Parameter-space metric of semicoherent searches for continuous gravitational waves

Continuous gravitational-wave (CW) signals such as emitted by spinning neutron stars are an important target class for current detectors. However, the enormous computational demand prohibits fully coherent broadband all-sky searches for prior unknown CW sources over wide ranges of parameter space and for yearlong observation times. More efficient hierarchical “semicoherent” search strategies divide the data into segments much shorter than one year, which are analyzed coherently; then detection statistics from different segments are combined incoherently. To optimally perform the incoherent combination, understanding of the underlying parameter-space structure is requisite. This problem is addressed here by using new coordinates on the parameter space, which yield the first analytical parameter-space metric for the incoherent combination step. This semicoherent metric applies to broadband all-sky surveys (also embedding directed searches at fixed sky position) for isolated CW sources. Furthermore, the additional metric resolution attained through the combination of segments is studied. From the search parameters (sky position, frequency, and frequency derivatives), solely the metric resolution in the frequency derivatives is found to significantly increase with the number of segments.

💡 Research Summary

Continuous gravitational‑wave (CW) signals from rotating neutron stars are among the most promising targets for ground‑based interferometers such as LIGO and Virgo. The standard fully coherent matched‑filtering approach, based on the F‑statistic, requires correlating the entire observation span (often a year or more) with a bank of templates that densely cover the multidimensional phase‑parameter space (sky position, intrinsic frequency, and one or more spin‑down derivatives). Because the number of required templates scales roughly as T_coh^p with the coherent integration time T_coh, a fully coherent all‑sky search quickly exceeds any realistic computational budget.

The paper addresses this bottleneck by developing a complete analytical description of the parameter‑space metric that governs the incoherent combination step of a hierarchical semi‑coherent search. In a semi‑coherent scheme the data are split into N short segments of duration T (T ≪ one year). Each segment is processed coherently on a coarse grid, producing a per‑segment F‑statistic value. The N per‑segment statistics are then summed (or otherwise combined) on a fine grid that is typically much denser. The crucial question is how to relate the coarse and fine grids so that the overall loss of signal‑to‑noise ratio (SNR) – quantified by the mismatch M – remains below a prescribed threshold while using the smallest possible number of templates.

The authors introduce a new set of coordinates on the phase‑parameter space that linearise the phase evolution across all segments. In these coordinates the phase derivative with respect to each parameter is a simple function of the segment midpoint t_j and the segment length T. This enables an exact evaluation of the coherent metric for each segment, \