Comparing the birth rate of stellar black holes in binary black hole mergers and long GRBs

Gravitational wave interferometers have proved the existence of a new class of binary black holes (BBHs) weighting tens of solar masses and they have provided the first reliable measurement of the rate of coalescing black holes (BHs) in the local universe. On another side, long gamma-ray bursts (GRBs) detected with gamma-ray satellites are believed to be associated with the birth of stellar mass BHs, providing a measure of the rate of these events across the history of the universe, thanks to the measure of their cosmological redshift. These two types of sources, which are subject to different detection biases and involve BHs born in different environments with potentially different characteristics, provide complementary information on the birth rate of stellar BHs. We compare here the birth rates of BHs found in BBH mergers and in long GRBs. We construct a simple model which makes reasonable assumptions on the history of GRB formation, and which takes into account some major uncertainties, like the beaming angle of GRBs or the delay between the formation of BBHs and their coalescence. We use this model to evaluate the ratio of the number of stellar mass BHs formed in BBH mergers to those formed in GRBs. We find that in our reference model the birth rate of stellar BHs in BBH mergers represents from few percent to 100% of the rate of long GRBs and that comparable birth rates are favored by models with moderate beaming angles. We briefly discuss this result in view of our understanding of the progenitors of GRBs and BBH mergers, and we emphasize that this ratio, which will be better constrained in the coming years, can be directly compared with the prediction of stellar evolution models if a single model is used to produce GRBs and of BBH mergers with the same assumptions.
Comment: 6 pages, 1 figure, revised version with equation 1 modified to take into account a power-law distribution of coalescence times