Models for the Observable System Parameters of Ultraluminous X-Ray Sources

We investigate the evolution of model populations of ultraluminous X-ray sources (ULXs), consisting of a black hole accretor in a binary with a donor star. Two of the models we consider invoke stellar-mass (up to ~25 M_☉) black hole binaries (LMBHs), generated with a binary population synthesis code, while a third model uses intermediate-mass (~1000 M_☉) black hole accretors (IMBHs). For each model, we computed 30,000 binary evolution sequences. A scheme for calculating the optical flux from ULXs is discussed. We present ``probability images'' for the color-magnitude diagrams (CMDs) and for the orbital period-X-ray luminosity (P_orb-L_x) plane. We show how a population of luminous X-ray sources in a cluster of stars evolves with time. The most probable ULX system parameters correspond to high-mass donors (of initial mass ≳25 M_☉) with effective O through late B spectral types, and P_orb between 1 and 10 days. Estimates of the numbers of ULXs in a typical galaxy as a function of L_x are also presented. We find that if LMBHs are allowed to have super-Eddington L_x, the binding energy parameter for the stellar envelope of the black hole progenitor must be λ ≲ 0.03 in order not to overproduce ULXs. Comparison of six known ULX counterparts with our model CMDs indicates that the IMBH model somewhat more closely matches the observations. We find that a significant contribution to the optical flux from the IMBH systems comes from intrinsic accretion disk radiation. In effect, IMBH systems, when operating at their maximum luminosities (10⁴¹-10⁴² ergs s⁻¹), are milli-AGNs. While models of IMBH systems during the X-ray phase are attractive, their formation mechanism remains uncertain.