Abstract
Accretion disks surrounding stellar mass black holes have been suggested as potential locations for the nucleosynthesis of light elements, which are our primary observational discriminant of multiple stellar populations within globular clusters. The population of enriched stars in globular clusters are enhanced in 14N, 23Na, and sometimes in 27Al and/or in 39K. In this study, our aim is to investigate the feasibility of initiating nucleosynthesis for these four elements in black hole accretion disks, considering various internal parameters such as the temperature of the gas and timescale of the accretion. To achieve this, we employed a 132-species reaction network. We used the slim disk model, suitable for the Super-Eddington mass accretion rate and for geometrically and optically thick disks. We explored the conditions related to the mass, mass accretion rate, viscosity, and radius of the black hole-accretion disk system that would allow for the creation of 14N, 23Na, 27Al, and 39K before the gas is accreted onto the central object. This happens when the nucleosynthesis timescale is shorter than the viscous timescale. Our findings reveal that there is no region in the parameter space where the formation of 23Na can occur and only a very limited region where the formation of 14N, 27Al, and 39K is plausible. Specifically, this occurs for black holes with masses lower than 10 solar masses (m < 10 M⊙), with a preference toward even lower mass values (m < 1 M⊙) and extremely low viscosity parameters (α < 10−3). Such values are highly unlikely based on current observations of stellar mass black holes. However, such low mass black holes could actually exist in the early universe, as so-called primordial black holes. In conclusion, our study suggests that the nucleosynthesis within black hole accretion disks of elements of interest for the multiple stellar populations, namely, 14N, 23Na, 27Al, and 39K is improbable, but not impossible, using the slim disk model. Future gravitational wave missions will help constrain the existence of tiny and light black holes.