Improved methods for detecting gravitational waves associated with short gamma-ray bursts

In the era of second generation ground-based gravitational wave detectors, short gamma-ray bursts (GRBs) will be among the most promising astrophysical events for joint electromagnetic and gravitational wave observation. A targeted, coherent search for gravitational wave compact binary merger signals in coincidence with short GRBs was developed and used to analyze data from the first generation LIGO and Virgo instruments. In this paper, we present improvements to this search that enhance our ability to detect gravitational wave counterparts to short GRBs. Specifically, we introduce an improved method for estimating the gravitational wave background to obtain the event significance required to make detections; implement a method of tiling extended sky regions, as required when searching for signals associated to poorly localized GRBs from the Fermi Gamma-ray Burst Monitor or the InterPlanetary Network; and incorporate astrophysical knowledge about the beaming of GRB emission to restrict the search parameter space. We describe the implementation of these enhancements and demonstrate how they improve the ability to observe binary merger gravitational wave signals associated with short GRBs. A targeted, coherent GRB search provides a 25% increase in distance sensitivity, or a doubling of the event rate, for well-localized GRBs when compared with a nontargeted, coincident analysis.

Figure 1

FAP as a function of the reweighted SNR detection statistic for a search performed for GRB 100928A, using time slides to reach $\mathrm{FAP}<{10}^{-5}$. The figure shows the background estimated with off-source only (787 trials) plotted in orange Y; the short slide analysis (8917 trials) plotted in green $\times$; both long and short slides (267185 trials) plotted in blue $+$. With short slides alone, we can estimate a significance of 1 part in ${10}^4$ while long and short slides give a background estimate to 1 in $3.7\times {10}^6$. The shaded regions show the 95% Jeffreys credible interval for each case, which assumes each time slide is a statistically independent trial. For clarity of presentation we have only plotted the 20 loudest trials for each search.

Figure 2

Comparison between the $+$, $\times$ amplitude terms as a function of inclination angle $\iota$. Note that even at 30° the difference is only $\sim 1\%$.

Figure 3

The background significance against detection statistic for a search performed for GRB 100928A. In red $\times$, we plot the background calculated using the circular polarization restriction and in blue $+$ we plot the background from the unrestricted search. In both cases, we perform time shifts of the data as discussed in Sec. 3. Over a broad range of SNR values, the circular polarization restriction reduces the background by a factor of 3. Equivalently, the required SNR to achieve a given FAP is reduced by about 0.25, equating to a 3% increase in the distance sensitivity of the search. For clarity of presentation we have only plotted the loudest 50 trials for each search.

Figure 4

An example patch of sky points projected onto the celestial sphere. The blue filled circles show the full grid, while the empty circles are those few points that map to unique differences in signal arrival time between LIGO’s Hanford and Livingston detectors. The parsed points do not form a straight line, but this is simply due to an artifact of the parsing routine and has no effect on the grid reduction.

Figure 5

The background significance against detection statistic for a search performed for GRB 100928A. In red $+$, we plot the background measured for a single point in the direction of GRB 100928A. In blue $\times$, we show the background for a sky patch of radius 15° (178 points), encompassing the location of the GRB. In green Y, we show the background for a different single-point search. The point was chosen as it contributed two of the ten loudest events in the patch search. For SNRs between 6.5 and 7.5, the background of the patch is around a factor of 20 above the single-point searches. The increase is expected as we are searching a large number of points, but they are not all independent. At low SNR the increase is smaller, due to clustering effects in the analysis. At larger SNR, the variations between the different analyses are all consistent with statistical fluctuations.

Figure 6

The fraction of artificially injected binary neutron star signals found louder than the loudest background event as a function of injected distance. The three curves represent three observational scenarios for a three detector network comprised of Virgo and both LIGO interferometers. In the scenario mimicking a BAT GRB (black solid line, error $\text{radius}=0.036°$) the pipeline searches a single point on the sky and finds 90% of signals within 20 Mpc. In the two scenarios mimicking a GBM GRB we see that by searching over a patch of points covering the large error box of 15° radius (red dashed line) the pipeline performs nearly as well as for the BAT GRB for signals below 15 Mpc. This is in stark contrast to the previous treatment for GBM-like GRBs (blue dotted line), which searched a single point at the center of the error box resulting in very poor rates of injection recovery. The increased number of trials resulting from multiple sky points leads to a tail of background events louder than any seen of the BAT single-point search, reducing the overall sensitivity of the patch search.

Figure 7

The fraction of artificially injected binary neutron star signals found louder than the loudest background event using only the LIGO Hanford and Livingston detectors, plotted as a function of injected distance. As in Fig. 6, we plot a scenario mimicking a BAT GRB (black solid line, error $\text{radius}=0.036°$) where the pipeline searches a single point in the sky. In this case, the pipeline finds 90% of signals within 18 Mpc. In the scenario where a GBM GRB with error box of 15° radius is searched at a single point (blue dotted line), we see poor signal recovery performance at small distances due to signal consistency effects, similar to the three detector case. The difference between the full patch of search points (red dashed line) and a set of points covering unique time delays between sites (green dot-dashed line) is noticeable at small distances, with the use of incorrect antenna response factors causing a drop in performance for the parsed patch. Again, the increased number of trials resulting from multiple sky points leads to a tail of background events louder than any seen in the BAT single-point search, reducing the overall sensitivity of multiple point searches.