Ultra-luminous X-ray sources and remnants of massive metal-poor stars

Massive metal-poor stars might form massive stellar black holes (BHs), with mass 25<=mBH/Msun<=80, via direct collapse. We derive the number of massive BHs (NBH) that are expected to form per galaxy through this mechanism. Such massive BHs might power most of the observed ultra-luminous X-ray sources (ULXs). We select a sample of 64 galaxies with X-ray coverage, measurements of the star formation rate (SFR) and of the metallicity. We find that NBH correlates with the number of observed ULXs per galaxy (NULX) in this sample. We discuss the dependence of our model on the SFR and on the metallicity. The SFR is found to be crucial, consistently with previous studies. The metallicity plays a role in our model, since a lower metallicity enhances the formation of massive BHs. Consistently with our model, the data indicate that there might be an anticorrelation between NULX, normalized to the SFR, and the metallicity. A larger and more homogeneous sample of metallicity measurements is required, in order to confirm our results.