Fully coherent follow-up of continuous gravitational-wave candidates: An application to Einstein@Home results

We characterize and present the details of the follow-up method used on the most significant outliers of the Hough Einstein@Home all-sky search for continuous gravitational waves [J. Aasi et al Phys. Rev. D 87, 042001 (2013)]. This follow-up method is based on the two-stage approach introduced by [M. Shaltev and R. Prix, Phys. Rev. D 87, 084057 (2013)], consisting of a semicoherent refinement followed by a fully coherent zoom. We quantify the efficiency of the follow-up pipeline using simulated signals in Gaussian noise. This pipeline does not search beyond first-order frequency spin-down, and therefore we also evaluate its robustness against second-order spin-down. We present the details of the Hough Einstein@Home follow-up [J. Aasi et al Phys. Rev. D 87, 042001 (2013)] on three hardware-injected signals and on the eight most significant search outliers of unknown origin.

Figure 1

Semicoherent metric mismatch of the subset of 2500 injections with $\overline{{\rho }^2}\in [5,6]$ at different stages of the Monte Carlo. Panel (a) shows the metric mismatch distribution after the original hierarchical search. Panel (b) shows the metric mismatch distribution after the prerefinement stage. Panel (c) shows the metric mismatch distribution after the refinement stage. The hatched bar in each panel shows the percentage of trials with ${\mu }^{*}\ge 1$.

Figure 2

The figure shows the ${\widetilde{2\mathcal{F}}}_{\mathrm{Z}}$ distribution after the fully coherent 4-D $\{\alpha ,\delta ,f,\dot{f}\}$ zoom stage of 15000 searches in pure Gaussian noise data without injected signals. The maximum value is ${\widetilde{2\mathcal{F}}}_{\mathrm{Z}}^{\max }=79.36$, and the mean value is $⟨{\widetilde{2\mathcal{F}}}_{\mathrm{Z}}⟩=51.40$ (dotted line). The labels 1,2,3 refer to the search outliers at roughly 434, 677, and 984 Hz, respectively (see Table 3). The vertical red line marks the noise threshold.

Figure 3

Monte Carlo study of the efficiency of the follow-up pipeline. Panel (a) shows the percentage of injected signals without second-order spin-down classified as recovered ($-S$), and with a non-Gaussian origin ($\times \neg G$), as function of the average $2\mathcal{F}$ value of the candidate after the original semicoherent Hough-transform search (${\overline{2\mathcal{F}}}_{\mathrm{c}}$). Panel (b) shows the percentage of injected signals with second-order spin-down classified as recovered ($-S$), and with a non-Gaussian origin ($\times \neg G$), as a function of ${\overline{2\mathcal{F}}}_{\mathrm{c}}$. The error bars account for 95% confidence level. The 90% detection probability is marked with the horizontal dashed line. The vertical dotted line denotes the $2\mathcal{F}$ threshold used to select candidates in [9].