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

摘要

First, for each case to be tested, a specific target inspiral signal isselected for parameter extraction. In a future real analysis, the target signalwould be a real signal actually observed by a gravitational wave detector suchas LISA. In this study, however, the target signals are themselves simulations.Some cases were selected to resemble sources likely to be detected by LISA whenit flies; others were selected to facilitate comparison with previous workusing Fisher matrix techniques. Then, for each target inspiral signal, a gridsearch of the input parameter space is conducted to determine the set of inputparameters that produce a simulated inspiral output signal compatible with thetarget. In this study, we consider four parameters: the two masses, the spin ofthe larger black hole, and the eccentricity of the orbit. Searching throughthis four dimensional parameter space requires that hundreds of possible inputsource parameter combinations be simulated for each target signal analyzed. Foreach input parameter combination, the detailed time history of the phase of theresulting inspiral is simulated and compared with the phase history of thetarget signal. The simulation, comparison, and grid search technique used inthis study requires more work than the Fisher matrix technique used in mostprevious studies of this topic. However, this method yields a detailed map ofthe acceptable region of input parameter space, in contrast to themultidimensional ellipsoids of the Fisher matrix method. Nevertheless, thefinal results are in general agreement with those obtained previously by theFisher matrix method, providing a partly independent confirmation of bothresults.