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;= mBHMsolar lt;= 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.