Using Simulation, Comparison and Grid Search To Find all Possible Binary Black Hole Source Parameters For Extreme Mass-Ratio Inspiral Gravitational Wave Signals

Abstract

First, for each case to be tested, a specific target inspiral signal is selected for parameter extraction. In a future real analysis, the target signal would be a real signal actually observed by a gravitational wave detector such as LISA. In this study, however, the target signals are themselves simulations. Some cases were selected to resemble sources likely to be detected by LISA when it flies; others were selected to facilitate comparison with previous work using Fisher matrix techniques. Then, for each target inspiral signal, a grid search of the input parameter space is conducted to determine the set of input parameters that produce a simulated inspiral output signal compatible with the target. In this study, we consider four parameters: the two masses, the spin of the larger black hole, and the eccentricity of the orbit. Searching through this four dimensional parameter space requires that hundreds of possible input source parameter combinations be simulated for each target signal analyzed. For each input parameter combination, the detailed time history of the phase of the resulting inspiral is simulated and compared with the phase history of the target signal. The simulation, comparison, and grid search technique used in this study requires more work than the Fisher matrix technique used in most previous studies of this topic. However, this method yields a detailed map of the acceptable region of input parameter space, in contrast to the multidimensional ellipsoids of the Fisher matrix method. Nevertheless, the final results are in general agreement with those obtained previously by the Fisher matrix method, providing a partly independent confirmation of both results.