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Massive metal‐poor stars might form massive stellar black holes (BHs), with mass  25 ≤ m  BH /M ⊙ ≤ 80 , via direct collapse. We derive the number of massive BHs ( N  BH ) 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  BH  correlates with the number of observed ULXs per galaxy ( N  ULX ) 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  ULX , normalized to the SFR, and the metallicity. A larger and more homogeneous sample of metallicity measurements is required, in order to confirm our results.

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