Comparing the birth rate of stellar black holes in binary black hole mergers and long gamma-ray bursts

Context. Gravitational wave interferometers have proven the existence of a new class of binary black hole (BBH) weighing tens of solar masses, and have provided the first reliable measurement of the rate of coalescing black holes (BHs) in the local Universe. Furthermore, 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.Aim. We compare the birth rates of BHs found in BBH mergers and in long GRBs.Methods. We construct a simple model that makes reasonable assumptions on the history of GRB formation, and 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.Results. We find that in our reference model the birth rate of stellar BHs in BBH mergers represents a significant fraction of the rate of long GRBs and that comparable birth rates are favored by models with moderate beaming angles. These numbers, however, do not consider subluminous GRBs, which may represent another population of sources associated with the birth of stellar mass BHs. 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 BBH mergers with the same assumptions.Key words: stars: black holes / gravitational waves / gamma-ray burst: general