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 &lt;= m<SUB>BH</SUB>/M<SUB>solar</SUB> &lt;= 80, via direct collapse. We derive the number of massive BHs (N<SUB>BH</SUB>) 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 N<SUB>BH</SUB> correlates with the number of observed ULXs per galaxy (N<SUB>ULX</SUB>) 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 N<SUB>ULX</SUB>, normalized to the SFR, and the metallicity. A larger and more homogeneous sample of metallicity measurements is required, in order to confirm our results.