On the Maximum Mass of Stellar Black Holes

We present the spectrum of compact object masses: neutron stars and black holes (BHs) that originate from single stars in different environments. In particular, we calculate the dependence of maximum BH mass on metallicity and on some specific wind mass loss rates (e.g., Hurley et al. and Vink et al.). Our calculations show that the highest mass BHs observed in the Galaxy Mbh ∼ 15 M☉ in the high metallicity environment (Z = Z☉ = 0.02) can be explained with stellar models and the wind mass loss rates adopted here. To reach this result we had to set luminous blue variable mass loss rates at the level of ∼10−4 M☉ yr−1 and to employ metallicity-dependent Wolf–Rayet winds. With such winds, calibrated on Galactic BH mass measurements, the maximum BH mass obtained for moderate metallicity (Z = 0.3 Z☉ = 0.006) is Mbh,max = 30 M☉. This is a rather striking finding as the mass of the most massive known stellar BH is Mbh = 23–34 M☉ and, in fact, it is located in a small star-forming galaxy with moderate metallicity. We find that in the very low (globular cluster-like) metallicity environment the maximum BH mass can be as high as Mbh,max = 80 M☉ (Z = 0.01 Z☉ = 0.0002). It is interesting to note that X-ray luminosity from Eddington-limited accretion onto an 80 M☉ BH is of the order of ∼1040 erg s−1 and is comparable to luminosities of some known ultra-luminous X-ray sources. We emphasize that our results were obtained for single stars only and that binary interactions may alter these maximum BH masses (e.g., accretion from a close companion). This is strictly a proof-of-principle study which demonstrates that stellar models can naturally explain even the most massive known stellar BHs.