"When the most massive stars perish, their cores may remain intact in the form of extremely dense and compact stars. These stellar remnants, called neutron stars, are on the cusp of becoming black holes and reach mass densities greater than an atomic nucleus in their centers. Although the interiors of neutron stars were difficult to investigate at the time of their discovery, the advent of modern space-based telescopes (e.g., Chandra X-ray Observatory) has pushed our understanding of the neutron star interior into exciting new realms. It has been shown that the neutron star interior spans an enormous range of densities and contains many phases of matter, and further theoretical progress must rely on numerical calculations of neutron star phenomena built with detailed nuclear physics input. To further investigate the properties of the neutron star interior, this dissertation constructs numerical models of neutron stars, applies models to various observations of neutron star high-energy phenomena, and draws new conclusions about the neutron star interior from these analyses. In particular, we model the neutron star's outermost 2248 1 km that encompasses the neutron star's envelope, ocean, and crust. The model must implement detailed nuclear physics to properly simulate the hydrostatic and thermal structure of the neutron star. We then apply our model to phenomena that occur in these layers, such as: thermonuclear bursts in the envelope, g-modes in the ocean, torsional oscillations of the crust, and crust cooling of neutron star transients. A comparison of models to observations provides new insights on the properties of dense matter that are often difficult to probe through terrestrial experiments. For example, models of the quiescent cooling of neutron stars, such as the accreting transient MAXI J0556-332, at late times into quiescence probe the thermal transport properties of the deep neutron star crust. This modeling provides independent data from astronomical observations on the nature of neutron superfluidity and the thermal conductivity of nuclear pasta. Our neutron star modeling efforts also pose new questions. For instance, reaction networks find that neutrino emission from cycling nuclear reactions is present in the neutron star ocean and crust, and potentially cools an accreting neutron star. This is a theory we attempt to verify using observations of neutron star transients and thermonuclear bursts, although it remains unclear if this cooling occurs. Furthermore, on some accreting neutron stars, more heat than supplied by nuclear reactions is needed to explain their high temperatures at the outset of quiescence. Although the presence of heating anomalies seems common, the source of extra heating is difficult to determine."--Pages ii-iii.
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