Rethinking the dynamical paradigm of low-mass stellar systems

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All large galaxies, including our own Milky Way, contain hundreds of 'globular clusters'. Each is a dense group of about a million stars held together by their mutual gravitational attraction. Through a mathematician's eye, they correspond to the deep-rooted problem of understanding the motion of N bodies interacting by long-range forces. Through an astronomer's telescope, they appear as local relics of the ancient universe, as they were among the first stellar structures to emerge at the dawn of the formation of galaxies. Observational astronomers have studied star clusters for decades, but in recent years the quality and range of these observations has leapt beyond the range of existing theory. In particular, the European space observatory Gaia is now measuring the positions and the velocities of thousands of stars in globular clusters of our Galaxy, with unprecedented accuracy. This new generation of data, coupled with measurements by the Hubble Space Telescope and other state-of-the-art and forthcoming astronomical facilities, enable theorists to explore, for the first time, the full 'phase space' of star clusters by studying both the position and velocity of their individual stars.Theorists' models are based on simplifying assumptions, and at present almost always include the ideas that the clusters are spherical, do not rotate, and are composed only of stars - all born at the same time. Three recent developments are undermining these assumptions and requiring us to treat the clusters as they are, and not as we would wish them to be: (i) the realisation that the motions of their stars is much more complex than we expected and that their internal rotation is the rule rather than the exception; (ii) the empirical evidence that the stars in clusters were not all born at once in a single population (an assumption which was once part of their very definition); and (iii) the recent discovery of a numerous 'hybrid' stellar systems which now makes arduous to trace the distinction between 'star clusters' and 'dwarf galaxies'. In addition, star clusters have recently been recognised as prolific cradles for small, 'stellar-mass', black holes and they have been long speculated to be the ideal birth site of larger, 'intermediate-mass', ones. Currently undetected, this class of astrophysical objects is a crucial missing link in the population of cosmic black holes. But new facilities such as the Laser Interferometer Gravitational-Wave Observatory and the Kamioka Gravitational Wave Detector will soon help us tackle this open problem from a new perspective. With a combination of mathematical techniques and numerical simulations, I aim to propose a more realistic description of the dynamics of star clusters, to interpret such new-generation astronomical data. As a result, this research programme will allow me to address three open problems in modern astrophysics: the origin of stars which are among the oldest in the universe, the possible existence a 'missing link' in the population of cosmic black holes, and the limits of the presence of invisible 'dark' matter in small stellar systems.A fundamental understanding of the history and evolution of these intriguing stellar systems will, therefore, provide a new perspective on the first building blocks of galaxies and on the origin of our Milky Way.