Numbers of IMBH binaries as a function of time for three different lower limits on the X‐ray luminosity for all systems (blue and purple curves), ﹩L_{\mathrm{X}\,}> 10^{39}﹩ ergs s−1 (green and cyan curves), and ﹩L_{\mathrm{X}\,}> 10^{40}﹩ ergs s−1 (red and orange curves). Values are derived from the results in Fig. 1. The color scheme is as follows: models A and C are shown by blue, green, and red, and models B and D by purple, cyan, and orange. In each case, the number of active systems at any given time is divided by 30,000 (the number of binaries evolved) to provide an estimate of the fractional "efficiency" for producing IMBH‐ULX binaries.