Samuel Bonsor

Dense stellar systems such as globular and nuclear star clusters have long been considered as environments ideally suited to harbour intermediate-mass black holes (IMBH). Still undetected, this class of astrophysical objects is a crucial missing link in the population of cosmic black holes. Current indirect observational searches for IMBHs inevitably rely on dynamical models, which are often unable to capture the true phase space complexity of the host stellar system.

In this contribution, we present a new family of self-consistent dynamical models describing a spherically symmetric, isotropic dense stellar system with a central black hole. The family is defined by a truncated isothermal distribution function in phase space, suitably modified to allow for the presence of a central point mass. We propose a novel treatment of the boundary conditions of the relevant Poisson equation, which is then solved approximately using matched asymptotics. Such an approach enables us to conduct a careful exploration of the parameter space of these models, which reveals the existence of a rapid change in the structure of the solution and the existence of two regimes, where the equilibria are dominated either by the mass of the black hole or the host system. This new class of models offers a fruitful playground for the study of the behaviour of the stars in the proximity of a central black hole within a realistic self-consistent potential.

The proposed prescription for the inclusion of the central point mass can be readily applied to more complex anisotropic, rotating, non-spherical equilibria, which will allow us to address a number of limitations of current modelling approaches and paves the way towards a more informative assessment of the presence of IMBHs in dense stellar systems.