All-sky search for periodic gravitational waves in the full S5 LIGO data

We report on an all-sky search for periodic gravitational waves in the frequency band 50–800 Hz and with the frequency time derivative in the range of 0 through $-6\times {10}^{-9}\mathrm{Hz}/\mathrm{s}$. Such a signal could be produced by a nearby spinning and slightly nonaxisymmetric isolated neutron star in our Galaxy. After recent improvements in the search program that yielded a $10\times$ increase in computational efficiency, we have searched in two years of data collected during LIGO’s fifth science run and have obtained the most sensitive all-sky upper limits on gravitational-wave strain to date. Near 150 Hz our upper limit on worst-case linearly polarized strain amplitude $h_0$ is $1\times {10}^{-24}$, while at the high end of our frequency range we achieve a worst-case upper limit of $3.8\times {10}^{-24}$ for all polarizations and sky locations. These results constitute a factor of 2 improvement upon previously published data. A new detection pipeline utilizing a loosely coherent algorithm was able to follow up weaker outliers, increasing the volume of space where signals can be detected by a factor of 10, but has not revealed any gravitational-wave signals. The pipeline has been tested for robustness with respect to deviations from the model of an isolated neutron star, such as caused by a low-mass or long-period binary companion.

Figure 1

Full S5 upper limits. The upper (green) curve shows worst-case upper limits in analyzed 0.25 Hz bands (see Table 1 for list of excluded bands). The lower (grey) curve shows upper limits assuming circularly polarized source. The values of solid points (marking non-Gaussian behavior) and circles (marking power line harmonics) are not considered reliable. They are shown to indicate contaminated bands.

Figure 2

Flow chart of PowerFlux code.

Figure 3

SNR skymap for hardware injection of a simulated signal. The circle is centered on the location of the injection. The high frequency of the signal (575 Hz) allows good localization.

Figure 4

Upper limit validation. Each point represents a separate injection. Established upper limit ($y$ axis) is compared against injected strain value ($x$ axis, red line).

Figure 5

Improvement of spin-down localization of injected test signals. The injected strain divided by the upper limit in this band (before injection) is shown on the $x$ axis. The difference between injection spin-down and spin-down of corresponding outlier is shown on the $y$ axis. Crosses, semicoherent; circles, loosely coherent.

Figure 6

Improvement of position localization of injected test signals. The injected strain divided by the upper limit in this band (before injection) is shown on the $x$ axis. The distance between injection sky location and that of corresponding outlier is shown on the $y$ axis. Crosses, semicoherent; circles, loosely coherent.

Figure 7

Improvement of frequency localization of injected test signals. The injected strain divided by the upper limit in this band (before injection) is shown on the $x$ axis. The difference between injection frequency and frequency of corresponding outlier is shown on the $y$ axis. Crosses, semicoherent; circles, loosely coherent.

Figure 8

Injection recovery from semicoherent analysis stage (crosses), after the first loosely coherent follow-up (circles) and after the second stage of loosely coherent follow-up (diagonal crosses). The injected strain divided by the upper limit in this band (before injection) is shown on the $x$ axis. The percentage of surviving injections is shown on the $y$ axis.

Figure 9

Relative increase in SNR of injected test signals from semicoherent to loosely coherent stage. The plot is restricted to injections that passed the coincidence test. The injected strain divided by the upper limit in this band (before injection) is shown on the $x$ axis. The ratio of loosely coherent SNR to semicoherent SNR is shown on the $y$ axis.

Figure 10

Relative increase in SNR from coherent combination of data from different interferometers. The plot is restricted to injections that passed the coincidence test. The injected strain divided by the upper limit in this band (before injection) is shown on the $x$ axis. The ratio of coherently combined loosely coherent SNR to loosely coherent SNR from the previous stage is shown on the $y$ axis.

Figure 11

Upper limit reconstruction versus depth of periodic frequency modulation for semicoherent search. The frequency modulation depth is shown on the $x$ axis. The red line marks the $280\mu \mathrm{Hz}$ boundary to the right of which we expect injections to start losing power. The $y$ axis shows the ratio between the upper limit and injected strain.

Figure 12

Upper limit reconstruction versus depth of periodic frequency modulation for loosely coherent search with parameter $\delta =\pi /2$. The frequency modulation depth is shown on the $x$ axis. The red line marks the $70\mu \mathrm{Hz}$ boundary to the right of which we expect injections to start losing power. The $y$ axis shows the ratio between the upper limit and injected strain.

Figure 13

Range of the PowerFlux search for neutron stars spinning down solely due to gravitational radiation. This is a superposition of two contour plots. The green 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 $ϵ(f,\dot{f})$. 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).