Accretion disks surrounding stellar mass black holes (BHs) 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 N14, Na23, and sometimes in Al27 and/or in K39. In this study, our aim is to investigate the feasibility of initiating nucleosynthesis for these four elements in BH 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 BH-accretion disk system that would allow for the creation of N14, Na23, Al27, and K39 before the gas is accreted onto the central object. Our findings reveal that there is no region in the parameter space where the formation of Na23 can occur and only a very limited region where the formation of N14, Al27, and K39 is plausible. Specifically, this occurs for BHs with masses lower than 10 solar masses, with a preference toward even lower mass values and extremely low viscosity parameters ($\alpha <10^{-3}$). Such values are highly unlikely based on current observations of stellar mass BHs. However, such low mass BHs could actually exist in the early universe, as so-called primordial BHs. In conclusion, our study suggests that the nucleosynthesis within BH accretion disks of four elements of interest for the multiple stellar populations is improbable, but not impossible, using the slim disk model.
Comment: 11 pages, 7 figures, 2 tables, Accepted by A&A