Hierarchical search method for gravitational waves from stellar-mass binary black holes in noisy space-based detector data

Future space-based laser interferometric detectors, such as the Laser Interferometer Space Antenna (LISA), will be able to detect gravitational waves (GWs) generated during the inspiral phase of stellar-mass binary black holes (SmBBHs). These detections contain a wealth of important information concerning astrophysical formation channels and fundamental physics constraints. However, the detection and characterization of GWs from SmBBHs poses a formidable data analysis challenge, arising from the large number of wave cycles that make the search extremely sensitive to mismatches in signal and template parameters in a likelihood-based approach. This makes the search for the maximum of the likelihood function over the signal parameter space an extremely difficult task, with grid-based deterministic global optimization methods becoming computationally infeasible. We present a data analysis method that addresses this problem using both algorithmic innovations and hardware acceleration driven by graphics processing units. The method follows a hierarchical approach in which a semicoherent $\mathcal{F}$-statistic is computed with different numbers of frequency domain partitions at different stages, with multiple particle swarm optimization (PSO) runs used in each stage for global optimization. An important step in the method is the judicious partitioning of the parameter space at each stage to improve the convergence probability of PSO and avoid premature convergence to noise-induced secondary maxima in the semicoherent $\mathcal{F}$-statistic. The hierarchy of stages confines the semicoherent searches to progressively smaller parameter ranges, with the final stage performing a search for the global maximum of the fully coherent $\mathcal{F}$-statistic. We test our method on 2.5 yr f a single LISA time delay interferometry combination and find that for an injected SmBBH signal with a signal-to-noise ratio between $\ensuremath{\approx}11$ and $\ensuremath{\approx}14$, the method can estimate (i) the chirp mass with a relative error of $\ensuremath{\lesssim}0.01%$, (ii) the time of coalescence within $\ensuremath{\approx}100\text{ }\text{ }\mathrm{s}$, (iii) the sky location within $\ensuremath{\approx}0.2\text{ }\text{ }{\mathrm{deg}}^{2}$, and (iv) orbital eccentricity at a fiducial signal frequency of 10 mHz with a relative error of $\ensuremath{\lesssim}1%$.