Research

 

As part of my PhD research with Prof. Frank van den Bosch at Yale, I am working on the dynamical evolution of self-gravitating, collisionless systems such as galaxies and cold dark matter halos. I have developed both perturbative as well as non-perturbative theories for the response of collisionless systems to gravitational perturbations/encounters.

 

I developed a general non-perturbative formalism to compute the energy transfer and mass-loss in penetrating, impulsive encounters between galaxies or dark matter halos, which I validated using N-body simulations. A proper treatment of near-resonant encounters, e.g., the dynamical friction driven in-fall of massive perturbers orbiting in spherical host systems, required more sophisticated analytical techniques. I generalized the standard LBK formalism and came up with a self-consistent perturbative formalism to compute the dynamical friction torque exerted on a perturber in a circular orbit. This proved to be a huge improvement over the standard theory since my self-consistent formalism presented a resolution (within the perturbative framework) to the outstanding problems of core-stalling, the cessation of dynamical friction driven in-fall of a perturber in the core region of a host system with cored density profile, and dynamical buoyancy, an enhancing torque counteracting dynamical friction and pushing the perturber outwards from deep inside the core. To capture the non-linear effects of core dynamics, I also developed a non-perturbative orbit-based formalism in the restricted three body framework that shed light on the near-resonant orbits of field particles responsible for dynamical friction, buoyancy and core-stalling. This elucidated that core-stalling arises from a bifurcation of the Lagrange points (fixed points in the co-rotating frame) at a certain critical radius in the core, on either side of which the orbital configuration is drastically different, culminating in friction outside and buoyancy inside the critical bifurcation radius. These dynamical phenomena present a promising avenue to constrain the nature of dark matter by looking for offsets of supermassive black holes and nuclear star clusters from the centers of dark matter dominated dwarf galaxies, the presence (absence) of which would favour a cored (cuspy) dark matter density profile.

 

I developed a perturbative formalism to describe the relaxation of disk galaxies exposed to external perturbations (e.g., imapcting satellite galaxies) through kinematic processes like phase-mixing that gives rise to spiral-shaped features in phase-space known as phase-space spirals. This theory can be applied in Galactoseismology: understanding the perturbative origin of the phase-space spirals observed by Gaia in the Solar neighborhood. The ultimate goal of this work is to use the frequency information contained in the phase-space spirals to constrain the gravitational potential and dark matter distribution of the Milky Way.

 

I am currently working on developing a general theory for the relaxation/equilibration of self-gravitating systems by non-perturbatively solving the Boltzmann and Poisson equations. This theory can rigorously describe the relaxation of galaxies and cold dark matter halos in the collisionless limit and that of self-interacting dark matter halos in presence of collisions.