Searches for continuous gravitational waves from Scorpius X-1 and XTE J1751-305 in LIGO’s sixth science run

Scorpius X-1 (Sco X-1) and x-ray transient XTE J1751-305 are low-mass x-ray binaries (LMXBs) that may emit continuous gravitational waves detectable in the band of ground-based interferometric observatories. Neutron stars in LMXBs could reach a torque-balance steady-state equilibrium in which angular momentum addition from infalling matter from the binary companion is balanced by angular momentum loss, conceivably due to gravitational-wave emission. Torque balance predicts a scale for detectable gravitational-wave strain based on observed x-ray flux. This paper describes a search for Sco X-1 and XTE J1751-305 in LIGO science run 6 data using the TwoSpect algorithm, based on searching for orbital modulations in the frequency domain. While no detections are claimed, upper limits on continuous gravitational-wave emission from Sco X-1 are obtained, spanning gravitational-wave frequencies from 40 to 2040 Hz and projected semimajor axes from 0.90 to 1.98 light-seconds. These upper limits are injection validated, equal any previous set in initial LIGO data, and extend over a broader parameter range. At optimal strain sensitivity, achieved at 165 Hz, the 95% confidence level random-polarization upper limit on dimensionless strain $h_0$ is approximately $1.8\times {10}^{-24}$. The closest approach to the torque-balance limit, within a factor of 27, is also at 165 Hz. Upper limits are set in particular narrow frequency bands of interest for J1751-305. These are the first upper limits known to date on $r$-mode emission from this XTE source. The TwoSpect method will be used in upcoming searches of Advanced LIGO and Virgo data.

Figure 1

Detection efficiency of 2000 injections into H1 data over [165.0, 166.0] Hz, with varying amplitude and Doppler parameters. A maximum-likelihood sigmoid fit is made to the unbinned binomial distribution of detected or nondetected injections (based on a threshold of ${\log }_{10}p<-7.75$); the figure shows binned detection probability estimates for illustration purposes only. The strain value (dashed vertical blue line) yielding 95% efficiency (dashed-and-dotted horizontal blue line) determines the strain upper limit in this band.

Figure 2

Upper limit validation, estimated $h_0$ vs injected $h_0$: 700 injections into S6 data in the [142.0, 142.7] Hz band. The uncalibrated “recovered” strain $h_{\mathrm{rec}}$ must be calibrated by scaling to an “estimated” $h_0={\rho }_{\mathrm{UL}}{h}_{\mathrm{rec}}$ such that it is greater than or equal to injected $h_0$ at least 95% of the time (red points). This must hold for all values of $h_0$. Applying the scaling factor to the loudest outlier in each band, as described in the text, yields a result consistent with the final 95% detection efficiency levels, exemplified by Fig. 1, thus validating the upper limits.

Figure 3

2D histogram with hexagonal bins of logarithmic $R$ statistic versus frequency $f_0$ for the Sco X-1 S6 search. Histogram for all templates (gray hex bins) and followed-up coincident templates only (blue dots). Variance in $R$ increases with $f_0$, because more pixels are incorporated into the statistic. However, $R$ remains zero mean. Line artifacts are present at many frequencies, extending to $R\approx 5\times 10^{13}$. The four outliers from Table 3 are marked (red crosshairs); they are at 656, 770, 957, and 1312 Hz.

Figure 4

2D histogram with hexagonal bins of doubly logarithmic (single-template) $p$ value versus frequency $f_0$ for the Sco X-1 S6 search. Histogram for all templates (gray hex bins) and followed-up coincident templates only (blue dots). Line artifacts align with those in Fig. 3. The four outliers from Table 3 are marked (red crosshairs); they are at 656, 770, 957, and 1312 Hz.

Figure 5

Doubly logarithmic horizontal scale for the distribution of $-{\log }_{10}(p)$ values. Histogram for all templates (gray) and followed-up coincident templates only (blue). For high values, $-{\log }_{10}(p)\propto R$. Note that these extreme values of $R$ are, as shown in Fig. 4, typically related to line artifacts in the data. Follow-up threshold of ${\log }_{10}p=-7.75$ shown in (red): a template in each observatory must reach this threshold and be coincident with the other observatory to qualify for follow-up. In comparison to theoretical expectations, templates with many equally weighted pixels would have Gaussian-distributed $R$, while templates dominated by a single pixel will have exponentially distributed $R$. On this figure’s axes, both such distributions would appear as concave-downward curves. The knee in the slope and extended right tail imply that extreme $-{\log }_{10}(p)$ values are part of distinct, unmodeled populations, such as the aforementioned line artifacts. In the absence of artifacts or signals, the below-threshold slope would continue.

Figure 6

Upper limit for average (random) polarization GW from Sco X-1 in S6, joint H1-L1, at 95% confidence (blue dots). Validated by determining the 95% detection efficiency in injections, this spectrum covers [40, 2040] Hz, using the lower upper limit from either observatory when both yielded results. Results are for 1-Hz bands (closed lower edge, open upper edge). Three bands (189, 1031, and 1041 Hz) have anomalously low upper limits that probably stem from spectral artifacts visible in the run-averaged SFT amplitude spectral density. Five near-overlapping bands total are marked (yellow triangles) where upper limits could not be set: four (343, 347, 687 and 688) Hz could not be fit because of additional artifacts yielding insufficient data for the search method, and 345 Hz could not be numerically determined by maximum likelihood. The region around 345 Hz contains the first harmonic of the interferometer suspension violin mode, responsible for these disturbances. Bifurcation in high-frequency limits arises from certain bands being contaminated in H1 and limit being set by the less-sensitive L1 interferometer. Results make no assumptions on $\cos \iota$. Note: torque balance (green line) assumes a 1.4 solar mass, 10 km neutron star.