Astrophysical dynamics

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I plan to explore the behaviour of astrophysical systems ranging from planets to the dark halos of galaxies. Since these systems are governed by gravity, which is scale-free, similar theoretical tools can be used to study all of them. - a promising candidate for cosmological dark matter, motivated by string theory, is a very light axion-like particle, sometimes called "fuzzy dark matter". In the most interesting mass range the de Broglie wavelength is comparable to the size of a galaxy. Among other novel effects, (i) fluctuating interference patterns in the dark matter lead to relaxation towards thermodynamic equilibrium in the halo, and (ii) a compact Bose-Einstein condensate or soliton forms at the centre of the galaxy. I plan to investigate the formation of the soliton and the relation between soliton mass and halo mass found in simulations. - supermassive black holes at the centres of galaxies are surrounded by dense star clusters. These should be in metastable thermal equilibria, i.e., maximum-entropy states subject to the constraint that the semimajor axes of the stellar orbits are frozen. We have shown that these equilibria exhibit a phase transition between spherical and lopsided configurations. I plan to explore this transition with simulations, and to investigate the rate of transients such as tidal disruption events and black-hole mergers in the lopsided state. - many stars are found in quadruple systems consisting of two close binaries orbiting their common centre of mass. In some cases the binaries have been captured into mutual orbital resonances as they evolve by tidal friction. The abundance of resonant systems as a function of stellar properties and orbital parameters provides novel constraints on the mechanism of tidal friction in binary stars, which I plan to investigate. - one of the main tasks of dynamical astronomy is to estimate the gravitational potential of a system (e.g., the Galaxy's dark halo) from a kinematic snapshot of a phase-mixed population of tracers (e.g., globular clusters or nearby satellite galaxies). I have derived a novel estimator that is several times more accurate than its competitors, and plan to apply this to a variety of systems using high-accuracy kinematic catalogues from the Gaia mission. - the Gaia catalogues allow us to explore in detail the phase-space distribution of stars in the solar neighbourhood. I have predicted that the star-star correlation function arising from disrupted binary stars should be detectable out to separations of a hundred parsecs or so and plan to measure this. - there are several claims that the planets in the ~700 known multi-planet systems exhibit strong similarities in mass and radius, implying that the formation of adjacent planets is correlated. If true, this result places unexpected constraints on the physics of planet formation. I plan to investigate this claim using a more plausible null hypothesis and sharper statistical tests borrowed from cosmology.