No abstract

The structure of neutron stars is considered from theoretical and observational perspectives. We demonstrate an important aspect of neutron star structure : the neutron star radius is primarily determined by the behavior of the pressure of matter in the vicinity of nuclear matter equilibrium density. In the event that extreme softening does not occur at these densities, the radius is virtually independent of the mass and is determined by the magnitude of the pressure. For equations of state with extreme softening or those that are self-bound, the radius is more sensitive to the mass. Our results show that in the absence of extreme softening, a measurement of the radius of a neutron star more accurate than about 1 km will usefully constrain the equation of state. We also show that the pressure near nuclear matter density is primarily a function of the density dependence of the nuclear symmetry energy, while the nuclear incompressibility and skewness parameters play secondary roles. In addition, we show that the moment of inertia and the binding energy of neutron stars, for a large class of equations of state, are nearly universal functions of the starÏs compactness. These features can be understood by considering two analytic, yet realistic, solutions of EinsteinÏs equations, by, respectively, Buchdahl and Tolman. We deduce useful approximations for the fraction of the moment of inertia residing in the crust, which is a function of the stellar compactness and, in addition, the pressure at the core-crust interface.

We investigate how current and proposed observations of neutron stars can lead to an understanding of the state of their interiors and the key unknowns: the typical neutron star radius and the neutron star maximum mass. We consider observations made not only with photons, ranging from radio waves to X-rays, but also those involving neutrinos and gravity waves. We detail how precision determinations of structural properties would lead to significant restrictions on the poorly understood equation of state near and beyond the equilibrium density of nuclear matter.To begin, a theoretical analysis of neutron star structure, including general relativistic limits to mass, compactness, and spin rates is made. A review is the made of recent observations such as pulsar timing (which leads to mass, spin period, glitch and moment of inertia estimates), optical and X-ray observations of cooling neutron stars (which lead to estimates of core temperatures and ages and inferences about the internal composition), and X-ray observations of accreting and bursting sources (which shed light on both the crustal properties and internal composition). Next, we discuss neutrino emission from proto-neutron stars and how neutrino observations of a supernova, from both current and planned detectors, might impact our knowledge of the interiors, mass and radii of neutron stars. We also explore the question of how superstrong magnetic fields could affect the equation of state and neutron star structure. This is followed by a look at binary mergers involving neutron stars and how the detection of gravity waves could unambiguously distinguish normal neutron stars from self-bound strange quark matter stars.