accretion disk. We apply our model to six different ULX optical counterparts observed with HST, and one observed with the ESO VLT, and determine the mass, radius and age of the donor stars in these systems. In addition, we obtained constraints for the black hole (BH) mass in some cases. We use the mass accretion rate implied by the X-ray luminosity of these sources as an additional constraint on the donor star, by assuming the mass transfer is driven by the stellar nuclear evolution. We find that in general the donors are older and less massive than previously thought, and are consistent with being of spectral type B. We discuss how these results affect our understanding of the evolution and history of ULXs. Where we can constrain the BH masses, we find them to be consistent with stellar mass BHs or intermediate mass BHs of order ∼ 100M⊙. We make predictions for future observations of optical/infrared ULX counterparts, calculating binary periods for different BH masses in each of the seven sources.