Optical models for ultraluminous X-ray sources

We investigate the evolution of the properties of model populations of ultraluminous X-ray sources (ULXs) consisting of a black-hole accretor in a binary with a donor star. We have computed models corresponding to two different. populations of black-hole binaries: one invokes stellar-mass (similar to 10 M-circle dot) black hole accretors(1) (LMBHs), and the second utilizes intermediate-mass (similar to 1000M(circle dot)) black holes (IMBHs). For each of the two populations, we computed 30,000 binary evolution sequences using a full Henyey stellar evolution code. The optical flux from the model ULXs includes contributions from the donor star and the accretion disk (the latter being due to X-ray irradiation as well as intrinsic viscous heating). We present. "probability images" for the ULX systems in planes of color-magnitude, orbital period vs. X-ray luminosity, and luminosity vs. evolution time. Estimates of the numbers of ULXs in a typical galaxy as a function of X-ray luminosity are also presented. Our model CMDs are compared with six ULX counterparts that have been discussed in the literature. Overall, the observed systems seem more closely related to model systems with very high-mass donors (greater than or similar to 25 M-circle dot) in binaries with IMBH accretors. However, significant difficulties remain with both the IMBH and stellar-mass black hole models.