Research

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 to be guided as much as possible by real observational 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. To me, galactic dynamics and plasma physics are, to a deep and useful extent, the same thing.

Below you’ll find a brief summary of some of the scientific projects I have worked on.

Dynamics of Star Clusters and Galaxies

I am interested in understanding the secular evolution of stellar systems like star clusters and galaxies. I provided the first application of the gravitational version of the Balescu-Lenard (BL) kinetic equation to spherical stellar clusters (Hamilton et al. 2018, Fouvry et al. 2021). This equation predicts how stellar systems evolve by accounting for the resonant interaction between stars as well as the polarization of the system by self-gravitating collective fluctuations.

The BL equation for stellar systems is typically derived in a very mathematically involved and physically opaque way. To rectify this, I borrowed ‘Feynman-diagram’ techniques from plasma kinetic theory to provide the shortest and simplest derivation of the BL equation using Rostoker’s principle (Hamilton 2020). Also, one key insight of recent years has been the importance 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 BL theory, but also wave-star interactions like in the quasilinear theory of plasmas (Hamilton & Heinemann 2020).

Many galaxies, including our own galaxy the Milky Way, have a ‘bar’ structure at their center— an elongated collection of millions of stars, that gradually rotates as if it were a solid body. Galaxies are also surrounded by massive dark matter haloes. When the rate at which the bar rotates resonates with a dark matter particle’s orbital frequency, the dark matter can suck angular momentum out of the bar, causing it to slow down.

Previous theories of this bar-halo interaction ignored the fact that dark matter particles are not only influenced by the bar, but also experience random ‘diffusive’ forces from other passing dark matter clumps, gas clouds, and so on. In Hamilton et al. (2022) we quantified the impact of diffusion on this delicate resonant process. In the non-diffusive limit we recovered the classic result of Tremaine & Weinberg that the friction vanishes under complete phase-mixing, but we showed that finite diffusion suppresses phase mixing, leading to a finite negative torque, suggesting that real galactic bars always decelerate. This work was a collaboration with 3 plasma physicists, none of whom had worked on galactic dynamics before. We realized that the mathematics we needed to solve the problem was precisely that used to understand energetic particle motion in tokamak fusion plasmas.

Dynamics of Binaries

Another key interest of mine is the dynamical evolution of binary systems, consisting of two objects (stars, black holes, or whatever) orbiting one another. Binaries are the astrophysicist’s harmonic oscillator: one can solve the unperturbed problem exactly (a Keplerian ellipse) and then develop understanding of more complex problems with perturbation theory.

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).

Another fascinating laboratory for investigating binary dynamics, and linking their dynamics to the structure of our Galaxy, is wide binaries – bound pairs of stars with semimajor axes 1000 AU and above. These are rather fragile systems are found in huge abundance in the Milky Way, and have highly unusual orbital properties, including a superthermal eccentricity distribution. These binaries are so wide that the collective gravitational field of the Galactic disk can modify their eccentricities completely. However, I showed in Hamilton (2022) that this effect cannot be responsible for producing the observed superthermal distribution. The mysteries of wide binaries keep on growing: in Hwang et al. (2022) we showed that twin wide binaries (those where the two stars have very similar masses) are even more eccentric still, perhaps pointing to a circumbinary disk origin.

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). I have also investigated in detail the interplay between secular evolution of binaries and gravitational wave emission (Hamilton & Rafikov 2022).