Neutron stars

Unveiling the secrets of gravity necessitates numerical relativity simulations of gravitational systems, as observations made by gravitational wave detectors expect an interpretation. In the other hand, these numerical simulations require physical and constraint-satisfying initial data. Therefore, the accuracy of simulations go hand in hand with the accuracy of initial data. As such, constructing accurate initial data is an indispensable task and it is the very subject of this dissertation.
Here, we present the newly developed pseudospectral code Elliptica, an infrastructure for construction of initial data for various binary and single gravitational systems of all kinds. The elliptic equations under consideration are solved on a single spatial hypersurface of the spacetime manifold. Using coordinate maps, the hypersurface is covered by patches whose boundaries can adapt to the surface of the compact objects. To solve elliptic equations with arbitrary boundary condition, Elliptica deploys a Schur complement domain decomposition method with a direct solver. In this version, we use cubed sphere coordinate maps and the fields are expanded using Chebyshev polynomials of the first kind. Here, we explain the building blocks of Elliptica and the initial data construction algorithm for black hole-neutron star binary systems. We perform convergence tests and evolve the data to validate our results. Within our framework, the neutron star can reach spin values close to breakup with arbitrary direction, while the black hole can have arbitrary spin with dimensionless spin magnitude ~ 0.8.

The main purpose of this dissertation is to study the inspiral and merger of binary neutron stars. The inspiral, in such a system, is caused by the loss of energy and angular momentum that is carried away by the emitted gravitational waves. Newly-formed neutron stars, after supernova explosions, are very hot. They cool down during the hundreds of millions of years, which is needed to bring the two stars in a neutron star binary close enough together to start investigating them with numerical relativity simulations. Thus, they can be considered as fluids at zero temperature to very high accuracy, when we start numerical simulations. In this description, the stars also have a well-defined star surface, beyond which there is a true vacuum. This vacuum, outside the stars, will persist until the stars get so close that mass can be ejected due to tidal forces, and later, when they come into contact and eject streams of hot matter. To date, all current numerical relativity programs use an artificial atmosphere from the very beginning. They do this, to avoid numerical problems arising from the sharp transition of the matter region to the vacuum outside the stars. To be more precise, they take the initial data and fill all the vacuum regions with a very low-density zero velocity atmosphere. While this atmosphere is not physical and used only for numerical reasons, it can still influence the results of the simulations. For example, studies of merger dynamics, merger remnant, disk mass, ejecta mass, and kinetic energy of ejecta, are hampered by the presence of the artificial zero velocity low-density material. To avoid this problem, we have developed a new method to evolve the neutron star systems, without the need for an artificial atmosphere. We describe this method, which we call vacuum method, we present tests with it, and compare it to the conventional atmosphere method. For these tests, we first consider the evolution of stable, oscillating, and collapsing single neutron stars. We also study simulations of the inspiral and merger of binaries using both methods. We find better mass conservation in low-density regions and near refinement boundaries, as well as better ejecta material conservation for the new method. However, the gravitational wave predictions produced by our simulations are almost identical for both methods, since they are mainly due to the bulk motion of the stars which is not strongly affected by the presence or absence of an artificial atmosphere.

The starting point of any general relativistic numerical simulation is a solution
of the Hamiltonian and momentum constraints that (ideally) represents an astrophysically realistic scenario. This dissertation presents a new method to produce initial data sets for binary neutron stars with arbitrary spins and orbital eccentricities. The method only provides approximate solutions to the constraints. However, it was
shown that the corresponding constraint violations subside after a few orbits, becoming
comparable to those found in evolutions of standard conformally flat, helically
symmetric binary initial data. This dissertation presents the first spinning neutron
star binary simulations in circular orbits with a orbital eccentricity less then 0.01. The
initial data sets corresponding to binaries with spins aligned, zero and anti-aligned
with the orbital angular momentum were evolved in time. These simulations show
the orbital “hang-up” effect previously seen in binary black holes. Additionally, they
show orbital eccentricities that can be up to one order of magnitude smaller than
those found in helically symmetric initial sets evolutions.

This thesis considers the neutrino-driven wind that arises from a proto-neutron star following a supernova explosion as a possible site for the synthesis of the heavy elements by the r-process. We first review the conditions necessary to obtain an r-process, the constraints on the r-process yields for each event, and show the neutrino-driven winds from proto-neutron stars are suitable for an r-process. We next discuss some of the modifications of the supernova code that were necessary in order to numerically simulate the neutrino-driven winds and steps necessary to initiate these conditions. Three important parameters of the wind characterizing the nucleosynthesis are the net electron fraction, the entropy per baryon, and the expansion time-scale. We derive approximate analytic expressions for the neutrino luminosities and mean energies, and the final entropy and net electron fraction of the wind, and compare those against a numerical simulation. We finally present the results of a numerical simulation of the first several seconds of the wind phase, and conclude with an assessment of whether or not an r-process will occur at this time.