First all-sky search for continuous gravitational waves from unknown sources in binary systems

We present the first results of an all-sky search for continuous gravitational waves from unknown spinning neutron stars in binary systems using LIGO and Virgo data. Using a specially developed analysis program, the TwoSpect algorithm, the search was carried out on data from the sixth LIGO science run and the second and third Virgo science runs. The search covers a range of frequencies from 20 Hz to 520 Hz, a range of orbital periods from 2 to $\sim 2,254\mathrm{h}$ and a frequency- and period-dependent range of frequency modulation depths from 0.277 to 100 mHz. This corresponds to a range of projected semimajor axes of the orbit from $\sim 0.6\times 10^{-3}\mathrm{ls}$ to $\sim 6,500\mathrm{ls}$ assuming the orbit of the binary is circular. While no plausible candidate gravitational wave events survive the pipeline, upper limits are set on the analyzed data. The most sensitive 95% confidence upper limit obtained on gravitational wave strain is $2.3\times 10^{-24}$ at 217 Hz, assuming the source waves are circularly polarized. Although this search has been optimized for circular binary orbits, the upper limits obtained remain valid for orbital eccentricities as large as 0.9. In addition, upper limits are placed on continuous gravitational wave emission from the low-mass x-ray binary Scorpius X-1 between 20 Hz and 57.25 Hz.

Figure 1

Nominal parameter space that is analyzed using the TwoSpect algorithm (shaded region). The bounding curves given by $\mathrm{\Delta }{f}_{\max }$ and $\mathrm{\Delta }{f}_{\min }$ are limitations of the analysis, while the initial search boundary of $\mathrm{\Delta }{f}_{\max }=0.1\mathrm{Hz}$ is a choice. Data marked by circles are ATNF catalog pulsars found in binary systems with rotation frequencies $\ge 10\mathrm{Hz}$ [using Eq. (8) and assuming $f_0=2\nu$].

Figure 2

All-sky strain upper limit results of S6/VSR2-3 for continuous gravitational waves assuming the source waves are circularly polarized (blue points) or randomly polarized from randomly oriented sources (red points). The vertical black lines indicate 0.25 Hz frequency bands in which no upper limits have been placed. The smoothness of the curve is interrupted due to various instrumental artifacts, such as the violin resonances of the mirror suspensions near 350 Hz.

Figure 3

The efficiency of signals passing the given coincidence requirements as a function of the injection amplitude (normalized to the upper limit value at the specific frequency of the injection).

Figure 4

Sco X-1 strain upper limit results of S6/VSR2-3 for continuous gravitational waves assuming the source waves are circularly polarized (lower points) or the source waves are randomly polarized with random pulsar orientations (upper points). The black vertical lines indicate 0.25 Hz frequency bands in which no upper limits have been placed.

Figure 5

Results from an upper limit validation test at 401 Hz, for circularly polarized waves. Each data point (blue circles) gives the 95% confidence upper limit set by TwoSpect for a given amplitude of a circularly polarized injection. The red line indicates a slope of 1. The upper limit procedure is valid provided that no more than 5% of the blue circle data points lie below the red line for any value of the injected amplitude.

Figure 6

Results from an upper limit validation test at 401 Hz, for randomly polarized waves. Each data point (blue circles) gives the 95% confidence upper limit set by TwoSpect for a given amplitude of a randomly polarized injection. The red line indicates a slope of 1. The upper limit procedure is valid provided that no more than 5% of the blue circle data points lie below the red line for any value of the injected amplitude.