All-sky search for periodic gravitational waves in the O1 LIGO data

We report on an all-sky search for periodic gravitational waves in the frequency band 20–475 Hz and with a frequency time derivative in the range of $[-1.0,+0.1]\times {10}^{-8}\mathrm{Hz}/\mathrm{s}$. Such a signal could be produced by a nearby spinning and slightly nonaxisymmetric isolated neutron star in our galaxy. This search uses the data from Advanced LIGO’s first observational run, O1. No periodic gravitational wave signals were observed, and upper limits were placed on their strengths. The lowest upper limits on worst-case (linearly polarized) strain amplitude $h_0$ are $\sim 4\times {10}^{-25}$ near 170 Hz. For a circularly polarized source (most favorable orientation), the smallest upper limits obtained are $\sim 1.5\times {10}^{-25}$. These upper limits refer to all sky locations and the entire range of frequency derivative values. For a population-averaged ensemble of sky locations and stellar orientations, the lowest upper limits obtained for the strain amplitude are $\sim 2.5\times {10}^{-25}$.

Figure 1

PowerFlux upper limit validation. Each point represents a separate injection in the 50–200 Hz frequency range. Each established upper limit (vertical axis) is compared against the injected strain value (horizontal axis, red line).

Figure 2

PowerFlux injection recovery. The injections were performed in the 50–200 Hz band. The injected strain divided by the upper limit in this band (before injection) is shown on the horizontal axis. The percentage of surviving injections is shown on the vertical axis, with a horizontal line drawn at the 95% level. Stage 0 is the output of the coincidence test after the initial semicoherent search.

Figure 3

A-dimensional distance between 56 injected signals in the band 64–65 Hz and the corresponding candidates (blue dots: before the follow-up; red circles: after the follow-up).

Figure 4

A-dimensional distance between 57 injected signals in the band 122–123 Hz and the corresponding candidates (blue dots: before the follow-up; red circles: after the follow-up).

Figure 5

Measured detection efficiency values for the band 423–424 Hz (circles) and their fit done using Eq. (5) (asterisks). The dashed line represents the full fitted curve. The dotted horizontal line indicates the 95% level of the detection efficiency.

Figure 6

Measured detection efficiency values for the band 51–52 Hz (circles) and their fit done using Eq. (5) (asterisks). The dashed line represents the full fitted curve. The dotted horizontal line indicates the 95% level of the detection efficiency.

Figure 7

Significance-${\chi }^2$ plane for 180000 simulated injected signals in the 50–100 Hz band together with the fitted mean curve (dotted-dashed line) and the veto curve (dashed line) corresponding to the mean ${\chi }^2$ plus five times its standard deviation for the H1-L1 combined data. The associated false dismissal rate (percentage of injections that are higher than the veto curve) is measured to be 0.12%.

Figure 8

Same as Fig. 7 for 320000 injections in the 100–200 Hz band. The false dismissal rate is 0.21%.

Figure 9

Same as Fig. 7 for 1840000 injections at frequencies higher than 200 Hz for the combined H1-L1 data. The false dismissal rate is 0.16%.

Figure 10

Characterization of the multidetector significance consistency veto using 4356 simulated injected signals in the 50–500 Hz range. Each point represents a separate injection. The horizontal axis corresponds to the theoretical expected significance value, $s_{\text{theo}}$, while the vertical axis is the difference between the theoretical and the measured value of significance, $s_{\text{multi}}^{*}$. The solid line is placed at a difference in significance of 1.6 that has only been exceeded by 3 injections.

Figure 11

Detection efficiency as a function of depth obtained for 22 frequency bands. Each dot corresponds to a set of 200 signal injections. The solid line (red) corresponds to the fitted sigmoid curve. The diamond shows the depth value corresponding to an averaged all-sky 95% detection efficiency, $D^{95\%}=24.2$ ($1/\sqrt{\mathrm{Hz}}$).

Figure 12

SkyHough O1 upper limits. The dotted (red) curve shows the averaged 95% confidence level upper limits for every analyzed 0.1-Hz band. The vertical (grey) lines indicate 194 0.1-Hz bands in which coincidence candidates were found and consequently no upper limits are set.

Figure 13

Time-Domain $\mathcal{F}$-statistic pipeline flowchart. Two main parts of the pipeline are the coherent $\mathcal{F}$-statistic search for candidate signals in time-domain segments, which is followed by a search for coincidences between candidates from different time-domain segments.

Figure 14

Time-Domain $\mathcal{F}$-statistic method of establishing upper limits from the Monte Carlo simulations with sigmoid fitting (an example for band No. 0666). Blue dots denote the results of the MC simulations for the range of amplitudes $h_0$ of injected signals with otherwise randomly chosen parameters. The green curve is the best fit of Eq. (15); the red dot corresponds to the 95% upper limit (see Fig. 18 for the summary of results for the whole range of searched frequencies).

Figure 15

PowerFlux O1 upper limits. The upper (yellow) curve shows worst-case (linearly polarized) 95% CL upper limits in analyzed 62.5 mHz bands. The lower (grey) curve shows upper limits assuming a circularly polarized source. The data for this plot can be found in [47].

Figure 16

Range of the PowerFlux search for neutron stars spinning down solely due to gravitational radiation. This is a superposition of two contour plots. The grey and red solid lines are contours of the maximum distance at which a neutron star could be detected as a function of gravitational wave frequency $f$ and its derivative $\dot{f}$. The dashed lines are contours of the corresponding ellipticity $\epsilon (f,\dot{f})$. The fine dotted line marks the maximum spin-down searched. Together these quantities tell us the maximum range of the search in terms of various populations (see text for details). The other three search pipelines have similar ranges for circularly polarized sources.

Figure 17

Upper limits for the FrequencyHough pipeline, in the range between 20 Hz and 475 Hz.

Figure 18

Time-Domain $\mathcal{F}$-statistic pipeline O1 upper limits. Black dots are the 95% confidence upper limits for each frequency; the red line denotes the H1 and L1 detectors’ average noise curve rescaled by the factor $27.5/\sqrt{T_0}$, where $T_0=516984\mathrm{s}$ is the observational time of the 6-day time series segment.

Figure 19

Fraction of the bandwidth vetoed for each band searched by the Time-Domain $\mathcal{F}$-statistic pipeline.

Figure 20

Time-Domain $\mathcal{F}$-statistic pipeline coincidence results as a function of the band frequency. Top panel: maximum coincidence multiplicity. Bottom panel: false alarm probability for the coincidence with the maximum multiplicity.

Figure 21

Upper limit comparison for the four search pipelines used in this analysis. The curves represent the source strain amplitude $h_0$ at which 95% of simulated signals would be detected. Three of the pipelines (FrequencyHough, SkyHough, Time-Domain $\mathcal{F}$-statistic) present population-averaged limits over the full sky and source polarization, while one pipeline (PowerFlux) presents strict all-sky limits for circular-polarization (most favorable orientation: black) and linear-polarization (least favorable orientation: cyan) sources. Converting the PowerFlux upper limits to validated population-averaged upper limits would require extensive, band-dependent Monte Carlo simulations, but previous studies suggest that such limits would lie in a region similar to that of the other pipelines. In addition, the population-averaged upper limits from the most recent Einstein@Home search are shown for comparison [32]. The Einstein@Home search explored the low frequencies, and a narrower spin-down range using a much longer coherence length (210 hours).

Figure 22

Peakmap projections for outlier 7 of the FrequencyHough search. The dotted blue line is for Hanford detector analysis, the green dashed line is for Livingston detector analysis and the continuous black line is for the joint search.

Figure 23

Joint Hough map for outlier 7 of the FrequencyHough search.