SEARCH FOR GRAVITATIONAL WAVES ASSOCIATED WITH GAMMA-RAY BURSTS DURING LIGO SCIENCE RUN 6 AND VIRGO SCIENCE RUNS 2 AND 3

Stellar collapse is notoriously difficult to model. It necessitates complex micro-physics and full three-dimensional simulations, which take years to complete for a single initial state. Many simulations that include some, but not all, physical aspects have been performed for non-extreme cases of core-collapse supernovae, which identified numerous potential GW burst emission channels; see Ott (2009) for a review. These models predict emission of up to 10⁻⁸ M_☉ c² through GWs. Given the sensitivity of current GW detectors, such GW emission models are not detectable from extragalactic progenitors.

However, in the extreme stellar collapse conditions which are necessary to power a GRB, more extreme GW emission channels can be considered. Several semi-analytical scenarios have been proposed which produce up to 10⁻² M_☉ c² in GWs, all of which correspond to some rotational instability developing in the GRB central engine (Davies et al. 2002; Fryer et al. 2002; Kobayashi & Mészáros 2003a; Shibata et al. 2003; Piro & Pfahl 2007; Corsi & Mészáros 2009; Romero et al. 2010). In each model the GWs are emitted by a quadrupolar mass distribution rotating around the GRB jet axis. Given the observation of a GRB, this axis is roughly pointing at the observer, which yields circularly polarized GWs (Kobayashi & Mészáros 2003b).

For extreme stellar collapses, the arrival of γ-rays can be significantly delayed with respect to the GW emission. Delays of up to 100 s can be due to several phenomena: the delayed emission of the relativistic jet (MacFadyen et al. 2001); sub-luminal propagation of the jet to the surface of the star in the collapsar model for long GRBs (see, for example, Aloy et al. 2000; Zhang et al. 2003; Wang & Meszaros 2007; Lazzati et al. 2009); and the duration, in the observer's frame, of the relativistic propagation of the jet before the onset of the prompt γ-ray emission (Vedrenne & Atteia 2009). For some GRBs, γ-ray precursors have been observed up to several hundred seconds before the main γ-ray emission peak (Koshut et al. 1995; Burlon et al. 2009, 2008; Lazzati 2005); the precursor could mark the initial event, with the main emission following after a delay.

The coalescence of two compact objects is usually thought of as a three-step process: an inspiral phase, where the orbit of the binary slowly shrinks due to the emission of GWs; a merger phase, when the two objects plunge together; and a ringdown phase, during which the newly created and excited black hole settles into a stationary state (Shibata & Taniguchi 2011). As the GWs emitted in the inspiral phase dominate the signal-to-noise ratio in current detectors, we focus on that phase only.¹¹⁷

We consider compact binaries consisting of two neutron stars (NS–NS) or a neutron star with a black hole (NS–BH). As the objects spiral together, the neutron star(s) are expected to tidally disrupt shortly before they coalesce, creating a massive torus. The matter in the torus can then produce highly relativistic jets, which are supposedly ejected along the axis of total angular momentum. While this picture is supported by recent numerical simulations (Foucart et al. 2011; Rezzolla et al. 2011), it has not yet been confirmed by complete simulations, and the influence of a tilted BH spin is uncertain.

Contrary to the long GRB case, the onset of γ-ray emission is delayed only up to a few seconds compared to the GW emission, as there is no dense material retaining the jet and other delay effects are at most as long as the GRB duration (Vedrenne & Atteia 2009). Semi-analytical calculations of the final stages of an NS–BH coalescence show that the majority of matter plunges onto the BH within ∼1 s (Davies et al. 2005). Numerical simulations of the mass transfer suggest a timescale of milliseconds or a few seconds at maximum (Faber et al. 2006; Rosswog 2006; Etienne et al. 2008; Shibata & Taniguchi 2008). Therefore, an observer in the cone of the collimated outflow is expected to observe the GW signal up to a few seconds before the electromagnetic signal from the prompt emission.

Both search pipelines identify an "on-source" time in which to search for an associated GW event. This time selection is expected to improve by a factor ∼1.5 the sensitivity of the search compared to an all-sky/all-time search (Kochanek & Piran 1993). For the GW burst search, we use the interval from 600 s before each GRB trigger to either 60 s or the T₉₀ time (whichever is larger) after the trigger as the window in which to search for a GW signal. This conservative window is large enough to take into account most plausible time delays between a GW signal from a progenitor and the onset of the gamma-ray signal, as discussed in Section 2.1. This window is also safely larger than any uncertainty in the definition of the measured GRB trigger time. For cases when less early GW data are available, a shorter window starting 120 s before the GRB trigger time is used. This still covers most time-delay scenarios. For the binary coalescence search, it is believed that the delay between the merger and the emission of γ-rays will be small, as discussed in Section 2.2. We therefore use an interval of 5 s prior to the GRB to 1 s following as the on-source window, which is wide enough to allow for uncertainties in the emission model and in the arrival time of the electromagnetic signal (Abbott et al. 2010a).

The on-source data are scanned by the search algorithms to detect possible GW transients (either coalescence or burst), referred to as "events." For both searches the analysis depends on the sky position of the GRB. GRBs reported by the Swift satellite have very small position uncertainty (≪1°; see Barthelmy et al. 2005), and the GW searches need only be performed at the reported sky location. For GRBs detected by the Gamma-ray Burst Monitor (GBM) on the Fermi satellite (Meegan et al. 2009), however, the sky localization region can be large (≫1°), and detection efficiency would be lost if the GW searches only used a single sky location. To resolve this problem, searches for poorly localized GRBs are done over a grid of sky positions, covering the sky localization region (Wąs 2011; Wąs et al. 2012). We assume a systematic 68% coverage error circle for the Fermi/GBM sky localizations with a radius of 32 with 70% probability and a radius of 95 with 30% probability (Connaughton 2011), which is added in quadrature to the reported statistical error.

Each pipeline orders events found in the on-source time according to a ranking statistic. To reduce the effect of non-stationary background noise, candidate events are subjected to checks that "veto" events overlapping in time with known instrumental or environmental disturbances (Aasi et al. 2012). The surviving event with the highest ranking statistic is taken to be the best candidate for a GW signal for that GRB; it is referred to as the loudest event (Brady et al. 2004; Biswas et al. 2009). To estimate the significance of the loudest event, the pipelines also analyze coincident data from a period surrounding the on-source data, where we do not expect a signal. The proximity of these off-source data to the on-source data makes it likely that the estimated background will properly reflect the noise properties in the on-source segment. The off-source data are processed identically to the on-source data; in particular, the same data-quality cuts and consistency tests are applied, and the same sky positions relative to the GW detector network are used. If necessary, to increase the background distribution statistics, multiple time shifts are applied to the data streams from different detector sites, and the off-source data re-analyzed for each time shift.

To determine if a GW is present in the on-source data, the loudest on-source event is compared to the distribution of loudest off-source events. A p-value is defined as the probability of obtaining such an event or louder in the on-source data, given the background distribution, under the null hypothesis. The triggers with the smallest p-values in the searches are subjected to additional follow-up studies to determine if the events can be associated with some non-GW noise artifact, for example due to an environmental disturbance.

Regardless of whether a statistically significant signal is present, we also set a 90% confidence level lower limit on the distance to the GRB progenitor for various signal models. This is done by adding simulated GW signals to the data and repeating the analyses. These signals, which are drawn from astrophysically motivated distributions described in the following sections, are used to calculate the maximum distance for which there is a 90% or greater chance that such a signal model, if present in the on-source region, would have produced an event with larger ranking statistic than the largest value actually measured.

The search procedure for GW bursts follows that used in the 2005–2007 GRB search (Abbott et al. 2010b). All GRBs are treated identically, without regard to redshift (if known), fluence, or classification. The on-source data are scanned by the X-Pipeline algorithm (Sutton et al. 2010; Wąs et al. 2012), which is designed to detect short GW bursts, ≲ 1 s, in the 60–500 Hz frequency range. X-Pipeline combines data from arbitrary sets of detectors, taking into account the antenna response and noise level of each detector to improve the search sensitivity. Time–frequency maps of the combined data streams are scanned for clusters of pixels with energy significantly higher than that expected from background noise. The resulting candidate GW events are characterized by a ranking statistic based on energy. We also apply consistency tests based on the signal correlations measured between the detectors, assuming a circularly polarized GW, to reduce the number of background events. (The circular polarization assumption is motivated by the fact that the GRB system rotation axis should be pointing roughly at the observer, as discussed in Section 2.1.) The stringency of these tests is tuned by comparing their effect on background events and simulated signal events. The background samples are constructed using the ±1.5 hr of data around the GRB trigger, excluding the on-source time. Approximately 800 time shifts of these off-source data are used to obtain a large sample of background events.

To obtain signal samples, simulated signals are added to the on-source data. The models of GW emission by extreme stellar collapse described in Section 2.1 do not predict the exact shape of the emitted GW signal. As an ad hoc model, we use the GW emission by a rigidly rotating quadrupolar mass moment with a Gaussian time evolution of its magnitude. For such a source with a rotation axis inclined by an angle ι with respect to the observer the received GW signal is a sine-Gaussian

$$\begin{eqnarray} &&{\left[\begin{array}{@{}c@{}}h_+(t) \\ h_\times (t) \end{array}\right]} &=& \frac{1}{r}\sqrt{\frac{G}{c^3}\frac{E_{\rm GW}}{f_0 Q} \frac{5}{4 \pi ^{3/2}}} \nonumber\\ && \times {\left[\begin{array}{@{}c@{}}(1+ \cos ^2 \iota) \cos\, (2 \pi f_0 t) \\ 2\cos \iota \sin\, (2 \pi f_0 t) \end{array}\right]}\exp \left[\! - \frac{(2 \pi f_0 t)^2}{2Q^2} \!\right], \quad\quad \end{eqnarray} \tag{ 1 }$$

where the signal frequency f₀ is equal to twice the rotation frequency, t is the time relative to the signal peak time, Q characterizes the number of cycles for which the quadrupolar mass moment is large, E_GW is the total radiated energy, and r is the distance to the source. We consider two sets¹²¹ of such signals with signal frequencies f₀ of 150 Hz and 300 Hz, which cover the sensitive frequency band of this GW burst search. The inclination angle is distributed uniformly in cos ι, with ι between 0° and 5°, which corresponds to the typical jet opening angle of ∼5° observed for long GRBs (Gal-Yam 2006; Racusin et al. 2009).

Systematic errors are marginalized over in the sensitivity estimation by "jittering" the simulated signals before adding them to the detector noise. This includes distributing injections across the sky according to the gamma-ray satellites' sky location error box, and jittering the signal amplitude, phase, and timing in each detector according to the given detector calibration errors (Accadia et al. 2011; Bartos et al. 2011). This procedure also ensures that the consistency tests used in the analysis are loose enough to allow for such errors.

The core of the coalescence search involves correlating the measured data against theoretically predicted waveforms using matched filtering (Helmstrom 1968). GWs from the inspiral phase of a coalescence are modeled by post-Newtonian approximants in the band of the detector's sensitivity for a wide range of binary masses (Blanchet 2006). The expected GW signal depends on the masses and spins of the NS and its companion (either NS or BH), as well as the distance to the source, its sky position, its inclination angle, and the polarization angle of the orbital axis. Matched filtering is most sensitive to the phase evolution of the signal, which depends on the binary masses and spins, the time of merger, and a fiducial phase. The time and phase can be determined analytically. Ignoring spin, we can therefore perform matched filtering over a discrete two-dimensional bank of templates which span the space of component masses. This bank is constructed such that the maximum loss in signal-to-noise ratio for a binary with negligible spins is 3% (Cokelaer 2007; Harry & Fairhurst 2011). For this search, as in the 2005–2007 GRB search (Abbott et al. 2010a), we used "TaylorF2" frequency domain templates, generated at 3.5 post-Newtonian order (Blanchet et al. 1995, 2004). While the spin of the components is ignored in the template waveforms, we evaluate the efficiency of the search using simulated signals including spin, as described below.

For each short GRB, the detector data streams are combined coherently and searched using the methods described in detail in Harry & Fairhurst (2011). Various signal consistency tests are then applied to reject non-stationary noise artifacts. These include χ² tests (Allen 2005; Hanna 2008), a null stream consistency test, and a re-weighting of the signal-to-noise ratio to take into account the values recorded by these tests. This is the first coherent search for coalescence signals; it has been found to be more sensitive to GW signals than the coincidence technique used in previous triggered coalescence searches of LIGO and Virgo data (Harry & Fairhurst 2011). Tests using the simulations described below have also shown that this focused coalescence search is a factor of ∼2 more sensitive to coalescence signals than the unmodeled search described in the previous section, justifying the use of a specialized search for this signal type.

To estimate the efficiency of the search and calculate exclusion distances for short GRBs, we draw simulations from two sets of astrophysically motivated compact binary systems: two neutron stars (NS–NS) and a neutron star with a black hole (NS–BH). The NS masses are chosen from a Gaussian distribution centered at 1.4 M_☉ (Kiziltan et al. 2010; Ozel et al. 2012) with a width of 0.2 M_☉ for the NS–NS case, and a broader spread of 0.4 M_☉ for the NS–BH systems, to account for larger uncertainties given the lack of observations for such systems. The BH masses are Gaussian distributed with a mean of 10 M_☉ and a width of 6 M_☉. The BH mass is restricted such that the total mass of the system is less than 25 M_☉. For masses greater than this, the NS would be "swallowed whole" by the BH, no massive torus would form, and no GRB would be produced (Duez 2010; Ferrari et al. 2010; Shibata & Taniguchi 2011).

Observed pulsar spin periods and assumptions about the spin-down rates of neutron stars place the NS spin periods at birth in the range of 10–140 ms, corresponding to an upper limit on S/m² of ⩽0.04 (Mandel & O'Shaughnessy 2010), where S denotes the spin of the neutron star and m its mass. However, neutron stars can be spun up to much higher spins (e.g., to 716 Hz; Hessels et al. 2006); hence we conservatively assume a maximum spin of S/m² < 0.4 corresponding to a ∼1 ms pulsar. Therefore, the spin magnitudes are drawn uniformly from the range [0, 0.4]. For BHs the magnitudes are chosen uniformly in the [0, 0.98) range (Mandel & O'Shaughnessy 2010). The spins are oriented randomly, with a constraint on the tilt angle (the angle between the spin direction of the BH and the orbital angular momentum). Since the merger needs to power a GRB, a sufficiently massive accretion disk around the BH is required. Population synthesis studies indicate that the tilt angle is predominantly below 45° (Belczynski et al. 2008); numerical simulations show that for tilt angles larger than 40° the mass of the disk will drop rapidly (Foucart et al. 2011) and BHs with tilt angle >60° will "swallow" the NS completely, leaving no accretion disk to power a GRB (Rantsiou et al. 2008). In our simulations we use the weakest of these three constraints and set the tilt angle to be <60°.

The outflow from a GRB is most likely to be along the direction of the total angular momentum J of the system as discussed in Section 2.2. Observations suggest that this outflow is confined within a cone, whose half-opening angle is estimated to range between several degrees to over 60° for short GRBs (see, e.g., Burrows et al. 2006; Grupe et al. 2006; Dietz 2011). Under the assumption that this cone is centered along the total angular momentum J of the system, we chose the inclination angle between J and the line of sight to the observer to be distributed within cones of half-opening angles 10°, 30°, 45°, and 90°. The majority of the results quoted in this work assume a 30° angle.

The coalescence time is uniform over the on-source region, and the sky position of the GRB is jittered according to the reported uncertainty of the location.

The quoted exclusion distances are marginalized over systematic errors that are inherent in this analysis. First, there is some uncertainty in how well our post-Newtonian templates will match real GW signals; we expect a loss in signal-to-noise ratio of up to 10% because of this mismatch (Abbott et al. 2009b). Second, there is uncertainty in the amplitude calibration of the detectors (Bartos et al. 2011; Accadia et al. 2011); phase and timing calibration uncertainties are also present, but are negligible compared to other sources of errors.

An opportunistic search for coalescence signals has also been performed on the long GRBs. This search is done to conservatively account for uncertainties in the details of the short/long GRB classification, and for uncertainties in the progenitor model of long GRBs for which an associated SN signature was excluded (Gehrels et al. 2006; Watson et al. 2007; Gao et al. 2010). We use the same analysis to check for a coalescence signal associated with long GRBs, but do not estimate exclusion distances as the compact binary coalescence progenitor model is unlikely for long GRBs.

In addition to evaluating individual p-values, we use a weighted binomial test to assess whether the obtained set of p-values is compatible with the uniform distribution expected from noise only, for both the GW burst and coalescence searches. This test looks for deviations from the null hypothesis in the 5% tail of lowest p-values weighted by the prior probability of detection (estimated from the GW search sensitivity). The weighted binomial test is an extension of the binomial test that has been used in previous searches for GW bursts associated with GRBs (Abbott et al. 2008b, 2010b). The combination of p-values with prior detection probabilities gives more weight to GRBs for which the GW detectors had better sensitivity and therefore the detection of a GW signal is more likely. The details of this test are given in Appendix A.

The result of the weighted binomial test is a single ranking statistic S_weighted. The statistical significance of the measured S_weighted is assessed by comparing to the background distribution of this statistic from Monte Carlo simulations with p-values uniformly distributed in [0, 1]. This yields the overall background probability of the measured set of p-values.

The distribution of p-values for each of the 150 GRBs analyzed by the GW burst search is shown in Figure 2. The weighted binomial test yields a background probability of 25%. Therefore, the distribution is consistent with no GW events being present.

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The smallest p-value, 0.15%, has been obtained for GRB 100917A. This GRB was localized on the sky by Swift; however no redshift measurement is available to date. The corresponding GW event was obtained by combining data from the H1, L1, and V1 detectors. A study of the environmental and instrumental channels at that time yields potential instrumental causes for this event, but is not conclusive. Regardless, the measured p-value is not significant as determined by the weighted binomial test, so this event is not a candidate for a GW detection.

The distribution of p-values for each of the 26 short GRBs analyzed by the coalescence search is shown in Figure 3. The result of the weighted binomial test yields a background probability of 8%, corresponding to a 1.8σ deviation from the null hypothesis. However, as we mentioned in Section 4, we use a lenient classification when deciding if GRBs are treated as short or long for the purposes of our analyses. If restrict our short GRB sample to the more commonly used criterion, T₉₀ < 2 s, then we find a background probability of 3%, corresponding to a 2.2σ deviation.

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This deviation was due to an event found in coincidence with GRB 100328A, which produced the smallest p-value of 1%, and was the GRB to which the search had the second best sensitivity. A follow-up investigation of this candidate determined that it was due to a noise artifact in the Hanford instrument, which was one of a class of glitches caused by a bad power supply which contaminated the length and angular control servos. No other noteworthy events were found by this search and thus there are no potential GW candidates. The opportunistic search for coalescence signals associated with long GRBs did not yield any candidate that was inconsistent with background noise.

For each GRB we derive a 90% confidence lower limit on the GRB progenitor distance for various emission models using the methodology described in Section 5.1.

The GW burst search provides lower limits on the generic GW burst signal emitted by a rotator described in Section 5.2 for each GRB. We assume that the source emitted E_GW = 10⁻² M_☉ c² of energy in GWs,¹²² that the jet opening angle is 5°, and consider emission frequencies of 150 Hz and 300 Hz. The distance limits are given in Tables 1 and 2, and their histogram is shown in Figure 4. The median exclusion distance is D ∼ 17 Mpc (E_GW/10⁻² M_☉ c²)^1/2 for emission at frequencies around 150 Hz, where the LIGO–Virgo detector network is most sensitive.

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The coalescence search sets lower limits on both the NS–NS and NS–BH models described in Section 5.3 for each short GRB, assuming a jet half-opening angle of 30°. The distance limits are given in Table 1 and a histogram of their values is shown in Figure 5. The median exclusion distance for NS–NS (NS–BH) coalescences is 16 Mpc (28 Mpc) for the 30° cone. We note that these exclusion distances are affected by the choice of signal parameter priors in Section 5.3; for example, Figure 6 shows the median exclusion distances for half-opening angles of 10°, 30°, 45°, and 90°. Since the amplitude of a GW signal is stronger for a face-on binary, the exclusion distance improves for smaller half-opening angles. With no restriction on the opening angle, the 90% exclusion distance decreases significantly, as there are orientations which will give very little observable GW signal in the detector network.

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The GW burst and compact binary coalescence exclusion distances may be compared to those from all-sky searches, which look for GWs without requiring association with a GRB or other external trigger. Figure 7 of Abadie et al. (2012a) presents 50%-confidence exclusion energies for the all-sky GW burst search on this same data set for an assumed source distance of 10 kpc, with a best limit of approximately E_GW = 2 × 10⁻⁸ M_☉ c² at 150 Hz. Rescaling to our nominal value of 10⁻² M_☉ c² gives an exclusion distance of ∼7 Mpc. Wąs (2011) performs a more rigorous comparison that accounts for the fraction of events that do not produce GRB triggers due to the γ-ray beaming. This indicates that for emission opening angles in the 5°–30° range, the GRB triggered search should detect a similar number of GW events coming from GRB progenitors as that detected by the all-sky search—between 0.1 and 6 times the number detected by the all-sky search. Furthermore, most of the GW events found by the GRB triggered search will be new detections not found by the all-sky search, illustrating the value of GRB satellites for GW detection.

The NS–NS/NS–BH models used for compact binary coalescence exclusions stand on much firmer theoretical ground than the model used for GW burst exclusions. The amplitude of a coalescence signal is well known and depends on the masses and spins of the compact objects whereas the GW burst energy emitted during a GRB is largely unknown and could be orders of magnitude smaller than the chosen nominal value of E_GW = 10⁻² M_☉ c². In the pessimistic scenario that GRB progenitors have a comparable GW emission to core-collapse supernovae, the emitted energy could be as low as E_GW ∼ 10⁻⁸ M_☉ c². Such a signal would only be observable with current GW detectors from a galactic source.

As well as a per-GRB distance exclusion, we set an exclusion on GRB population parameters by combining results from the set of analyzed GRBs. To do this, we use a simple population model, where all GRB progenitors have the same GW emission (standard sirens), and perform exclusion on cumulative distance distributions. We parameterize the distance distribution with two components: a fraction F of GRBs distributed with a constant comoving density rate¹²³ up to a luminosity distance R, and a fraction 1 − F at effectively infinite distance. This simple model yields a parameterization of astrophysical GRB distance distribution models that predict a uniform local rate density and a more complex dependence at redshift >0.1, as the large-redshift part of the distribution is well beyond the sensitivity of current GW detectors. The exclusion is then performed in the (F, R) plane. Full details of the exclusion method are given in Appendix B.

The exclusion for GW bursts at 150 Hz with E_GW = 10⁻² M_☉ c² is shown in Figure 7, whereas the exclusion for the coalescence model for short GRBs is shown in Figure 8. Both exclusions are shown in terms of redshift, where we assume a flat ΛCDM cosmology with Hubble constant H₀ = 70 km s⁻¹ Mpc⁻¹, dark matter content Ω_M = 0.27, and dark energy content Ω_Λ = 0.73 (Komatsu et al. 2011). The exclusion at low redshift is dictated by the number of GRBs analyzed and at high redshift by the typical sensitive range of the search. These exclusions assume 100% purity of the GRB sample. For purity p the cumulative distribution should be rescaled by 1/p; for instance, only one-third of our short GRB sample has a T₉₀ < 2 s. For comparison, each figure also shows the distribution of measured GRB redshifts, for all Swift GRBs (Figure 7) or for all short GRBs (Figure 8). While the distribution of GRBs with measured redshifts includes various observational biases compared to the distribution of all GRBs detected electromagnetically (and on which we perform exclusions), it is clear that the exclusions from the current coalescence and GW burst searches are not sufficient to put any additional constraint on the nature of GRBs.

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While this search for GW signals in coincidence with observed GRBs was not at the sensitivity necessary to detect such coincidences, it is interesting to consider the chances of detection with the Advanced LIGO/Virgo detectors (Acernese et al. 2009; Harry et al. 2010), which should become operational in 2015. At their design sensitivity, these detectors should offer a factor of 10 improvement in distance sensitivity to both GW burst and coalescence signals, dramatically improving the chances to make a GW observation of an electromagnetically detected GRB.

In Figures 7 and 8 we extrapolate the current exclusion curves to the advanced detector era by assuming a factor 10 increase in sensitivity of the GW detectors and a factor 5 increase in the number of GRBs analyzed (equivalent to approximately 2.5 years of live observing time at the rate that GRBs are currently being reported). These extrapolations show that detection is quite possible in the advanced detector era. Even if a detection is not made, targeted GW searches will allow us to place astrophysically relevant constraints on GRB population models.

For long GRBs, the Advanced LIGO/Virgo detectors will be able to test optimistic scenarios for GW emission—those that produce ∼10⁻² M_☉ c² in the most sensitive frequency band of the detectors. The sensitive range for these systems will include the local population of sub-luminous GRBs that produce the low-redshift excess in Figure 7. We note, however, that GW burst emission with significantly lower E_GW or at non-optimal frequencies is unlikely to be detectable.

For short GRBs, a coincident GW detection appears quite possible. This conclusion is consistent with simple estimates such as that of Metzger & Berger (2012), who estimate a coincident observation rate of 3 yr⁻¹ (0.3 yr⁻¹) for NS–BH systems (NS–NS systems) with the advanced detectors. The precise rate of occurrence will depend on the typical masses of the compact objects; we are sensitive to NS–BH systems at a larger distance than NS–NS systems. The distribution of binary component spins and the jet opening angle will also affect the received GW signal strength. The detection rate will also depend on the shape of the short GRB cumulative distance curve at low redshift. One must also remember that we used a very optimistic definition of short GRBs to avoid missing a potential signal. It is likely that some of the short GRBs that we analyzed for coalescence signals were not produced by a compact binary progenitor. Even in the case that no coalescence signals are detected in coincidence with short GRBs in the advanced detector era, it should be possible to place astrophysically interesting constraints on the physical characteristics of progenitors of short GRBs.

Finally, we note that these extrapolations carry a number of other uncertainties. In particular, the actual performance of future detectors is unknown. Furthermore, the extrapolations depend on how well the sky will be covered by gamma-ray satellites in 2015 and later compared to the present day.