Sensitivity of Neutron Star Properties to the Equation of State

The subject of this doctoral dissertation is to study the equations of state of nuclear and neutron-star matter. We tackle this problem by employing several models of the relativistic effective interactions. The relativistic effective interactions and their applications to the ground-state properties of medium to heavy nuclei have enjoyed enormous success for the past three decades. With just a few model parameters calibrated to the ground state properties of the closed-shell nuclei, these models exhibit and encode a great amount of physics. However, theses models are untested far away from their narrow window of applicability. In particular, while these models tend to agree on the saturation properties of symmetric nuclear matter, they largely disagree on its density and isospin dependence, especially in the region of high densities and large proton-neutron asymmetries. In order to better understand the properties of nuclear matter at these extreme regions of isospin asymmetry and high-densities, we will apply these models to predict several neutron star properties. Since the matter in the neutron stars are very neutron-rich, while the density of matter in neutron stars spans over a wide range of magnitudes, these compact objects remain unique laboratories for probing the equation of state of neutron-rich matter under conditions unattainable by terrestrial experiments. Thus it is expected that at least the following neutron star properties must be sensitive to the underlying equation of state: maximum mass, typical radii, moments of inertia (both total and crustal), redshifts, and cooling mechanism. We present numerical solutions and in some cases also analytical solutions to each of the properties above. In particular, the sensitivity of the stellar moment of inertia to the neutron-star matter equation of state is examined using accurately-calibrated relativistic mean-field models. We probe this sensitivity by tuning both the density dependence of the symmetry energy and the high density component of the equation of state, properties that are at present poorly constrained by existing laboratory data. Particularly attractive is the study of the fraction of the moment of inertia contained in the solid crust. Analytic treatments of the crustal moment of inertia reveal a high sensitivity to the transition pressure at the core-crust interface. Motivated by a recent astrophysical measurement of the pressure of cold matter above nuclear-matter saturation density, we compute the equation of state of neutron-star matter using various accurately calibrated relativistic models. We found the predictions of these models to be in fairly good agreement with the measured equation of state. In the effort to explain the observational data we introduce a new relativistic effective interaction that is simultaneously constrained by the properties of finite nuclei, their collective excitations, and neutron-star properties. By adjusting two of the empirical parameters of the theory, one can efficiently tune the neutron skin thickness of $^{208}$Pb and the maximum neutron star mass. The new effective interaction is moderately soft at intermediate densities and relatively stiff at high densities. It is fitted to a neutron skin thickness in $^{208}$Pb of only $R_{rm n} - R_{rm p} = 0.16$ fm and a moderately large maximum neutron star mass of 1.94 $M_{rm Sun}$ consistent with the latest observation. Last, theoretical uncertainties in the predictions of relativistic mean-field models are estimated using a chi-square minimization procedure that is implemented by studying the small oscillations around the chi-square minimum. It is shown that such statistical analysis provides access to a wealth of information that would normally remain hidden. The power of covariance analysis is illustrated in two relativistic mean field models. By performing this analysis one obtains meaningful theoretical uncertainties for both model parameters and predicted observables. Moreover, it is shown, how covariance analysis is able to establish robust correlations between physical observables.