Quasi-stationary distributions for the collective motions of a binary astrophysical system: A Langevin dynamics approach

Previously, we showed that the orbital motions of a binary system (e.g., two stars clusters in mutual interaction) can be modeled as a Brownian particle immersed in two heat baths (describing the thermodynamic incidence of the internal degrees of freedom). The fluctuations arising from the interaction of this effective particle with the baths lead to dynamical instabilities-escape and collapse events. Now, we focus on determining the quasi-stationary distribution of an ensemble of systems evolving under this stochastic model, specifically in the regime influenced by escape events. To this end, we develop numerical methods to compute the energy distribution of such an ensemble of systems. Notably, the resulting distribution exhibits lowered isothermal profiles akin to those observed in the structure of stellar clusters, such as the King distribution, which correspond to quasi-stationary states with positive heat capacities.