In this dissertation, four topics related to the physics and astrophysics of neutron stars are studied. Two first topics deal with microscopical physics processes in the star outer crust and the last two with macroscopical properties of a star, such as mass and radius.
In the first topic, the thermodynamical and transport properties of a dilute gas in which particles interact through a delta-shell potential are investigated. Through variations of a single parameter related to the strength and size of the delta-shell potential, the scattering length and effective range that determine the low-energy elastic scattering cross sections can be varied over wide ranges including the case of the unitary limit (infinite scattering length). It is found that the coefficients of shear viscosity, thermal conductivity and diffusion all decrease when the scattering length becomes very large and also when resonances occur as the temperature is increased. The calculated ratios of the shear viscosity to entropy density as a function of temperature for various interaction strengths (and therefore scattering lengths) were found to lie well above the recently suggested minimal value of (4π)-1 ℏ/kB. A new result is the value of (4/5) for the dimensionless ratio of the energy density times the diffusion coefficient to viscosity for a dilute gas in the unitary limit. Whether or not this ratio changes upon the inclusion of more than two-body interactions is an interesting avenue for future investigations. These investigations shed pedagogical light on the issue of the thermal and transport properties of an interacting system in the unitary limit, of much current interest in both atomic physics and nuclear physics in which very long scattering lengths feature prominently at very low energies.
In the second topic, the shear viscosity of a Yukawa liquid, a model for the outer crust of a neutron star, is calculated in both the classical and quantum regimes. Results of semi-analytic calculations in both regimes are presented for various temperatures and densities, and compared with those of classical molecular dynamical simulations performed for the same system by collaborators from Indiana University. For heavy-ion plasmas, as energetically favored in the outer crust of a neutron star, excellent agreement was found between the results of semi-analytic calculations and those of molecular dynamical simulations. However, in the case of light-ion plasmas, substantial differences were found between the results of quantum and classical cases, which underscores the importance of incorporating quantum effects in molecular dynamical simulations, even in the dilute limit.
In the third topic, first steps are taken to reconstruct the uncertain high-density nuclear equation of state from the measured masses and radii of several individual stars. Inherent errors of the measurements are incorporated into the analysis. A new inversion procedure of the Tolman-Oppenheimer-Volkov stellar structure equation is developed so that a model independent dense matter of equation can be derived from observations. Successful tests of the inversion procedure emphasize the need to determine the masses and especially the radii of several individual stars. The aim here is to provide a benchmark equation of state for theoretical advances to be made.
The fourth topic is concerned with the emerging field of gravitational-wave detections and its ability to shed light on the dense matter equation of state. In an external tidal gravitational field, as for example in binary star configurations, each star deforms and acquires a quadrupole moment. The quadrupole polarizability given by the coefficient of proportionality between the induced moment and the field called the tidal Love number after the English mathematician Love. By calculating Love numbers for several model equations of state, connections between the underlying equation of state, star structure and the tidal Love numbers of normal neutron stars and self-bound strange quark matter stars are established. It is shown that the measurement of the Love number from the gravitational signals produced from inspiraling binaries can distinguish between normal and self-bound structures of neutron stars as they are characterized by distinctly different magnitudes of Love numbers.