Neutron stars are amongst the most compact and exotic objects in the universe. When born in pairs, their eventual merging is responsible for some of the most energetic phenomena and plays a significant role in the chemical evolution of galaxies. This thesis combines analytical calculations with observations of stellar abundances to gain further insight into how these binaries are formed and the nucleosynthesis that takes place once they eventually merge under the influence of gravitational radiation.

We derive a relation between key parameters governing the process of bringing neutron stars to separations at which they are able to merge within a Hubble time. We also examine the conditions at the onset of a stellar merger through detailed stellar modeling of an observed progenitor system. We utilize observed stellar abundances to place stringent constraints on the progenitor site of r-process nucleosynthesis and find it to be consistent with expectations from neutron star mergers. We further utilize these stellar abundances to place constraints on another proposed site of the r-process, namely the collapsar, and find the abundances to be in tension with theoretical predictions of the model. Finally, we use stellar abundances to make predictions of future electromagnetic transients to be detected from these mergers and to test their viability as an r-process production mechanism throughout cosmic time.

In this dissertation, we combine two different approaches — chemical evolution modeling and direct observations of the gas distributed around a galaxy — to study the gas cycling into and out of galaxies. The interplay of fundamental astrophysical processes that drive this baryon cycle, such as star formation and evolution, gas accretion from the cosmic web, and galactic winds, shapes the evolution of galaxies. These processes also determine the galactic gas enrichment history which is preserved in the stellar abundances of low mass stars that are still alive today. Therefore, stellar chemical abundance patterns can be used to indirectly illuminate the evolution of gas in and around galaxies.

For the first part of this thesis, we build a flexible one-zone chemical evolution model to decode the star-by-star abundance patterns of nearby galaxies or the average abundance ratios derived from the integrated-light of distant galaxies. We characterize how and why these processes affect the observed stellar abundances and validate our code by modeling the stellar abundances of the Milky Way's geometrically-selected thick disk. We then utilize our chemical evolution model to help elucidate how the stellar populations of elliptical galaxies can simultaneously exhibit greater $\alpha$-enhancement and higher metallicities with increasing galaxy mass. Recent papers suggest that more massive ellipticals require more top-heavy IMFs. In contrast, we find that while a galaxy-mass dependent IMF is not precluded, the abundance patterns of these galaxies can also be explained if more massive ellipticals form their stars on shorter timescale and have outflows that are less enriched and/or are less efficiently driven by supernovae.

In the second part of this thesis, we present direct observations of emission from a very bright enormous Lyman-$\alpha$ nebula (the Slug) that is illuminated by a nearby quasar at $z\sim2.3$. This is a rare opportunity to examine the physical properties of gas surrounding a galaxy that even extends beyond the halo into the intergalactic medium. We successfully detect H$\alpha$ emission from the Slug, indicating that the observed Ly$\alpha$ is produced \textemph{in situ} by hydrogen recombination and traces highly-ionized, optically-thick, dense clumps of cool gas.

One of the most promising avenues for studying supermassive black holes (SMBHs) in the local Universe is through tidal disruption events (TDEs). TDEs occur when unlucky stars pass too close to a black hole and are torn apart and consumed. This often pushes the black holes to their critical Eddington limits, outshining their galactic centers and encoding the resultant light curves with a wealth of information about the disrupter and disruptee (e.g. Rees et al. 1988). Observations of TDEs are quickly becoming commonplace (e.g. van Velzen et al. 2020), with over 50 confirmed disruptions discovered in the last decade, and thousands more expected to be observed by upcoming time-domain surveys such as the Vera Rubin Observatory. These phenomena provide an exciting opportunity to study SMBHs in quiescent galaxies, the stellar populations in galactic nuclei, and the physics of black hole accretion under well defined conditions. In this thesis I develop a new model for the light curves of tidal disruption events, and combine it with data from observed tidal disruption events and dynamical models of galactic nuclei to learn about the properties and evolution of the supermassive black holes at the centers of galaxies as well as the stars that surround them.

I first describe the components of the light curve model, and use it to fit a population of observed TDEs. I show that the model can estimate the masses of the disrupting black holes as well as other properties of the system. I then use energy and efficiency estimates from the models to constrain the emission mechanism, as the source of the emission for the majority of these transients is hidden inside a layer of stellar debris and cannot be observed directly. I compare my results to similar measurements of active galactic nuclei. Next, I combine the light curve models with data from the spectra and host galaxies of TDEs to put constraints on the masses of disrupted stars for several events. I find that they have high nitrogen-to-carbon abundances, implying stellar masses $\gtrsim 1 - 2 M_\odot$. These `moderately massive' stars are over-represented by a factor of $\gtrsim 10^2$ compared to the overall stellar population of the hosts. Finally, I explore how SMBH binaries can increase the rates of tidal disruptions in post-merger galaxies, and how TDEs can, in turn, help us discover SMBH binaries.

This thesis uses computational modeling to study of phases of dramatic interaction that intersperse stellar lifetimes. In galactic centers stars trace dangerously wandering orbits dictated by the combined gravitational force of a central, supermassive black hole and all of the surrounding stars. In binary systems, stars' evolution -- which causes their radii to increase substantially -- can bring initially non-interacting systems into contact. Moments of strong stellar interaction transform stars, their subsequent evolution, and the stellar environments they inhabit.

In tidal disruption events, a star is partially or completely destroyed as tidal forces from a supermassive black hole overwhelm the star's self gravity. A portion of the stellar debris falls back to the black hole powering a luminous flare as it accretes. This thesis studies the relative event rates and properties of tidal disruption events for stars across the stellar evolutionary spectrum. Tidal disruptions of giant stars occur with high specific frequency; these objects' extended envelopes make them vulnerable to disruption. More-compact white dwarf stars are tidally disrupted relatively rarely. Their transients are also of very different duration and luminosity. Giant star disruptions power accretion flares with timescales of tens to hundreds of years; white dwarf disruption flares take hours to days. White dwarf tidal interactions can additionally trigger thermonuclear burning and lead to transients with signatures similar to type I supernovae.

In binary star systems, a phase of hydrodynamic interaction called a common envelope episode occurs when one star evolves to swallow its companion. Dragged by the surrounding gas, the companion star spirals through the envelope to tighter orbits. This thesis studies accretion and flow morphologies during this phase. Density gradients across the gravitationally-focussed material lead to a strong angular momentum barrier to accretion during common envelope. Typical accretion efficiencies are in the range of 1 percent the Hoyle-Lyttleton accretion rate. This implies that compact objects embedded in common envelopes do not grow significantly during this phase, increasing their mass by at most a few percent. This thesis models the properties of a recent stellar-merger powered transient to derive constraints on this long-uncertain phase of binary star evolution.

A physical understanding of the high energy interactions between black holes and stars, coupled with the context of their galactic birthplaces, will allow us to use these systems as tools to better understand black holes at all masses, the lives and deaths of stars, and the dynamics in galactic centers. This dissertation is concerned with interactions at different physical scales: At the solar radius scale, we present the first simulations of successful common envelope ejection leading to binary neutron star formation in 3D hydrodynamics. At the AU scale, we discuss the tidal disruption of a star by a supermassive black hole. We construct the "tidal disruption menu" of objects and black holes that lead to observable tidal disruption flares. We use an analytic framework to calculate the composition of the fallback material onto the supermassive black hole as a function of time. We present the first simulations of tidal disruptions of stars with realistic structures and compositions, which predict abundance anomalies at the peak timescale. We present the STARS library, a grid of simulations interpolated to provide the mass fallback rate to the black hole for a main-sequence star of any mass, age, and impact parameter. We show that all of our simulations can be reduced to a single relationship. Connecting these phenomena to kpc-scale galaxy physics, we present a systematic study of tidal disruption event host galaxies in the context of the local galaxy population, and in particular our finding that they are highly centrally concentrated. Finally, at cosmological scales, we present a study on the obstacles to constructing de Sitter space in theories of quantum gravity. We find that, within controlled approximations, one lacks the tools to construct de Sitter space in string theory.

This thesis focuses on describing what happens when a binary neutron star merges. It uses numerical simulations to study the different dominant physics before and after the merger. In August 17, 2017, the first binary neutron star merger was observed by LIGO/Virgo, the gravitational wave observatory. Great efforts by astronomers all around the globe allowed for the electromagnetic follow-up of the event. The discovery, named GW170817, showed evidence that binary neutron stars can produce gamma-ray bursts, and also synthesize heavy elements, such as gold and platinum.

This thesis studies the intriguing question of how binary neutron stars have been able to assemble and merge within the timespan the Universe has existed. One of the preferred channels is called common envelope evolution. This happens when, in a binary of massive stars, the more massive star (the primary) evolves, expands and engulfs its companion. Drag forces from the envelope slow down the companion and tighten the orbit. The energy from the orbit will be transferred to the envelope and will potentially have enough energy to unbind the envelope. The result is the very rapid creation of a tighter binary. This thesis studies the accretion flows around the companion, given that the envelope has a gradient. Material will be focused on the companion (the secondary), but due to the density gradient, there will be an angular momentum barrier that inhibits accretion onto the secondary. We study how different microphysical parameters of the envelope affect the angular momentum redistribution.

It is widely believed that the merger of GW170817 was a hyper-massive neutron star that after a certain delay time collapsed into a black hole surrounded by an accretion disk. Material in the disk will lose angular momentum due to magnetic stresses, eventually falling into the black hole and driving a relativistic, beamed jet. The jet will interact with winds launched during the hyper-massive neutron star phase. This thesis studies jet-wind interactions, since they lead to non-thermal emission. We used numerical simulations in order to constrain certain parameters of the binary itself, such as the delay time between the merger and the collapse to a black hole.

Several other outfows are expected to occur after the merger, including an outflow driven from magnetic stresses in the accretion disk. The outflow will cool, expand and create heavy elements via the r-process. This elements will then radioactivelydecay and be observed. In the inner regions of the disk, the high temperatures and densities will ignite the creation of neutrinos and anti-neutrinos via weak reactions. In the outer region of the disk, free nucleons will recombine into alpha-particles, which will release nuclear binding energy. Both the neutrinos and the recombination energy will greatly affect the outflow, especially the electron fraction. The electron fraction is key in determining the final abundance of elements. This thesis studies the impact that neutrinos and a finite-temperature equation of state have on the outflow.

At the simplest level, gravitational sources are considered to be point-like and in solitude, with a radial force that falls off as r^-2. In reality, all astrophysical objects aside from black holes are extended in space, and can be deformed by the tidal forces arising from the proximity of companion objects with large average densities. When these forces are weak, the response of an object to a tide can be through a decomposition into basis functions, but this approach fails when the tide is strong enough to deform an object by a distance equal to its own size. Under these circumstances, a hydrodynamical representation of the object is required to understand the true tidal response.

In this thesis, we present a number of examples of physical systems in which tides dominate the dynamics. First, we consider the case of a star that encounters a supermassive black hole (SMBH) in a deeply penetrating encounter, resulting in a dramatic compression that produces shocks that would be observable in the X-ray. Second, we present the results of hydrodynamical simulations that demonstrate a new mechanism for igniting Type Ia supernovae from binary systems composed of two white dwarfs undergoing Roche-lobe overflow. Third, we investigate the survival prospects of giant planets that have been scattered into highly eccentricity orbits and are exposed to a strong tide applied by their parent star. Fourth, we systematically map the fallback rate resulting from the tidal disruptions of stars by SMBHs. Finally, we use what we have learned about the feeding rate to model determine the highest-likelihood model for an observed prototypical tidal disruption event.

In the era of transient, multimessenger astrophysics, dramatic interactions between stellar partners are an essential ingredient in the production of the fantastic light show to which we bear witness. Common envelope interactions, in which a star engulfs a companion, are commonly invoked as the presumed formation channel of numerous exotic close binaries and merger products, from binary black holes to too-bright Algol-type stars and the elusive Thorne-Zytkow object. In this dissertation, I apply a combination of semi-analytical models and high-resolution hydrodynamical simulations in different dimensionalities to understand the role of inspiral dynamics in defining post-common envelope outcomes and to further the development of a fully descriptive, predictive theoretical framework for common envelope. I first define the range of applicability for the common envelope drag formalism, which offers a potential alternative to both global simulations and the oversimplified energy formalism in widespread use to model common envelope outcomes. I then develop a semi-analytical framework as an alternative to the energy formalism that incorporates the physical timescales most relevant to common envelope inspiral to predict how a common envelope event will proceed. Shifting to a focus on specific outcomes, I present a numerical framework that combines one- and three-dimensional hydrodynamics to capture the computationally restrictive range of timescales relevant to stellar mergers, constraining the origins of the B[e] supergiant R4 in the Small Magellanic Cloud as a post-common envelope merger product. Finally, I demonstrate through analytical and numerical modeling of merger via common envelope that Thorne-Zytkow objects are likely not a product of common envelope evolution in field binaries.

Star formation cannot proceed without the existence of an extensive gas reservoir. In particular, the supply of gas to form stars in dwarf galaxies and star clusters requires overcoming a variety of difficulties - namely, the effectiveness of different feedback mechanisms in removing gas from these shallow gravitational potentials. In addition, the supply of external gas to these systems is determined by the large scale galactic structure in which they reside. This thesis employs computational hydrodynamics coupled with physically realistic subgrid feedback prescriptions to resolve the interplay between the small scale feedback mechanisms and larger scale gas flows to determine the amount of gas a shallow potential can accumulate.

First, we consider the flow of gas external to dwarf galaxies and star clusters into their cores as a generalized accretion process. Second, we explore the enhancement of gas accretion rates onto the compact members of young star clusters when the flow of external gas into the cluster cores is large. Third, we discuss how external gas flows initiated by the presence of a massive nuclear star cluster can enhance central massive black hole accretion rates during galaxy mergers. Fourth, we change our focus to exploring internal stellar wind retention in proto-globular clusters as a mechanism to supply gas for multiple episodes of star formation. Finally, the implications of stellar wind retention on the current gas reservoir in globular clusters is discussed.