Numerical Integration for Neutron Star Binaries in Eccentric Orbits

Abstract

This dissertation try to focus on new paradigm of initial data and its evolution for Einsteins field equation when spacetime has matter field. To make proper initial data, we carry out test employing boosted Tolmann-Oppenhiemmer-Volkoff(TOV) star. TOV star assumes perfect fluid obeying polytropic process and metric keeps spherical symmetry. It is static and stationary solution so it shows stable maximum density oscillation. On the other hand, when TOV star got boosted, maximum density oscillation become excited. Such a behaviour provide good hint for error which will arise at binary system. We presents initial data for binary in the eccentric orbit employing double TOV stars. Rotation configuration in the binary should have vanishing vorticity. To deal with such a configuration, constant coordinate velocity approximation is utilized. Moreover, initial external field due to companion is ignored because we want to look at contribution of relativistic hydrodynamics part. So, metric combination is not superposition but sewing TOV solution at the boundary line containing origin. We simply compare initial data of us and LORENE initial data which solves constraints equations via multi grid method. Key difference is high frequency mode of density oscillation and gravitational wave due to surface mode of neutron star. While binary system is evolving, spurious oscillation occurs around 500 coordinate time when eccentricity is about 0.17. According to result of boosted TOV star, boost parameter might be attributed to such as oscillation and pressure perturbation is applied to treat the problems. Because boost can spoil relativistic equilibrium, we use strong Bernuollis theorem which assert homogeneous injection energy to renew equilibrium. For highly eccentric orbit, stars collide each other before showing spurious oscillation. Though perturbed binary delivers relived maximum density oscillation, other part is excited at last 6, 7 percent. Relatively high constraint violation is remained problem but it can be resolved by smoothing lapse function and metric at boundary line.