Accreting neutron stars in low-mass X-ray binary (LMXB) systems provide an avenue for studyingthe thermal properties of the crust and core. When material falls onto a neutron star’s surface, the matter in its outer layers is compressed and nuclear reactions are induced. In quasi-persistent transient systems, accretion outbursts last years to decades followed by periods of quiescence that can last years to decades. During an outburst, the accretion-induced reactions heat the crust out of thermal equilibrium with the core. When accretion ends, the core cools back into thermal equilibrium with the core which we can observe as a decrease in surface temperature: the cooling curve. The shape of the cooling curve depends on the thermal properties of the crust. In this work, I model the thermal evolution of the crust. By fitting models to observed cooling curves, I estimate the crust properties such as the core temperature (?c), the impurity of the composition (?imp), and the accretion-induced heating in the shallow layers (?sh) and depths of the crust (?in). Prior to this work, the cooling curves of several LMXBs have been independently analyzed. It is unknown to what extent different neutron stars share crust properties, such as composition and accretion-induced heating. In this thesis, I perform joint fits of five LMXBs, in which I simultaneously fit the cooling curves of all sources with the value of ?imp, ?sh, or ?in being shared across all sources. I compare the goodness-of-fit of the joint fits to independent fits for each source. I find that jointly fitting ?imp or ?sh has little impact on the quality of the fits, suggesting that the sources either do share the same value for these parameters or that the data does not sufficiently constrain them. When jointly fitting ?sh, the quality of the fits significantly decreases, suggesting that different sources must have different values of ?sh. The predicted composition, accretion-induced heating rates, and location of heat release depend on the behavior of free neutrons in the deep crust. Crust models that allow free neutrons to diffuse throughout the inner crust predict that the crust is more pure and the inner heating rate is lower than models that do not. Additionally, some nuclear models predict the existence of non-spherical “pasta” phases of nuclear matter at the bottom of the crust. A pasta layer acts as a thermally insulating layer in thermal evolution models and its presence affects the rate of cooling. I compare models that allow neutron diffusion to those that do not, and models with pasta layers to those that do not by estimating the Bayesian evidence with nested modeling. I find that the cooling curves of the five LMXBs to which I fit the models do not consistently favor the same models. This is inconsistent with expectations because the the existence of pasta and diffusion of free neutrons depend solely on the local density; in particular, they are not expected to depend on the accretion history and therefore should not differ among neutron stars.
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