INCREASING THE ACCURACY OF BINARY NEUTRON STARSIMULATIONS WITH AN IMPROVED VACUUM TREATMENT

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.