Physics of Compact Stars

This thesis starts with a pedagogical introduction to the study of white dwarfs and neutron stars. We will present a step-by-step study of compact stars in hydrostatic equilibrium leading to the equations of stellar structure. Through the use of a simple finite-difference algorithm, solutions to the equations for stellar structure both for white dwarfs and neutron stars are presented. While doing so, we will also introduce the physics of the equation of state and insights on dealing with units and rescaling the equations. The next project consists of the development of a 'semi-classical' model to describe the equation of state of neutron-rich matter in the 'Coulomb frustrated' phase known as nuclear pasta. In recent simulations we have resorted to a classical model that, while simple, captures the essential physics of the nuclear pasta, which consists of the interplay between long range Coulomb repulsion and short range nuclear attraction. However, for the nuclear pasta the de Broglie wavelength is comparable to the average inter-particle separation. Therefore, fermionic correlations are expected to become important. In an effort to address this challenge, a fictitious 'Pauli potential' is introduced to mimic the fermionic correlations. In this thesis we will examine two issues. First, we will address some of the inherent difficulties in a widely used version of the Pauli potential. Second, we will refine the potential in a manner consistent with the most basic properties of a degenerate free Fermi gas, such as its momentum distribution and its two-body correlation function. With the newly refined potential, we study various physical observables, such as the two-body correlation function via Metropolis Monte-Carlo simulations.