Kinematic complexity and black holes in dense star clusters

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, which 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. This general lack of direct observational evidence has made indirect approaches, using the dynamics of the stars within a globular cluster, an important tool in the search for IMBHs. In these approaches we use global properties of the cluster (density, velocity dispersion etc.) to infer the presence of a black hole, rather than "seeing" it. This relies on having accurate models of a globular cluster, which is where my work is currently focused.

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 hubbble space telescope and GAIA, 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 adapting a method for the inclusion of a central black hole at the centre of a galaxy, to the context of a globular cluster. Essentially we take a commonly used globular cluster model, the King model, and use the equation of hydrostatic equilibrium to derive a modifed boundary condition that takes account of 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 in this case. This behaviour has been noted by previous authors but a full characterisation is still needed. 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 that was developed by my supervisor. This will provide a new class of 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, for example.

MAC-MIGS develops computational modelling and its application to a range of economic sectors, including high-value manufacturing, energy, finance and healthcare. These fields contribute over £500 billion to the UK economy. The CDT involves collaborations with more than a dozen companies and organisations, including large corporations (AkzoNobel, IBM, Dassault, P&G, Aberdeen Standard Investments, Intel), mid-size firms, particularly in the engineering and power sectors (NM Group, which provides monitoring services to power grid operators in 30 countries, Artemis Intelligent Power, the world leader in digital displacement hydraulics, Leonardo, a provider of defense, security and aerospace services, and Oliver Wymans, a management consultancy firm) and startups such as Brainnwave, which develops data-modelling solutions, and Opengosim which designs state-of-the-art and massively parallel software for subsurface reservoir simulation. Government and other agencies involved will include the British Geological Survey, Forestry Commission, James Hutton Institute, and Scottish National Heritage. Engagement will be via internships, short projects and PhD projects. BIS has stated that "Organisations using computer generated modelling and simulations and Big Data analytics create better products, get greater insights, and gain competitive advantage over traditional development processes". Our partners share this vision and are keen to develop deeper collaborations with us over the duration of the CDT.

Our CDT will achieve the following:

- Produce 76 highly skilled mathematical scientists and professionals, ready to take up positions in academia or in companies such as our partners. The students will have exposure to projects, modelling camps and high-level international collaborations.

- Deliver economic and societal benefits through student research projects developed in close collaboration with our partners in industry, business and government and other agencies.

- Create pathways for impact on computer science, chemistry, physics and engineering by involving interdisciplinary partners from Heriot-Watt and Edinburgh Universities in the supervision and training of our students.

- Organise a large number of lectures and seminars which will be open to staff and students of the two universities. Such lectures will inform the wide university communities about the state-of-the-art in computational and mathematical modelling.

- Work with other CDTs both in Edinburgh and beyond to organise a series of workshops for undergraduates, intended to foster an increased uptake of PhD studentship places in technical areas by female students and those from ethnic minorities, with potential impact on the broader UK CDT landscape.

- Organise industrial sandpits and modelling camps which offer the possibility for our partners to present a challenge arising in their work, and to explore innovative ways to tackle that challenge, fully involving the CDT students. This will kick-start a change in the corporate mindset by exposing the relevant staff to new approaches.

- Develop a new course, "Entrepreneurship for Doctoral Students in the Mathematical Sciences" in conjunction with Converge Challenge (Scotland's largest entrepreneurial training programme) and UoE's School of Business. This and other support measures will develop an innovation culture and facilitate the translation of our students' ideas into commercial activities.