Full band all-sky search for periodic gravitational waves in the O1 LIGO data

We report on a new all-sky search for periodic gravitational waves in the frequency band 475–2000 Hz and with a frequency time derivative in the range of $[-1.0,+0.1]\times 10^{-8}\mathrm{Hz}/\mathrm{s}$. Potential signals 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 gravitational-wave signals were observed, and upper limits were placed on their strengths. For completeness, results from the separately published low-frequency search 20–475 Hz are included as well. Our lowest upper limit on worst-case (linearly polarized) strain amplitude $h_0$ is $\sim 4\times 10^{-25}$ near 170 Hz, while at the high end of our frequency range, we achieve a worst-case upper limit of $1.3\times 10^{-24}$. For a circularly polarized source (most favorable orientation), the smallest upper limit obtained is $\sim 1.5\times 10^{-25}$.

Figure 1

O1 upper limits. The dimensionless strain (vertical axis) is plotted against signal frequency. Looking at the right side of the plot, the upper (red) curve shows Time Domain F-statistic 95% C.L. population averaged upper limits, the next lower curve (blue) shows maximum population average upper limits from SkyHough, followed by yellow curve showing PowerFlux worst-case (linearly polarized) 95% C.L. upper limits in analyzed bands. PowerFlux upper limits are maximized over sky and all intrinsic signal parameters for each frequency band displayed. The lower (black) curve shows upper limits assuming a circularly polarized source. We include the data from the low-frequency paper [31] to present the entire range 20–2000 Hz. As the computational demands grow with frequencies, each pipeline tunes parameters to reduce computation load. This accounts for jumps in curves at 475, 1200, and 1475 Hz. The SkyHough upper limit curve shows the maximum of the range of different upper limits shown in Fig. 7 with different upper limit values corresponding to different search depths. Because of highly non-Gaussian data, the SkyHough search depths are not expected to be well estimated for each individual search band but are representative of the noise behavior in the entire frequency range. The data for this plot can be found in Ref. [39].

Figure 2

PowerFlux upper limit validation. Each point represents a separate injection in the 475–1475 Hz frequency range. Each established upper limit (vertical axis) is compared against the injected strain value (horizontal axis, red line). The plot for the high-frequency range 1475–2000 Hz is very similar and not included in this paper.

Figure 3

PowerFlux injection recovery. The injections were performed in the 475–1475 Hz band. The injected strain divided by the upper limit in this band computed without 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. The plot for high-frequency range 1475–2000 Hz is very similar and not included here.

Figure 4

Detection efficiency as a function of depth obtained for the 0.1 Hz frequency band starting at 580.2 Hz. Each red dot corresponds to a set of 400 signal injections, and error bars on the data points represent the $2{\sigma }_E$ standard binomial error. The (black) solid line corresponds to the fitted sigmoid curve, and the (blue) shaded envelope corresponds to the $2{\sigma }_F$ calculated according to Eq. (10). The diamond shows the depth value corresponding to the 95% detection efficiency, ${\mathcal{D}}^{95\%}$, along with the $2{\sigma }_F$ uncertainty in black markers.

Figure 5

Depth values corresponding to the 95% detection efficiency, ${\mathcal{D}}^{95\%}$, obtained for 18 0.1 Hz frequency bands between 475 and 1200 Hz, along with their corresponding $2{\sigma }_F$ uncertainties from the sigmoid fit in red markers. The average of the measured depths at different frequencies is $⟨{\mathcal{D}}^{95\%}{⟩}_{\text{Low}}=20.5{\mathrm{Hz}}^{-1/2}$.

Figure 6

Depth values corresponding to the 95% detection efficiency, ${\mathcal{D}}^{95\%}$, obtained for 18 0.1 Hz frequency bands between 1200 and 2000 Hz, along with their corresponding $2{\sigma }_F$ uncertainties in red markers. The average of the measured depths at different frequencies is $⟨{\mathcal{D}}^{95\%}{⟩}_{\text{High}}=16.5{\mathrm{Hz}}^{-1/2}$.

Figure 7

SkyHough O1 upper limits. The solid (blue) line shows the averaged 95% C.L. upper limits on the gravitational wave amplitude for every analyzed 0.1 Hz band. The vertical (grey) lines indicate 25 0.1 Hz bands in which outliers were found and consequently no upper limits were set. The lighter region around the upper limit represents the 7.4% and 15% uncertainty levels. The jump in sensitivity and uncertainty at 1200 Hz corresponds to the decrease in the sky grid resolution during the search, tuned to reduce the computational load.

Figure 8

Range of the PowerFlux search for neutron stars spinning down solely due to gravitational radiation. This is a superposition of two contour plots. The gray 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 the text for details).

Figure 9

Time-Domain $\mathcal{F}$-statistic pipeline O1 upper limits. Black dots are the 95% confidence upper limits for each frequency, and the red line denotes the H1 and L1 detectors’ average noise curve rescaled by the factor $38/\sqrt{T_0}$, where $T_0=172328\mathrm{s}$ is the observational time of the 2-sidereal-day time series segment. The factor of 38 is larger than the factor of 27.5 obtained in the low-frequency search, indicating loss of sensitivity due to a looser grid of templates used here.

Figure 10

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