Numerical Simulation of Binary Black Hole Spacetimes and a Novel Approach to Outer Boundary Conditions
Creators: name: Seiler, Jennifer
Publisher: name: Gottfried Wilhelm Leibniz Universität Hannover
Year: 2010
Subjects: Astrophysics

description: With ground-based gravitational wave detectors at design sensitivity, and a space-based detector in planning stages, the need for accurate gravitational wave templates for signal recognition by detector pipelines has become an urgent problem.  With that in mind, and the fact that binary black hole inspirals and mergers are the strongest potential source for gravitational wave signals for online detectors, my research has focused on improving the accuracy and well-posedness of numerical simulations, and on the generation of gravitational waveforms from numerical simulations both for detector template generation and for astrophysical predictions.  For simulations of highly dynamical relativistic vacuum space-times I derived accurate and well-posed formulations of the Einstein equations for numerical evolutions.  I herein propose a set of well-posed, constraint-preserving boundary conditions for artificial boundaries for a first order in time and second order in space `generalized harmonic' formulation of the Einstein equations.  I tested these conditions both for black hole spacetimes and for a series of robust stability tests, and show that these conditions reduce noise, reduce constraint violation, and increase stability for relativistic simulations.  Additionally, I propose novel, well-posed, constraint-preserving boundary conditions for the more commonly used BSSN evolution system for standard ``1+\log'' and Gamma-driver gauge conditions.  I ran numerical evolutions of symmetric and asymmetric binary black hole mergers in large numbers to explore the parameter space of binary black hole inspirals and derive a statistical and phenomenological view of the physical qualities of binary merger remnants.  I ran binary black hole inspiral simulations using both quasi-circular and post-Newtonian derived initial orbital binary inspiral parameters, and ``puncture'' initial data, and extracted physics from a number of initial data sequences in order to establish bounds on phenomenological formulae for the final spin and recoil velocity of merged black holes from arbitrary initial data parameters.  With the data from those parameter studies we focus on gravitational-wave emission to quantify how much spin effects contribute to the signal-to-noise ratio and to the relative event rates for the representative ranges in masses and detectors. I show that equal-spin binaries with maximum spin aligned with the orbital angular momentum are more than ``three times as loud'' as the corresponding binaries with anti-aligned spins.  Finally, we derive a simple expression for the energy radiated in gravitational waves and find that the binaries have efficiencies between 3.6% and 10%.    Finally, I present an analytical inspiral-merger-ringdown gravitational waveforms from black-hole (BH) binaries with non-precessing spins by matching a post-Newtonian description of the inspiral to our numerical calculations, we obtain a waveform family with a conveniently small number of physical parameters. These waveforms will allow us to detect a larger parameter space of BH binary coalescence, to explore various scientific questions related to GW astronomy, and could dramatically improve the expected detection rates of GW detectors.