We have computed models for ultraluminous X-ray sources ( “ ULXs ” ) consisting of a black-hole accretor of intermediate mass ( “ IMBH ” ; e.g. , \sim 1000 ~ { } M _ { \odot } ) and a captured donor star .
For each of four different sets of initial donor masses and orbital separations , we computed 30,000 binary evolution models using a full Henyey stellar evolution code .
To our knowledge this is the first time that a population of X-ray binaries this large has been carried out with other than approximation methods , and it serves to demonstrate the feasibility of this approach to large-scale population studies of mass-transfer binaries .
In the present study , we find that in order to have a plausible efficiency for producing active ULX systems with IMBHs having luminosities \gtrsim 10 ^ { 40 } ergs s ^ { -1 } , there are two basic requirements for the capture of companion/donor stars .
First , the donor stars should be massive , i.e. , \gtrsim 8 ~ { } M _ { \odot } .
Second , the initial orbital separations , after circularization , should be close , i.e. , \lesssim 6 - 30 times the radius of the donor star when on the main sequence .
Even under these optimistic conditions , we show that the production rate of IMBH-ULX systems may fall short of the observed values by factors of 10-100 .