I am a dynamicist. By this I mean that I try to understand and predict the dynamical evolution of a wide variety of astrophysical systems, such as binary black holes, star clusters, and galaxies. To do this I use the tools of theoretical physics (e.g. Hamiltonian mechanics, nonequilibrium statistical mechanics and kinetic theory), but I also employ numerical simulations and try (when possible) to be guided by real data.

For most of the systems I am interested in, the predominant force is gravity. However, because of the similarity between the Newtonian gravitational force and the Coulomb electrical force, many problems I care about have analogues in plasma physics. Thus I often find it useful to borrow tools from the kinetic theory of plasmas and apply them to gravitational dynamics.

My published research to date has been focused on (i) the dynamics of astrophysical binaries, and (ii) the kinetic theory of stellar systems.

Dynamics of Binaries

In my PhD I developed a general secular theory for the dynamical evolution of any binary orbiting an arbitrary axisymmetric potential. The formalism is applicable to a wide variety of astrophysical systems and also brings several classic problems under a simple unified framework: for instance, (i) the hierarchical three-body problem and (ii) the problem of Oort comets torqued by the Galactic tide both arise as special cases of the general secular theory (Hamilton & Rafikov 2019a). The theory demonstrates that large-amplitude eccentricity oscillations typified by the Lidov-Kozai mechanism — and often invoked to explain e.g. black hole mergers and hot jupiter formation — are in fact quite general whenever a wide binary orbits an axisymmetric host system, such as a globular cluster (Hamilton & Rafikov 2019b). Cluster-tide driven eccentricity excitation constitutes a new merger channel for the black hole and neutron star binary mergers currently being detected by LIGO/Virgo (Hamilton & Rafikov 2019c). Such binaries are crucially affected by general relativistic apsidal precession, and I have built this effect into the formalism (Hamilton & Rafikov 2021).

Kinetic Theory of Stellar Systems

I was first to apply the gravitational version of the Balescu-Lenard kinetic equation to spherical stellar clusters (Hamilton et al. 2018, Fouvry et al. 2021), and I have provided the shortest and simplest derivation of this equation to date using Rostoker’s principle (Hamilton 2020). One key insight of recent years has been the imprtance of large scale density waves (normal modes) in driving the evolution of stellar systems. I wrote down a kinetic theory for stellar systems that accounts both for star-star interactions like Balescu-Lenard theory, but also wave-star interactions like in the quasilinear theory of plasmas (Hamilton & Heinemann 2020).