Simultaneous search for multi-target Galactic binary gravitational waves

The search for Galactic binary gravitational waves is a critical challenge for future space-based gravitational wave detectors, such as LISA. We propose an innovative approach to simultaneously explore gravitational waves originating from Galactic binaries by developing a new local maxima particle swarm optimization algorithm. This new approach effectively addresses the inaccuracies often associated with signal subtraction contamination, a challenge for traditional iterative subtraction methods, particularly when dealing with low signal-to-noise ratio (SNR) signals (e.g., $\mathrm{SNR}<15$). We also account for the effects of overlapping signals and degeneracy noise. To demonstrate the effectiveness of our approach, we use residuals from the LISA mock data challenge (LDC1-4), where 10,982 injected sources with $\mathrm{SNR}\ensuremath{\ge}15$ have been removed. For the remaining sources with $\mathrm{SNR}<15$, our method successfully identifies 6,508 signals, yielding a false alarm rate of ${\mathrm{FAS}}_{0.8}=36.8%$. By focusing on a subset of sources---specifically, those with $f>3\text{ }\text{ }\mathrm{mHz}$ and those with $f\ensuremath{\le}3\text{ }\text{ }\mathrm{mHz}$ but $\mathrm{SNR}\ensuremath{\ge}13$---we identify 3,406 signals, with a reduced false alarm rate of ${\mathrm{FAS}}_{0.8}=22.5%$. We further demonstrate that, within the same detection SNR range, our method achieves a comparable or lower FAS than other existing methods.