Searching for gravitational waves from binary coalescence

We describe the implementation of a search for gravitational waves from compact binary coalescences in LIGO and Virgo data. This all-sky, all-time, multidetector search for binary coalescence has been used to search data taken in recent LIGO and Virgo runs. The search is built around a matched filter analysis of the data, augmented by numerous signal consistency tests designed to distinguish artifacts of non-Gaussian detector noise from potential detections. We demonstrate the search performance using Gaussian noise and data from the fifth LIGO science run and demonstrate that the signal consistency tests are capable of mitigating the effect of non-Gaussian noise and providing a sensitivity comparable to that achieved in Gaussian noise.

Figure 1

Structure of the ihope pipeline. Template bank creation, matched filtering, and coincidence testing are described in Sec. 2. To mitigate the effect of non-Gaussian noise, signal, and amplitude consistency tests are performed on triggers and data quality vetoes are applied; the calculation and applitcation of these tests are described in Sec. 3. Surviving triggers are ranked by their false alarm rate FAR, and the efficiency of the pipeline is evaluated using simulated signals. These final steps are described in Sec. 4.

Figure 2

A typical template bank for a low-mass CBC inspiral search, as plotted in $m_1\mathrm{\text{−}}{m}_2$ space (top panel) and ${\tau }_0\mathrm{\text{−}}{\tau }_3$ space (bottom panel). Templates are distributed more evenly over ${\tau }_0$ and ${\tau }_3$, since the parameter-space metric is approximately flat in those coordinates.

Figure 3

Distribution of single detector trigger SNRs in a month of simulated Gaussian noise in blue (dark gray) and real S5 LIGO data in red (light gray) from the Hanford interferometer H1.

Figure 4

Distribution of average parameter-space distance between coincident triggers associated with simulated GW signals in a month of representative S5 data, as recovered by the LIGO H1 and L1 detectors. The solid, vertical black line represents the threshold for triggers to be considered coincident; triggers to the right of this line were not considered to be coincident. The small number of simulated signals which failed coincidence were ones where the signal did not have sufficient SNR in at least one of the detectors to be a convincing detection. This cut does not cause signals to be missed that might otherwise be claimed as detections.

Figure 5

Distribution of single detector SNRs for H1 coincident triggers in a month of simulated Gaussian noise in blue (dark gray) and representative S5 data in red (light gray). Coincidence was evaluated after time-shifting the SNR time series, so that only background coincidences caused by noise would be included. Comparison with Fig. 3 shows that the coincidence requirement reduces the high-SNR tail, but by no means eliminates it.

Figure 6

The ${\chi }^2$ test plotted against SNR for triggers in a month of representative S5 data after the ${\chi }^2$ test has been applied, and the $r^2$ cut has been applied for triggers with $\rho <12$. The blue crosses mark time shifted background triggers, the red pluses mark simulated-GW triggers. The grey shaded region bounded by a black dashed line denotes the area in which triggers are vetoed by the chi-squared cut (Sec. 3a). The solid, colored lines on the plots indicate lines of constant effective SNR (top panel) and new SNR (bottom panel), which are described in Sec. 3e. Larger values of effective/new SNR are at the bottom and right end of the plots.

Figure 7

Value of SNR and ${\chi }^2$ as a function of time, for a simulated CBC signal with $\mathrm{SNR}=300$ in a stretch of S5 data from the H1 detector. The SNR shows a characteristic rise and fall around the signal. The ${\chi }^2$ value is small at the time of the signal, but increases steeply to either side as the template waveform is offset from the signal in the data.

Figure 8

The time $\Delta T$ that the ${\chi }^2$ is above the threshold $p{r}^2$ as a function of SNR, for all second-stage H1 triggers in a month of representative S5 data. The blue (dark gray) crosses mark all background triggers that fail the cut; blue (dark gray) circles indicate background triggers that pass it. Red (light gray) symbols mark simulated-GW triggers, with only a single signal removed by the cut.

Figure 9

Distribution of $\kappa$ [Eq. (16)], the fractional difference in the effective distances measured by H1 and H2 for coincident triggers in those detectors in a month of representative S5 data. Background triggers plotted in blue (dark gray) tend to have larger than simulated-GW triggers shown in red (light gray).

Figure 10

Distribution of single detector SNRs for H1 triggers found in coincidence with L1 triggers (in time shifts) in a month of simulated Gaussian noise in blue (dark gray) and representative S5 data in red (light gray). These triggers have survived ${\chi }^2$, $r^2$, and H1–H2 amplitude-consistency tests, as well as DQ vetoes.

Figure 11

Distribution of single detector new SNR, ${\rho }_{\mathrm{new}}$, for H1 triggers found in coincidence with L1 triggers (in time shifts) in a month of simulated Gaussian noise in blue (dark gray) and representative S5 data in red (light gray). The tail of high (SNR) triggers due to non-Gaussian noise has been virtually eliminated—a remarkable achievement given that the first stage of the pipeline generated single-detector triggers with $\mathrm{SNR}>1,000$.

Figure 12

Fraction of time-shift coincident triggers between H1 and L1 in a month of representative S5 data that have combined new SNR greater than or equal to the $x$-axis value, for three chirp-mass bins. The distribution from a month of Gaussian noise is also shown for comparison. The tails of the distributions become more shallow for larger chirp masses $\mathcal{M}$, so triggers with higher $\mathcal{M}$ are more likely to have higher SNRs.

Figure 13

Cumulative histogram of triggers above and IFAR threshold for all time-shift triggers in H1H2L1 triple-coincident time from a representative month of S5 data. The black dashed line marks the expected cumulative number of background triggers in the in-time data, as estimated from the time-shift analyses. The shaded regions mark its 1- and $2\mathrm{\text{−}}\sigma$ variation and the thin grey lines show the cumulative number for 20 of the time shifts, providing an additional indication of the expected deviation from the mean.

Figure 14

Decisive distance versus chirp mass, $\mathcal{M}$, (see main text for definition) of found and missed injections in one month of S5 data. Red crosses are missed injections; colored circles are injections found with nonzero combined FAR, which can be read off the color map on the right; dark-blue stars are injections found with triggers louder than any in the background from 100 time shifts. Nearby injections that are missed or found with high FARs are followed up to check for problems in the pipeline, and to improve data quality.

Figure 15

Search efficiency for BNS injections in a month of representative S5 data and in Gaussian noise, for a false-alarm rate equal to the FAR of the loudest foreground trigger in each analysis.