Hierarchical follow-up of subthreshold candidates of an all-sky Einstein@Home search for continuous gravitational waves on LIGO sixth science run data

We report results of an all-sky search for periodic gravitational waves with frequency between 50 and 510 Hz from isolated compact objects, e.g., neutron stars. A new hierarchical multistage approach is taken, supported by the computing power of the Einstein@Home project, allowing us to probe more deeply than ever before. 16 million subthreshold candidates from the initial search [LIGO Scientific and Virgo Collaborations, Phys. Rev. D 94, 102002 (2016)] are followed up in four stages. None of those candidates is consistent with an isolated gravitational wave emitter, and 90% confidence level upper limits are placed on the amplitudes of continuous waves from the target population. Between 170.5 and 171 Hz, we set the most constraining 90% confidence upper limit on the strain amplitude $h_0$ at $4.3\times {10}^{-25}$, while at the high end of our frequency range, we achieve an upper limit of $7.6\times {10}^{-25}$. These are the most constraining all-sky upper limits to date and constrain the ellipticity of rotating compact objects emitting at 300 Hz at a distance $D$ to less than $6\times {10}^{-7}$ $[\frac{D}{100\mathrm{pc}}]$.

Figure 1

These are the mismatch histograms of the four follow-up searches, so the $y$ axis represents normalized counts. For a given search and search setup, the mismatch distribution depends on the template grid. The injection-and-recovery Monte Carlo studies to determine these distributions were performed without noise.

Figure 2

Candidates that are followed up in Stage-1: the distribution of their detection statistic values $2\overline{\mathcal{F}}$ (left plot) and their distribution as a function of frequency (right plot). Most notable are two outliers around $\approx 53\mathrm{Hz}$ close enough in frequency that they are not resolvable in the left plot.

Figure 3

Loudest from each of the Stage-1 searches: the distribution of their detection statistic values $2\overline{\mathcal{F}}$ (left plot) and their distribution as a function of frequency (right plot). The red line marks $2\overline{\mathcal{F}}=6.109$, which is the threshold at and above which candidates are passed on to stage 2. The two outliers at $\approx 53\mathrm{Hz}$ also visible in the previous stage remain notable, and another one becomes visible, at $\approx 266\mathrm{Hz}$.

Figure 4

Fraction of signals that are recovered with a detection statistic value larger than or equal to the threshold value after the Stage-1 follow-up.

Figure 5

Loudest from each of the Stage-2 searches: the distribution of their detection statistic values $2\overline{\mathcal{F}}$ (left plot) and their distribution as a function of frequency (right plot). The red line marks $2\overline{\mathcal{F}}=7.38$, which is the threshold at and above which candidates are passed on to stage 3. The two outliers at $\approx 53\mathrm{Hz}$ and the one at $\approx 266\mathrm{Hz}$ from the previous stage remain significant. A new candidate stands out of the bulk of the distribution at $\approx 220\mathrm{Hz}$, and two new candidates begin to appear at $\approx 50\mathrm{Hz}$.

Figure 6

Fraction of signals that are recovered with a detection statistic value larger than or equal to the threshold value after the Stage-2 follow-up.

Figure 7

Loudest from each of the Stage-3 searches: the distribution of their detection statistic values $2\overline{\mathcal{F}}$ (left plot) and their distribution as a function of frequency (right plot). The red line marks $2\overline{\mathcal{F}}=8.82$, which is the threshold at and above which candidates are passed on to stage 4. The two outliers at $\approx 53\mathrm{Hz}$ and the one at $\approx 266\mathrm{Hz}$ well visible in all the previous stages remain significant; these are the ones that are clearly outside of the bulk of the distribution. The candidate that at Stage-2 was at $\approx 220\mathrm{Hz}$ has now fallen below threshold, whereas the two at $\approx 50\mathrm{Hz}$ have risen above threshold. Five new candidates have emerged just above threshold.

Figure 8

Fraction of signals that are recovered with a detection statistic value larger than or equal to the threshold value (vertical line) after the Stage-3 follow-up. The dashed line is a linear extrapolation based on the last two data points to guide the eye to the false dismissal value for signals at threshold. This line is a conservative estimate in the sense that it overestimates the false dismissal.

Figure 9

Fraction of signals that are recovered with a detection statistic value larger than or equal to the threshold value (vertical line) after the Stage-4 follow-up. The dashed line is a linear extrapolation based on the last two data points to guide the eye to the false dismissal value for signals at threshold. This line is a conservative estimate in the sense that it overestimates the false dismissal.

Figure 10

90% confidence upper limits on the gravitational wave amplitude of continuous gravitational wave signals with frequency in 0.5 Hz bands and with spindown values within the searched range. The lowest set of points (black circles) is the result of this search. For comparison, we show the upper limits from only the stage-0 results [5]. These lie on the curve above the lowest one and are marked by dark blue diamonds. The results from a previous broad all-sky survey [13] are the top curve (lighter circles and crosses) above 100 Hz. In the lower frequency range, we compare with a search on Virgo data contemporary to the LIGO S6 data [14].

Figure 11

Ellipticity $\epsilon$ of a source at a distance $d$ emitting continuous gravitational waves that would have been detected by this search. The dashed line shows the spindown ellipticity for the highest magnitude spindown parameter value searched: $2.6\times {10}^{-9}\mathrm{Hz}/\mathrm{s}$. The spindown ellipticity is the ellipticity necessary for all the lost rotational kinetic energy to be emitted in gravitational waves. If we assume that the observed spindown is all actual spindown of the object, then no ellipticities could be possible above the dashed curve. In reality, the observed and actual spindowns could differ due to radial motion of the source. In this case, the actual spindown of the object may even be larger than the apparent one. In this case, our search would be sensitive to objects with ellipticities above the dashed line.