In double white dwarf (WD) systems with sufficiently short initial orbital periods, angular momentum losses from gravitational wave radiation shrink the orbit and can lead to the merger of the WDs. Simulations of the merger show that the less massive WD is tidally disrupted, forming a disk around the more massive WD. Beginning with output from WD merger simulations, I study the subsequent viscous evolution using multi-dimensional hydrodynamical simulations. I find that the remnants evolve towards a spherical end-state, where the rotationally-supported disk has been converted into a hot, thermally-supported envelope. I then map these results into a stellar evolution code and evolve them over thermal and nuclear timescales. This is a necessary procedure to self-consistently study the long-term outcomes of WD mergers. I apply this to the merger of two carbon-oxygen WDs with a total mass in excess of the Chandrasekhar mass. My work follows the evolution of the remnants for longer than previous calculations and finds alternating episodes of fusion and contraction can lead to the formation and subsequent collapse of an iron core. I also characterize the observable properties of the remnant during this evolution. Additionally, I develop a framework to compute weak reaction rates that are essential in the evolution of massive, accreting WDs. I apply these results to understand the evolution of oxygen-neon WDs towards accretion-induced collapse to a neutron star.

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The flow of gas through the circumgalactic medium (CGM) regulates galaxy growth over cosmic time. Observations have recently revealed a complex multi-phase structure in the CGM that has challenged many of the established theories and highlights significant gaps in our understanding of this critical aspect of galaxy formation. The spatial scales relevant to the CGM span a huge range with its structure and evolution determined by small-scale processes—such as the launching of galactic winds by clustered supernovae and thermal instability in the hydrostatic halo—and large-scale processes—such as cosmological accretion. I will describe my efforts to use controlled numerical simulations to understand the details and interplay of these multi-scale processes in order to develop a coherent picture of the CGM that is consistent with observations.

We investigate the interaction between low-frequency magnetohydrodynamic (MHD) turbulence and a distribution of charged particles. Understanding this physics is central to understanding the heating of the solar wind, as well as the heating and acceleration of other collisionless plasmas.

Our central method is to simulate weakly compressible MHD turbulence using the *Athena* code, along with a distribution of test particles which feel the electromagnetic fields of the turbulence. We also construct analytic models of transit-time damping (TTD), which results from the mirror force caused by compressible (fast or slow) MHD waves. Standard linear-theory models in the literature require an exact resonance between particle and wave velocities to accelerate particles. The models developed in this thesis go beyond standard linear theory to account for the fact that wave-particle interactions decorrelate over a short time, which allows particles with velocities off resonance to undergo acceleration and velocity diffusion. We use the test particle simulation results to calibrate and distinguish between different models for this velocity diffusion. Test particle heating is larger than the linear theory prediction, due to continued acceleration of particles with velocities off-resonance.

We also include an artificial pitch-angle scattering to the test particle motion, representing the effect of high-frequency waves or velocity-space instabilities. For low scattering rates, we find that the scattering enforces isotropy and enhances heating by a modest factor. For much higher scattering rates, the acceleration is instead due to a non-resonant effect, as particles “frozen” into the fluid adiabatically gain and lose energy as eddies expand and contract. Lastly, we generalize our calculations to allow for relativistic test particles. Linear theory predicts that relativistic particles with velocities much higher than the speed of waves comprising the turbulence would undergo no acceleration; resonance-broadening modifies this conclusion and allows for a continued Fermi-like acceleration process. This may affect the observed spectra of black hole accretion disks by accelerating relativistic particles into a quasi-powerlaw tail.

In nature, it is not unusual to find stably stratified fluid adjacent to convectively unstable fluid. This can occur in the Earth's atmosphere, where the troposphere is convective and the stratosphere is stably stratified; in lakes, where surface solar heating can drive convection above stably stratified fresh water; in the oceans, where geothermal heating can drive convection near the ocean floor, but the water above is stably stratified due to salinity gradients; possible in the Earth's liquid core, where gradients in thermal conductivity and composition diffusivities maybe lead to different layers of stable or unstable liquid metal; and, in stars, as most stars contain at least one convective and at least one radiative (stably stratified) zone. Internal waves propagate in stably stratified fluids. The characterization of the internal waves generated by convection is an open problem in geophysical and astrophysical fluid dynamics.

Internal waves can play a dynamically important role via nonlocal transport. Momentum transport by convectively excited internal waves is thought to generate the quasi-biennial oscillation of zonal wind in the equatorial stratosphere, an important physical phenomenon used to calibrate global climate models. Angular momentum transport by convectively excited internal waves may play a crucial role in setting the initial rotation rates of neutron stars. In the last year of life of a massive star, convectively excited internal waves may transport even energy to the surface layers to unbind them, launching a wind. In each of these cases, internal waves are able to transport some quantity—momentum, angular momentum, energy—across large, stable buoyancy gradients. Thus, internal waves represent an important, if unusual, transport mechanism.

This thesis advances our understanding of internal wave generation by convection. Chapter 2 provides an underlying theoretical framework to study this problem. It describes a detailed calculation of the internal gravity wave spectrum, using the Lighthill theory of wave excitation by turbulence. We use a Green's function approach, in which we convolve a convective source term with the Green's function of different internal gravity waves. The remainder of the thesis is a circuitous attempt to verify these analytical predictions.

I test the predictions of Chapter 2 via numerical simulation. The first step is to identify a code suitable for this study. I helped develop the Dedalus code framework to study internal wave generation by convection. Dedalus can solve many different partial differential equations using the pseudo-spectral numerical method. In Chapter 3, I demonstrate Dedalus' ability to solve different equations used to model convection in astrophysics. I consider both the propagation and damping of internal waves, and the properties of low Rayleigh number convective steady states, in six different equation sets used in the astrophysics literature. This shows that Dedalus can be used to solve the equations of interest.

Next, in Chapter 4, I verify the high accuracy of Dedalus by comparing it to the popular astrophysics code Athena in a standard Kelvin–Helmholtz instability test problem. Dedalus performs admirably in comparison to Athena, and provides a high standard for other codes solving the fully compressible Navier–Stokes equations. Chapter 5 demonstrates that Dedalus can simulate convective adjacent to a stably stratified region, by studying convective mixing near carbon flames. The convective overshoot and mixing is well-resolved, and is able to generate internal waves.

Confident in Dedalus' ability to study the problem at hand, Chapter 6 describes simulations inspired by water experiments of internal wave generation by convection. The experiments exploit water’s unusual property that its density maximum is at 4C, rather than at 0C. We use a similar equation of state in Dedalus, and study internal gravity waves generation by convection in a water-like fluid. We test two models of wave generation: bulk excitation (equivalent to the Lighthill theory described in Chapter 2), and surface excitation. We find the bulk excitation model accurately reproduces the waves generated in the simulations, validating the calculations of Chapter 2.

Massive stars are the ultimate source for nearly all the elements necessary for life. The first stars forge these elements from the sparse set of ingredients supplied by the Big Bang, and distribute enriched ashes throughout their galactic homes via their winds and explosive deaths. Subsequent generations follow suit, assembling from the enriched ashes of their predecessors. Over the last several decades, the astrophysics community has developed a sophisticated theoretical picture of the evolution of these stars, but it remains an incomplete accounting of the rich set of observations. Using state of the art models of massive stars, I have investigated the internal processes taking place throughout the life-cycles of stars spanning those from the first generation (“Population III”) to the present-day (“Population I”). I will argue that early-generation stars were not highly unstable to perturbations, contrary to a host of past investigations, if a correct accounting is made for the viscous effect of convection. For later generations, those with near solar metallicity, I find that this very same convection may excite gravity-mode oscillations that produce observable brightness variations at the stellar surface when the stars are near the main sequence. If confirmed with modern high-precision monitoring experiments, like *Kepler* and *CoRoT*, the properties of observed gravity modes in massive stars could provide a direct probe of the poorly constrained physics of gravity mode excitation by convection. Finally, jumping forward in stellar evolutionary time, I propose and explore an entirely new mechanism to explain the giant eruptions observed and inferred to occur during the final phases of massive stellar evolution. This mechanism taps into the vast nuclear fusion luminosity, and accompanying convective luminosity, in the stellar core to excite waves capable of carrying a super-Eddington luminosity out to the stellar envelope. This energy transfer from the core to the envelope has the potential to unbind a significant amount of mass in close proximity to a star's eventual explosion as a core collapse supernova.

Galaxy clusters are the most massive structures in the universe and, in the hierarchical pattern of cosmological structure formation, the largest objects in the universe form last. Galaxy clusters are thus interesting objects for a number of reasons. Three examples relevant to this thesis are:

1. Constraining the properties of dark energy: Due to the hierarchical nature of structure formation, the largest objects in the universe form last. The cluster mass function is thus sensitive to the entire expansion history of the universe and can be used to constrain the properties of dark energy. This constraint complements others derived from the CMB or from Type Ia supernovae and provides an important, independent confirmation of such methods. In particular, clusters provide detailed information about the equation of state parameter w because they sample a large redshift range z ∼ 0 − 1.

2. Probing galaxy formation: Clusters contain the most massive galaxies in the uni- verse, and the most massive black holes; because clusters form so late, we can still witness the assembly of these objects in the nearby universe. Clusters thus provide a more detailed view of galaxy formation than is possible in studies of lower-mass ob- jects. An important example comes from x-ray studies of clusters, which unexpectedly found that star formation in massive galaxies in clusters is closely correlated with the properties of the hot, virialized gas in their halos. This correlation persists despite the enormous separation in temperature, in dynamical time-scales, and in length-scales between the virialized gas in the halo and the star-forming regions in the galaxy. This remains a challenge to interpret theoretically.

3. Developing our knowledge of dilute plasmas: The masses and sizes of galaxy clusters imply that the plasma which permeates them is both very hot (∼ 108 K) and very dilute (∼ 10−2 cm−3). This plasma is collisional enough to be considered a fluid, but collisionless enough to develop significant anisotropies with respect to the local magnetic field. This interesting regime is one of the frontiers in theoretical studies of fluid dynamics. Unlike other astrophysical environments of similar collisionality (e. g. accretion disk coronae), galaxy clusters are optically thin and subtend large angles on the sky. Thus, they are easily observed in the x-ray (to constrain thermal processes) and in the radio (to constrain non-thermal processes) and provide a wonderful environment to develop our understanding of dilute plasmas.

This thesis studies the dynamics of the hot gas in galaxy clusters, which touches on all three of the above topics.

Chapter 2 shows that galaxy clusters are likely to be unstable to a new, vigorous form of convection. As a dynamical process which involves thermodynamic and magnetic properties of the gas, this convection bears directly on our understanding of the physics of dilute plas- mas. Furthermore, by moving metals and thermal energy through the cluster, convection may change the cooling rate of the gas and thus significantly impact the process of galaxy formation. Cluster convection also impacts the use of clusters as cosmological probes. Con- vection may drive turbulence in clusters with mean Mach numbers of order-unity. This changes the force balance in clusters, decreasing the thermal energy of a cluster of a given mass. Current methods for using clusters to constrain dark energy rely on observational probes of the thermal energy as a proxy for total mass. The accuracy of these methods depends on how vigorous cluster convection is.

Chapter 3 studies thermal instability in galaxy clusters. I argue that clusters are all likely to be thermally unstable, but that this instability only grows to large amplitude in a subset of systems. Later studies have applied this result to galaxy formation in clusters and shown that one can reproduce some features of the well-known non-self-similarity at the high mass end of the galaxy luminosity function.

Chapters 4 and 5 extends my work on convection (and, eventually, thermal instability) to consider the cosmological context of galaxy formation. This work aims to remove any arbitrary initial and boundary conditions from my simulations and is an important step toward a self-consistent model for the plasma physics in clusters.

A star that wanders too close to the massive black hole (BH) in the center of a galaxy is headed for trouble: within a distance *r*_{T} ~ *r*_{*}(*M*_{BH}/*M*_{*})^{1/3} (where *r*_{*} and *M*_{*} are the star's radius and mass, and *M*_{BH} is the BH's mass), the BH's tidal gravity overcomes the binding gravity of the star, and the star is shredded into a stream of stellar debris. Studying this process of tidal disruption has the potential to give us insights into how central BHs and their surrounding stellar population grow and evolve. Motivated by new and upcoming rapid-cadence optical transient surveys, which should detect and allow study of tidal disruption events (TDEs) in unprecedented detail, I make theoretical predictions of the observable properties of these events to aid in their detection, identification, and interpretation. I find that stellar debris falling towards the BH is likely driven off again by radiation pressure at early times when the feeding rate is super-Eddington: this outflow has a large photosphere and relatively cool temperature, producing a luminous (~ 10^{43} - few × 10^{44} erg s^{-1}) transient event at *optical* wavelengths. I predict that new transient surveys such as the Palomar Transient Factory are likely to find tens to hundreds of these events. I further predict the spectroscopic signature of super-Eddington outflows&mdash broad, blueshifted absorption lines in the ultraviolet&mdash which should help confirm and teach us more about TDE candidates. Finding that the observable appearance of TDEs depends not only on BH mass but on pericenter radius of the star's last fateful orbit, I derive a theoretical expression for the disruption rate as a function of pericenter and apply it to the galaxy NGC 4467 using real observational data, laying the groundwork for more extensive studies in the future. Finally, I also present my work on the debris disk surrounding the star AU Mic, in which I propose an explanation for the physical processes of dust dynamics that give rise to the observed disk profile.

We consider three aspects of tidal interactions in close binary systems. 1) We first develop a framework for predicting and interpreting photometric observations of eccentric binaries, which we term tidal asteroseismology. In such systems, the Fourier transform of the observed lightcurve is expected to consist of pulsations at harmonics of the orbital frequency. We use linear stellar perturbation theory to predict the expected pulsation amplitude spectra. Our numerical model does not assume adiabaticity, and accounts for stellar rotation in the traditional approximation. We apply our model to the recently discovered Kepler system KOI-54, a 42-day face-on stellar binary with e=0.83. Our modeling yields pulsation spectra that are semi-quantitatively consistent with observations of KOI-54. KOI-54's spectrum also contains several nonharmonic pulsations, which can be explained by nonlinear three-mode coupling. 2) We next consider the situation of a white dwarf (WD) binary inspiraling due to the emission of gravitational waves. We show that resonance locks, previously considered in binaries with an early-type star, occur universally in WD binaries. In a resonance lock, the orbital and spin frequencies evolve in lockstep, so that the tidal forcing frequency is approximately constant and a particular normal mode remains resonant, producing efficient tidal dissipation and nearly synchronous rotation. We derive analytic formulas for the tidal quality factor and tidal heating rate during a g-mode resonance lock, and verify our results numerically. We apply our analysis to the 13-minute double-WD binary J0651, and show that our predictions are roughly consistent with observations. 3) Lastly, we examine the general dynamics of resonance locking in more detail. Previous analyses of resonance locking, including my own earlier work, invoke the adiabatic (a.k.a. Lorentzian) approximation for the mode amplitude, valid only in the limit of relatively strong mode damping. We relax this approximation, analytically derive conditions under which the fixed point associated with resonance locking is stable, and further check our analytic results with numerical integration of the coupled mode, spin, and orbital evolution equations. These show that resonance locking can sometimes take the form of complex limit cycles or even chaotic trajectories. We also show that resonance locks can accelerate the course of tidal evolution in eccentric systems.

Sagittarius A* (Sgr A*), the roughly 4 million solar mass black hole at the center of our galaxy, is arguably the best natural test-bed for supermassive black hole accretion models. Its close proximity allows for detailed observations to be made across the electromagnetic spectrum that provide strong, multi-scale constraints on analytic and numerical calculations. These include exciting new event horizon scale results that directly probe the strong field regime for the first time. Spanning roughly 7 orders of magnitude in radius, the accretion system begins at ~ parsec scales where a large population of Wolf-Rayet (WR) stars interact via powerful stellar winds. A fraction of the wind material accretes to the event horizon scales, heating up and radiating on the way down to provide the observed multi-wavelength emission. Detailed modeling of this process requires 3D numerical simulations spanning as large of a dynamical range as possible. The goal of this thesis has been to improve the predictive power of such simulations applied to Sgr A* by limiting the number of free parameters that they contain. This is done by incorporating more theoretical and observational knowledge into the calculations, for example, what collisionless physics tells us about how electrons/ions are heated in a turbulent medium and the properties of the winds of the WR stars. The resulting simulations have shown excellent agreement with a wide range of observational constraints and could have major implications for how the accretion flow around Sgr A* is modeled in the future. The techniques presented here are also applicable to other low luminosity AGN and X-ray binaries.

The usefulness of large-scale structure as a probe of cosmology and structure formation is increasing as large deep surveys in multi-wavelength bands are becoming possible. The observational analysis of large-scale structure guided by large volume numerical simulations are beginning to offer us complementary information and crosschecks of cosmological parameters estimated from the anisotropies in Cosmic Microwave Background (CMB) radiation. Understanding structure formation and evolution and even galaxy formation history is also being aided by observations of different redshift snapshots of the Universe, using various tracers of large-scale structure.

This dissertation work covers aspects of large-scale structure from the baryon acoustic oscillation scale, to that of large scale filaments and galaxy clusters. First, I discuss a large- scale structure use for high precision cosmology. I investigate the reconstruction of Baryon Acoustic Oscillation (BAO) peak within the context of Lagrangian perturbation theory, testing its validity in a large suite of cosmological volume N-body simulations. Then I consider galaxy clusters and the large scale filaments surrounding them in a high resolution N-body simulation. I investigate the geometrical properties of galaxy cluster neighborhoods, focusing on the filaments connected to clusters. Using mock observations of galaxy clusters, I explore the the correlations of scatter in galaxy cluster mass estimates from multi-wavelength observations and different measurement techniques. I also examine the sources of the correlated scatter by considering the intrinsic and environmental properties of clusters.