School of Mathematics

Student Research Article - Sam Bonsor

PhD Student Sam Bonsor has written the following article as part of our series of Student Research Articles!

Globular clusters are large, dense collections of tens of thousands, or millions of stars all bound together by gravity. They are also one of the main candidates as hosts of intermediate-mass black holes (IMBH). As the name suggests, these are black holes with masses higher than those formed from the collapse of individual stars, called stellar-mass black holes. These have masses in the 10-100 solar mass range, but significantly less than the supermassive black holes which are typically found in the centres of galaxies and can have masses in the millions, or billions of solar masses.

Until recently there was no direct observational evidence of the existence of an IMBH, let alone one within a globular cluster. The recent signal GW190521, detected by the gravitational wave observatories LIGO and Virgo, is consistent with a merger of two stellar-mass black holes to leave a remnant with a mass of ~150 solar masses, just within the mass range to be considered an IMBH. This is the first, and only, observation of an IMBH by direct means. With this general lack of direct observational evidence, indirect approaches using the dynamics of the stars within a globular cluster are important in the search for IMBHs. In these approaches, we use global properties of the star cluster (density, velocity dispersion etc.) to infer the presence of the gravity of a black hole, rather than "seeing" it directly. This strategy relies on having accurate models of a globular cluster, which is where my work is focused at the moment.

Traditionally, globular clusters have been well modelled under the assumptions of spherical symmetry, and lack of internal rotation. However, recent high-quality data, especially from the Hubble Space Telescope and the Gaia satellite, has allowed the determination of the internal kinematics of many globular clusters, in detail, for the first time. This has revealed that many globular cluster exhibit both significant degrees of internal rotation and anisotropy in velocity space. These are effects that haven't been taken account of in much of the literature examining the presence of IMBHs in globular clusters.

My research is looking to address this by developing new families of dynamical models that include the presence of a black hole at the centre of a globular cluster. Essentially, we first take a phase space distribution function which defines a truncated isothermal sphere, a traditional model for a globular cluster. We then use the equation of hydrostatic equilibrium to derive a modified boundary condition for the associated Poisson equation, this is how we account for the central black hole. Initially, we will examine the spherical, non-rotating case as a test bed for the method - looking first to explain the rapid transitional behaviour between two distinct physical regimes which emerged in our analysis. We will then move on to apply the same procedure to include the influence of a central black hole within a model for a rigidly rotating cluster. This will provide one of the first self-consistent equilibrium models for a rotating globular cluster with a central black hole.

Once these models have been constructed, we will then be in a position to examine a range of interesting questions. For example, examining how the IMBH affects the properties of the cluster, which will potentially aid in the indirect search for IMBHs within globular clusters. With the advent of gravitational wave astronomy there are also questions to be answered about how the combination of a black hole and kinematic complexity may affect the rate at which black hole mergers are seen, and, more generally, how black holes form and evolve in dense stellar systems such as globular clusters.

All in all, it's an exciting time to be in this area of research!