Fragmentation of young massive clusters in binary components: an application of Griddy Gibbs Sampler

The study of the process of hierarchical fragmentation of molecular clouds within Young Massive Clusters required modeling the Initial Mass Function by considering both binary and single-star components. Components of masses from the Gaia Early Data Release 3 (EDR3) dataset were estimated using the mass–luminosity relationship and the contribution of each mass to the total system was analyzed in the current research. Stochastic models describing the contribution of each component are developed for binary as well as single stars incorporating the escape mass theory of the assumed pair. Binary masses, fitted to suitable bi-variate distributions, were simulated using Griddy Gibbs sampler, a Markov Chain Monte Carlo (MCMC) algorithm. Stellar masses of single stars were simulated using data from suitable uni-variate distribution. The mass spectrum of the binary, as well as single star components, were then considered together to determine the initial mass function. The resulting mass function under opacity limited fragmentation scenario is further investigated at different projected distances from the cluster core to the radius where the signature of mass segregation is found.