Date of Award
Spring 2023
Document Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Astronomy
First Advisor
van den Bosch, Frank
Abstract
In the $\Lambda$CDM paradigm of cosmology, structure formation occurs via gravitational encounters and mergers between self-gravitating structures like galaxies and dark matter halos. This perturbs galaxies and halos out of equilibrium. These systems are collisionless, i.e., cannot relax within the Hubble time via two-body encounters, thereby prevailing in a state of non-equilibrium or quasi-equilibrium at best. However, such perturbed collisionless systems can relax via other mechanisms such as phase-mixing, Landau damping and violent relaxation. Phase-mixing and Landau damping take several dynamical times to achieve completion. Both these processes can be described using a linear order perturbation of the collisionless Boltzmann and Poisson equations under the assumption of a sufficiently weak perturbation. Phase-mixing is the coarse-grained destruction of a coherent response to a perturbation due to an intrinsic spread in the oscillation frequencies of the field particles. Landau damping is the fine-grained damping of the response due to energy exchanges driven by gravitational interactions between the particles, which is also known as a collective effect. Unlike the linear phenomena of phase-mixing and Landau damping, violent relaxation is fundamentally a non-linear effect and is a rapid process, achieving completion within a dynamical time. Moreover, violent relaxation is self-limiting in nature, rendering an end state that may be very different from the Maxwellian velocity distribution that ensues from two-body/collisional relaxation. While a perturbed collisionless system (subject) undergoes relaxation via the above processes, the subject response simultaneously exerts a back reaction on the perturber and slowly changes its orbital dynamics, typically draining its orbital energy and angular momentum. This phenomenon is a type of secular evolution and is known as dynamical friction. It is the key process by which the relative orbital energy of interacting galaxies and halos is dumped into their internal energies, often resulting in their merger. Gravitational encounters and dynamical friction are therefore at the basis of all structure formation in the universe. Depending on how the timescale of perturbation ($\tau_{\mathrm{P}}$) compares to the oscillation periods ($\tau$) of field particles in the subject, gravitational perturbations can be impulsive ($\tau_{\mathrm{P}}<\tau$), resonant ($\tau_{\mathrm{P}}\sim\tau$) or adiabatic ($\tau_{\mathrm{P}}>\tau$). This dissertation investigates how gravitational encounters and collisionless relaxation occur in these three different regimes. First, we provide a general non-perturbative formalism to compute the energy change in impulsive encounters, which properly describes penetrating encounters, unlike the standard approach that only works for distant encounters. Next, we develop a comprehensive linear perturbative formalism to compute the response of a stellar disk to external perturbations. We study the cases of an infinite isothermal slab as well as a realistic disk galaxy in a non-responsive dark matter halo. The disk response phase-mixes away due to different oscillation frequencies of the stars, giving rise to local phase-space spirals. A vertically anti-symmetric (symmetric) perturbation gives rise to a bending (breathing) mode response of the disk, which triggers a one-armed (two-armed) spiral in the $z-v_z$ phase-space. Perturbations slower than the vertical oscillation period ($\tau_z$), i.e., those with $\tau_{\mathrm{P}}>\tau_z$, induce stronger bending modes, while faster ones trigger more pronounced breathing modes. This translates to more distant encounters with satellite galaxies causing stronger bending mode perturbations. We analyze the response of the Milky Way (MW) disk to encounters with its satellite galaxies, and find that Sagittarius (Sgr) dominates the Solar neighborhood response among all the satellites. This makes Sgr the dominant contender among the MW satellites to have triggered the Gaia phase-spiral. Collisional diffusion due to the scattering of disk stars by structures like giant molecular clouds can result in a super-exponential damping of the phase-spiral amplitude on a fine-grained level. The diffusion timescale in the Solar neighborhood of the MW disk turns out to be $\tau_{\mathrm{D}}^{\odot}\sim 0.6-0.7$ Gyr. This sets an approximate upper limit of $\tau_{\mathrm{D}}^{\odot}$ to the time elapsed since perturbation so that the resultant Solar neighborhood phase-spiral survives collisional damping and is detectable. Only sufficiently impulsive perturbations can trigger phase-spirals; adiabatic ones cannot. Near-resonant parts of the phase-space undergo gradual phase-mixing and do not develop phase-spirals. It is the near-resonant response of the subject that exerts the maximum torque on the perturber, driving its orbital inspiral via dynamical friction. In the final chapters of this dissertation, we develop a general theory for dynamical friction on a perturber in circular orbit in a spherical host galaxy. This explains the origin of secular phenomena in $N$-body simulations of cored galaxies that are unexplained in the standard Chandrasekhar and resonance theories for dynamical friction: (i) core-stalling, the apparent cessation of dynamical friction driven infall in the core region of galaxies with a central constant density core, (ii) super-Chandrasekhar friction, an accelerated infall phase prior to core-stalling, and (iii) dynamical buoyancy, an enhancing torque that can counteract dynamical friction and push out the perturber from inside the core region. We relax the adiabatic and secular approximations adopted in the derivation of the LBK torque in the standard resonance theory, and provide a fully self-consistent perturbative formalism for dynamical friction. Unlike the LBK torque that arises exclusively from resonances between the field particles and the perturber, the self-consistent torque depends on the entire infall history of the perturber ({\textit{memory effect}}), has a significant contribution from the {\textit{near-resonant orbits}}, and flips sign within a certain radius in the core region. To overcome the limitations of linear perturbation theory near the core-stalling radius, we develop a novel, non-perturbative, orbit-based treatment of dynamical friction. Here we model dynamical friction as a circular restricted three body problem, wherein we identify the near-co-rotation resonant horse-shoe, Pac-Man and tadpole orbits of field particles as the dominant contributors to dynamical friction or buoyancy. Outside the core region, all these orbits exert friction. As the perturber enters the core region, it tidally disrupts the core and the inner Lagrange points undergo a bifurcation. This drastically alters the orbital topology: the friction exerting horse-shoe orbits disappear and the Pac-Man orbits become dominant. A shallow distribution function gradient along these Pac-Man orbits gives rise to an enhancing torque or dynamical buoyancy. We argue that core-stalling occurs near the radius of Lagrange point bifurcation, which marks the transition from friction to buoyancy. Bifurcation of Lagrange points and therefore core-stalling are exclusive to a galaxy with a constant density core and are absent in one with a central NFW-like cusp. We discuss some profound astrophysical implications of core-stalling and buoyancy, e.g., the potential choking of supermassive black hole (SMBH) mergers in cored galaxies, leading to a significant population of off-center, wandering SMBHs. This has implications for future detections of gravitational wave events due to SMBH mergers by Laser Interferometer Space Antenna (LISA).
Recommended Citation
Banik, Uddipan, "Pushing the Frontiers of Non-equilibrium Dynamics of Collisionless and Weakly Collisional Self-gravitating Systems" (2023). Yale Graduate School of Arts and Sciences Dissertations. 992.
https://elischolar.library.yale.edu/gsas_dissertations/992
