Optimizing the choice of analysis method for all-sky searches for continuous gravitational waves with Einstein@Home

Rapidly rotating neutron stars are promising sources of continuous gravitational wave radiation for the LIGO and Virgo interferometers. The majority of neutron stars in our galaxy have not been identified with electromagnetic observations. All-sky searches for isolated neutron stars offer the potential to detect gravitational waves from these unidentified sources. The parameter space of these blind all-sky searches, which also cover a large range of frequencies and frequency derivatives, presents a significant computational challenge. Various methods have been designed to perform these searches within the limits of available computing resources. Recently, a search method called Weave has been proposed to achieve template placement with a minimal number of templates. We employ a mock data challenge to assess the ability of this method to recover signals in an all-sky search for unknown neutron stars, and compare its search sensitivity with that of the global correlation transform method (GCT), which has been used for all-sky searches with the Einstein@Home volunteer computing project for a number of years. We find that the Weave method is 14% more sensitive than GCT for an all-sky search on Einstein@Home, with a sensitivity depth of $57.9\pm 0.6$ $\frac{1}{\sqrt{\mathrm{Hz}}}$ at 90% detection efficiency, compared to ${50.8}_{-1.1}^{+0.7}$ $\frac{1}{\sqrt{\mathrm{Hz}}}$ for GCT. This corresponds to a 50% increase in the volume of sky where we are sensitive with the Weave search. We also find that the Weave search recovers candidates closer to the true signal position. In the all-sky search studied here the improvement in candidate localization would lead to a factor of 70 reduction in the computing cost required to follow up the same number of candidates. We assess the feasibility of deploying the search on Einstein@Home, and find that Weave requires significantly more memory than is typically available on a volunteer computer. We conclude that, while GCT remains the best choice for deployment on Einstein@Home due to its lower memory requirements, Weave presents significant advantages for the subsequent hierarchical follow-up searches of interesting candidates.

Figure 1

Histogram of the mismatch between the maximum $2\overline{\mathcal{F}}$, the $2\overline{\mathcal{F}}$ of a search template at the exact signal parameters, and the loudest recovered $2\overline{\mathcal{F}}$ from a GCT search (red) and a Weave search (blue).

Figure 2

The distribution of recovered $2{\overline{\mathcal{F}}}_{\max }$ values in 600 repeated runs over Gaussian noise for GCT (top) and Weave (bottom). If the search templates were independent the measured $2{\overline{\mathcal{F}}}_{\max }$ (grey) would agree with expected $2{\overline{\mathcal{F}}}_{\max }$ for $N_{\text{templates}}$ (green). The effective number of templates is obtained with a fit to the measured $2{\overline{\mathcal{F}}}_{\max }$, the results of the fit are shown in orange.

Figure 3

The distance between the signal and the recovered candidate, in frequency, spindown and sky position, when the candidate with the highest SNR is chosen for Weave (blue) and GCT (red). The search can recover more than one candidate per injection. For strong signals, there are in fact many detection candidates around the signals true parameter values. We study the distribution for the distances of candidates from the true signal parameter values for the detection candidates with the highest $2\overline{\mathcal{F}}$. The dR distribution extends beyond the limits shown in the plot with the max dR value at 0.27 for Weave and 0.38 for GCT.

Figure 4

Measured detection efficiency of Weave (blue dashed line) and GCT (red solid line) for the MDC injections. The curves and error bands are obtained by fitting sigmoids to the data, see Sec. 6d2. Note that in [26] the signal strength is normalized by a different definition of $S_h$, where the harmonic sum over per-detector PSDs is used instead of the harmonic mean. One can approximately convert the MDC results into sensitivity depth at any efficiency by multiplying by $\sqrt{N_{\det }}\approx 1.4$, as 2 detectors were used.

Figure 5

Measured detection efficiency for Weave (blue dashed line) and GCT (red solid line) for injections in Gaussian noise which are uniform in $|\cos \iota |$ at fixed $\sqrt{S_h}/h_0(\frac{1}{\sqrt{\mathrm{Hz}}})$.