Search for Gravitational-wave Signals Associated with Gamma-Ray Bursts during the Second Observing Run of Advanced LIGO and Advanced Virgo

Gamma-ray bursts (GRBs) are high-energy astrophysical transients originating throughout the universe that are observed more than once per day on average. The prompt gamma-ray emission is thought to emanate from highly relativistic jets powered by matter interacting with a compact central object such as an accreting black hole (BH) or a magnetar (Woosley 1993). Broadly speaking, GRBs are divided into two subpopulations based on duration and spectral hardness (Kouveliotou et al. 1993).

Long-soft bursts generally have durations ≳2 s. The favored model is the core-collapse supernova (SN) of a rapidly rotating massive star (Woosley & Bloom 2006; Mösta et al. 2015). This connection was observationally supported by the presence of SN 1998bw within the error box of the long GRB 980425 (Galama et al. 1998) and the later strong association of SN 2003dh with GRB 030329 (Hjorth et al. 2003; Stanek et al. 2003). The core-collapse process will produce some gravitational radiation (Fryer & New 2011). Rotational instabilities may give rise to much more significant gravitational-wave (GW) emission, however, and could be observable from beyond the Milky Way (Davies et al. 2002; Fryer et al. 2002; Kobayashi & Meszaros 2003; Shibata et al. 2003; Piro & Pfahl 2007; Corsi & Meszaros 2009; Romero et al. 2010; Gossan et al. 2016).

Neutron star (NS) binaries have long been proposed as the progenitors of short-hard GRBs (Blinnikov et al. 1984; Paczynski 1986; Eichler et al. 1989; Narayan et al. 1992). The detection of the GW transient GW170817, an NS binary merger (Abbott et al. 2017a, 2017e, 2019b), in coincidence with the short GRB 170817A (Goldstein et al. 2017; Savchenko et al. 2017), confirmed that such mergers can produce short GRBs. An optical detection of a counterpart (Coulter et al. 2017) was followed by panchromatic observations identifying kilonova and afterglow emission (see Abbott et al. 2017f, and references therein).

The unusually low flux of GRB 170817A and its light-curve evolution suggested an off-axis GRB with a relativistic structured jet or cocoon that either propagated into the universe successfully or was choked (Rossi et al. 2002; Hallinan et al. 2017; Kasliwal et al. 2017; Lamb & Kobayashi 2017; Troja et al. 2017; Gottlieb et al. 2018; Lazzati et al. 2018; Zhang et al. 2018). Later, very long baseline interferometry observations indicated a successfully launched relativistic jet (Mooley et al. 2018; Ghirlanda et al. 2019). The center of this jet appears to have been directed at an angle of approximately 15°–30° from the line of sight (Lazzati et al. 2018; Mooley et al. 2018). Analysis of the first 10 yr of Fermi Gamma-ray Burst Monitor (GBM) data suggests that GRB 170817A may belong to a population of local, low-luminosity short GRBs with similar spectral features (von Kienlin et al. 2019). The multimessenger observations of this event have proven to be extremely rich, providing insights about the structure of NSs (Margalit & Metzger 2017; Abbott et al. 2018; De et al. 2018; Most et al. 2018; Radice et al. 2018), the local cosmological expansion rate (Abbott et al. 2017b, 2019b; Hotokezaka et al. 2019), and heavy-element nucleosynthesis (Abbott et al. 2017d; Chornock et al. 2017; Cowperthwaite et al. 2017; Drout et al. 2017; Kasen et al. 2017; Smartt et al. 2017), to name a few.

In this paper we present targeted GW follow-up of GRBs—long and short—reported during the second observing run of Advanced LIGO and Advanced Virgo (O2). The observing run spanned 2016 November 30 to 2017 August 25, with Advanced Virgo commencing observations on 2017 August 1. As a measure of their sensitivities, the Advanced LIGO instruments had sky- and orientation-averaged binary neutron star (BNS) ranges between 65 and 100 Mpc throughout the run, while for Advanced Virgo this range was approximately 25 Mpc (Abbott et al. 2019a). In addition to GW170817, seven binary BH mergers were previously identified during O2, with a further three binary BHs observed during the first observing run (Abbott et al. 2019a).

We discuss the population of GRBs included in our analyses in Section 2 and summarize the methods used in Section 3. We then present the results of a modeled binary merger analysis targeting short-hard GRBs in Section 4 and an unmodeled analysis targeting all GRBs in Section 5, followed by discussion in Section 6 and concluding remarks in Section 7.

The GRB sample contains events disseminated by the Gamma-ray Coordinates Network (GCN),¹⁹⁷ with additional information gathered from the Swift BAT catalog¹⁹⁸ (Lien et al. 2016), the online Swift GRB Archive,¹⁹⁹ the Fermi GBM Burst Catalog²⁰⁰ (Gruber et al. 2014; von Kienlin et al. 2014; Bhat et al. 2016), and the Interplanetary Network (IPN; Hurley et al. 2003).²⁰¹ An automated system called VALID (Coyne 2015) cross-checks the time and localization parameters of the Swift and Fermi events against the published catalog with automated literature searches. In total, from 2016 November through 2017 August, there were 242 bursts detected in the combined Swift + Fermi catalog. We received a total of 52 bursts localized by the IPN, with many bursts appearing in both catalogs. GRBs that were poorly localized were removed from our sample, as were GRBs that did not occur during a period of stable, science-quality data taken by the available GW detectors.

For the purposes of this work, GRBs are classified (as in Abbott et al. 2017g) based on their T₉₀ value—the period over which 90% of the flux was observed—and its uncertainty δT₉₀. GRBs with a value of T₉₀ + δT₉₀ < 2 s are short, and those with T₉₀ + δT₉₀ > 4 s are long. The remaining GRBs are ambiguous.

As in Abbott et al. (2017g), a generic unmodeled GW transient search (Sutton et al. 2010; Was et al. 2012) was performed for all GRBs for which 660 s of coincident data was available from two GW detectors, regardless of classification. A modeled search for coalescing binary GW signals (Harry & Fairhurst 2011; Williamson et al. 2014) was performed for all short and ambiguous GRBs with at least 1664 s of data in one or more detectors. This scheme resulted in 98 GRBs being analyzed with our unmodeled method and 42 analyzed with our modeled method.

To cover all possible GW emission mechanisms, we consider two search methods: a modeled search for binary merger signals from short or ambiguous GRBs, and an unmodeled search for GWs from all GRBs. Neither of these methods has changed since previous published results (Abbott et al. 2017a, 2017g), so we provide summary overviews here.

3.1. Modeled Search for Binary Mergers

3.2. Unmodeled Search for Generic Transients

We analyzed 42 short and ambiguous GRBs with the modeled search during O2. As previously reported, the analysis identifies GW170817 in association with GRB 170817A (Abbott et al. 2017e) in a manner consistent with other GW analyses (Abbott et al. 2017a, 2019b). In our analysis of GRB 170817A reported here, where improved data calibration and noise subtraction have been incorporated, this signal was seen with a measured p-value of <9.38 × 10⁻⁶ and a coherent S/N of 31.26, far in excess of the loudest background.

We detected no GW signals with significant p-values in association with any of the other GRBs. The p-value distribution for the 41 GRBs other than GRB 170817A is shown in Figure 1. For GRBs without any associated on-source trigger we plot an upper limit on the p-value of 1 and a lower limit given by counting the background trials that similarly had no trigger. The expected distribution under the no-signal hypothesis is shown by the dashed black line, with dotted lines denoting a 2σ deviation about the no-signal distribution. To quantify population consistency with the no-signal hypothesis, we use the weighted binomial test outlined in Abadie et al. (2012b). This test considers the lowest 5% of p-values in the population, weighted by the prior probability of detection based on the detector network sensitivity at the time and in the direction of the GRB. We do not include GW170817, as it is a definite GW detection. This results in a p-value of 0.30; thus, we did not find significant evidence for a population of unidentified subthreshold signals with this test.

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In addition to GRB 170817A, there were six instances of on-source candidates with p-values less than 0.1. The second most significant p-value was $0.0068$, associated with GRB 170125102 from the Fermi GBM burst catalog. These six candidates were the subjects of further data quality checks to assess whether they could be caused by known instrumental noise sources. After careful scrutiny of the data, there were no clear noise artifacts identified as being responsible for any of these candidates. We also ran Bayesian parameter estimation analyses using LALInference (Veitch et al. 2015) to quantify the evidence for the presence of a coherent subthreshold NS binary merger signal in the data versus incoherent or Gaussian instrumental noise (Isi et al. 2018). The results of these studies are summarized in more detail in Table 2. In particular, we quote Bayes factors (BFs) to quantify the support for a coherent signal over incoherent or Gaussian noise, where a value less than 1 favors noise over signal and values greater than ∼3 are generally required before considering support to be substantial (Kass & Raftery 1995). Some studies have previously looked at the distributions of these BFs in the presence of weak signals and instrumental noise (Veitch & Vecchio 2008; Isi et al. 2018), although in somewhat different contexts to the low-mass targeted coherent search reported here. An in-depth study tailored to this analysis is beyond the scope of this work. However, given that these candidates were initially identified by our coherent matched filter analysis with low S/N, we might expect the BFs to indicate the presence of some degree of coherent power. Our follow-up results reflect this expectation and appear consistent with the search results, with neither significant evidence in favor of incoherent or purely Gaussian noise nor significant evidence in favor of the presence of signals in addition to GW170817 (i.e., $\tfrac{1}{3}\lesssim \mathrm{BF}\lesssim 3$ in all cases). The largest BF was $2.08$ in the case of 170726249 (p-value = $0.0262$). We also note that, in the absence of a signal with moderate S/N, inferred posterior probability distributions will be prior dominated, and in the presence of non-Gaussian noise fluctuations parameter estimation methods may return broad posteriors with multiple peaks, even for typically well-constrained parameters such as the chirp mass (Huang et al. 2018). We observe these posterior features in our follow-up analyses as noted in Table 2.

Table 2.  Results of Follow-up Studies of PyGRB Candidates with p < 0.1

GRB Name	p-value	BF	$\hat{\rho }$	Comment
161210524	0.0933	1.45	6.51	Weak Bayesian evidence in favor of a coherent signal over noise. Chirp mass posterior is broad with multiple peaks.
170125102	0.0068	0.88	6.23	Weak Bayesian evidence in favor of noise over a coherent signal. Posteriors show no significant information gain over priors. Chirp mass posterior is broad and multimodal.
170206453	0.0418	0.94	6.89	Weak Bayesian evidence in favor of noise over a coherent signal. Chirp mass posterior is broad with multiple peaks.
170219002	0.0307	0.88	5.96	Weak Bayesian evidence in favor of noise over a coherent signal. Posteriors show minimal information gain over priors. Chirp mass posterior is broad with multiple peaks.
170614505	0.0856	0.46	6.43	Weak Bayesian evidence in favor of noise over a coherent signal. Posteriors show no significant information gain over priors. Chirp mass posterior is broad with multiple peaks.
170726249	0.0262	2.08	6.91	Weak Bayesian evidence in favor of a coherent signal over noise. Chirp mass posterior is broad with a single peak.

Note. Bayes factors (BFs) quantify the Bayesian odds ratio between the hypothesis that there is a coherent NS binary merger signal in the data and the hypothesis that the data contain only instrumental noise, which may be purely Gaussian or include incoherent non-Gaussianities (see Equation (1) and accompanying discussion in Isi et al. 2018). At low S/N, inferred posterior probability distributions tend to be prior dominated and, in the presence of non-Gaussian noise fluctuations, may exhibit multiple peaks, even for typically well-constrained parameters such as the chirp mass (Huang et al. 2018). We report here $\hat{\rho }$, the network matched filter S/N corresponding to the maximum of the likelihood as estimated by LALInference.

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GRB 170817A is known to have originated at a distance of ∼43 Mpc in the galaxy NGC 4993 (Abbott et al. 2017e). We have plotted the cumulative 90% exclusion distances for the remaining short and ambiguous GRBs in Figure 2. For each of our three simulated signal classes we quote the median of the 41D₉₀ results in Table 1.

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A total of 98 GRBs were analyzed using the generic transient method, and no significant events were found except for GRB 170817A. The generic method recovered a signal for GRB 170817A consistent with the previously reported signal GW170817 at a p-value of 3.1 × 10⁻⁴. This value differs slightly from that reported in Abbott et al. (2017e), which can be explained by various changes in the configuration of X-Pipeline. First, the clustering of pixels in time–frequency maps was previously done over a 7 × 7 pixel grid, whereas in the analysis reported here all clustering is done in a 3 × 3 grid. Second, in the case of GRB 170817A the coherent veto tests were tuned (as described in Section III of Sutton et al. 2010) to maximize the sensitivity of the search to injections of BNS waveforms on the 99.99999th percentile loudest data segment. Here, we go back to the coherent veto tuning used in previous searches that uses the background data segment containing the 95th percentile loudest background event to all injected waveform families.

For the population of results we have compared the distribution of p-values against the expected distribution under the no-signal hypothesis, shown in Figure 3. We find a combined p-value of 0.75 (0.75 in O1) looking at the most significant 5% of events from the unmodeled search using the weighted binomial test from Abadie et al. (2012a).

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For GRBs other than GRB 170817A we place 90% confidence level lower limits on the distance D₉₀ assuming various emission models. The distribution of these lower limits for two models, ADI model A (van Putten 2001; van Putten et al. 2014) and a circular sine-Gaussian with central frequency of 150 Hz (Abbott et al. 2017g), is shown in Figure 4. These limits depend on detector sensitivity, which changes over time and sky location; systematic errors due to mismatch of a true GW signal and the waveforms used in simulations; and amplitude and phase errors from detector calibration. In Table 1 we provide population median exclusion limits for each model used, which vary from 15 to 113 Mpc. Some of these limits differ by an order of magnitude owing to our limited knowledge of burst-type source emission models. The median D₉₀ values compare favorably with those from the first observing run, either increasing or staying the same depending on the specific signal model.

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Aside from GW170817, no GWs associated with GRBs were detected in O2. The median D₉₀ values for each class of signal/source type provide an estimate of roughly how sensitive the searches were to such signals over the course of the entirety of O2, and these are given in Table 1. In Table 3 we provide information on each GRB that was analyzed, including selected D₉₀ results where relevant.

The nondetection of GW counterparts for 41 short and ambiguous GRBs analyzed by PyGRB can be combined with observed GRBs and the observation of GW170817 to obtain bounds on the short GRB-BNS rate as a function of redshift.

To evaluate this rate given the uncertainty in the jet structure profile of the short-GRB population, we model the GRB luminosity function as a broken power law following Wanderman & Piran (2015), but extended at low luminosities with a second break with an associated free parameter γ_L, as in Abbott et al. (2017e). This extension at low luminosity is an effective model of the short-GRB jet structure that yields low luminosities for mergers seen at a wide angle from their rotation axis:

$$\begin{eqnarray}{\phi }_{o}({L}_{{\rm{i}}})=\left\{\begin{array}{ll}{\left(\displaystyle \frac{{L}_{{\rm{i}}}}{{L}_{\star \star }}\right)}^{-{\gamma }_{L}}{\left(\displaystyle \frac{{L}_{\star \star }}{{L}_{\star }}\right)}^{-{\alpha }_{L}} & {L}_{{\rm{i}}}\lt {L}_{\star \star }\\ {\left(\displaystyle \frac{{L}_{{\rm{i}}}}{{L}_{\star }}\right)}^{-{\alpha }_{L}} & {L}_{\star \star }\lt {L}_{{\rm{i}}}\lt {L}_{\star }\\ {\left(\displaystyle \frac{{L}_{{\rm{i}}}}{{L}_{\star }}\right)}^{-{\beta }_{L}} & {L}_{{\rm{i}}}\gt {L}_{\star },\end{array}\right.\end{eqnarray} \tag{ 1 }$$

where L_i is the isotropic equivalent energy and the parameters L_⋆ ≃ 2 × 10⁵² erg s⁻¹, L_⋆⋆ ≃ 5 × 10⁴⁹ erg s⁻¹, α_L ≃ 1, and β_L ≃ 2 were used to fit the observed short-GRB redshift distribution. We assume a threshold value for detectability in Fermi-GBM of 2 photons cm⁻² s⁻¹ for the 64 ms peak photon flux in the 50–300 keV band. Furthermore, we model the short-GRB spectrum using a Band function (Band et al. 1993) with E_peak = 800 keV, α_Band = −0.5, and β_Band = −2.25. This yields an observed redshift distribution normalized by a total Fermi-GBM detection rate of 40 short GRBs per year.

In order to constrain the free parameter γ_L, we start with an uninformative prior on γ_L, which yields a flat prior on the logarithm of the local rate density. Using the redshift distribution for a given γ_L, we use Monte Carlo sampling to compute the probability of obtaining the O2 results presented here (41 nondetections and a single detection). This yields a posterior on γ_L with 90% confidence bounds of [0.04, 0.98]. The corresponding rates as a function of redshift are shown in Figure 5 in magenta.

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These bounds can be compared to other measurements and models of the short-GRB redshift distribution. For instance, the sample of observed short-GRB redshifts without GRB 170817A is shown in Figure 5 by the brown lines (Abbott et al. 2017e, and references therein). We also show the cumulative Fermi detection rate as a function of redshift in green, calculated following the framework in Howell et al. (2019). This assumes that all short GRBs are associated with BNS mergers and estimates the Fermi-GBM detection rate by scaling the BNS source rate evolution with redshift by the Fermi-GBM detection efficiency. Finally, the current estimate of the local BNS merger rate of ${1210}_{-1040}^{+3230}$ Gpc⁻³ yr⁻¹ (Abbott et al. 2019a) is shown in black for reference. We find that the posterior bounds from the modeled O2 GRB analysis overlap with the BNS merger rate and Fermi-GBM-detected short-GRB rate at low redshift. At high redshift there is agreement with the observed short-GRB redshift distribution and the Fermi-GBM detection rate.

For the 2019–2020 LIGO-Virgo observing run we expect to see 1–30 BNS coalescences, while at design sensitivity LIGO-Virgo could detect 4–97 BNS mergers per year. Using the framework provided in Howell et al. (2019), we estimate joint GW-GRB detection rates with Fermi-GBM of 0.07–1.80 per year for the 2019–2020 LIGO-Virgo observing run and 0.15–3.90 per year at design sensitivity. We note that although the BNS detection rate for LIGO-Virgo at design sensitivity is around three times higher than that of the 2019–2020 observing run, the joint GW-GRB detection increases by only a factor of about two. This discrepancy highlights the fact that faint, wide-angle emission will remain detectable for only nearby mergers, meaning that additional joint GW BNS detections facilitated by improved GW detector sensitivity will require the system to have small inclinations in order to produce a detectable GRB.

We have performed targeted analyses for GWs in association with GRBs during O2, searching for NS binary merger signals from short GRBs with a modeled analysis and GW burst signals from all GRBs with an unmodeled analysis. GW170817 is confirmed by both methods as a strong detection associated with GRB 170817A, entirely consistent with previously published results. No further GW signals were found as a result of these analyses, and there is no strong evidence found in our results for subthreshold signals. We set lower bounds on the distances to progenitors for a number of emission models, which include the largest D₉₀ values published so far for some individual GRBs (Abadie et al. 2012a; Abbott et al. 2017g).

Based on the results of the modeled search, we performed a population model analysis in Section 6 and place bounds on a twice-broken power-law short-GRB luminosity function that is consistent with both the measured BNS merger rate and the Fermi-GBM observed short-GRB rate, and therefore with the hypothesis that BNS mergers are generally short-GRB progenitors. Further multimessenger observations should provide tighter constraints on GRB emission models and event rates and investigate whether NS–BH mergers also power short GRBs. We expect to observe 0.07–1.80 joint GRB-GW events per year in conjunction with Fermi-GBM during the 2019–2020 LIGO-Virgo observing run and 0.15–3.90 per year when GW detectors are operating at their design sensitivities.

The authors gratefully acknowledge the support of the United States National Science Foundation (NSF) for the construction and operation of the LIGO Laboratory and Advanced LIGO, as well as the Science and Technology Facilities Council (STFC) of the United Kingdom, the Max-Planck-Society (MPS), and the State of Niedersachsen/Germany for support of the construction of Advanced LIGO and construction and operation of the GEO600 detector. Additional support for Advanced LIGO was provided by the Australian Research Council. The authors gratefully acknowledge the Italian Istituto Nazionale di Fisica Nucleare (INFN), the French Centre National de la Recherche Scientifique (CNRS), and the Foundation for Fundamental Research on Matter supported by the Netherlands Organisation for Scientific Research, for the construction and operation of the Virgo detector and the creation and support of the EGO consortium. The authors also gratefully acknowledge research support from these agencies, as well as by the Council of Scientific and Industrial Research of India; the Department of Science and Technology, India; the Science & Engineering Research Board (SERB), India; the Ministry of Human Resource Development, India; the Spanish Agencia Estatal de Investigación; the Vicepresidència i Conselleria d'Innovació Recerca i Turisme and the Conselleria d'Educació i Universitat del Govern de les Illes Balears; the Conselleria d'Educació Investigació Cultura i Esport de la Generalitat Valenciana; the National Science Centre of Poland; the Swiss National Science Foundation (SNSF); the Russian Foundation for Basic Research; the Russian Science Foundation; the European Commission; the European Regional Development Funds (ERDF); the Royal Society; the Scottish Funding Council; the Scottish Universities Physics Alliance; the Hungarian Scientific Research Fund (OTKA); the Lyon Institute of Origins (LIO); the Paris Île-de-France Region; the National Research, Development and Innovation Office Hungary (NKFIH); the National Research Foundation of Korea; Industry Canada and the Province of Ontario through the Ministry of Economic Development and Innovation; the Natural Science and Engineering Research Council Canada; the Canadian Institute for Advanced Research; the Brazilian Ministry of Science, Technology, Innovations, and Communications; the International Center for Theoretical Physics South American Institute for Fundamental Research (ICTP-SAIFR); the Research Grants Council of Hong Kong; the National Natural Science Foundation of China (NSFC); the Leverhulme Trust; the Research Corporation; the Ministry of Science and Technology (MOST), Taiwan; and the Kavli Foundation. The authors gratefully acknowledge the support of the NSF, STFC, INFN, and CNRS for provision of computational resources. D.S.S., D.D.F., R.L.A., and A.V.K. acknowledge support from RSF grant 17-12-01378.

Facilities: LIGO - Laser Interferometer Gravitational-Wave Observatory, EGO:Virgo - , Fermi (GBM) - , Swift (BAT) - , INTEGRAL - , WIND (KONUS) - , Odyssey. -

Software: Matplotlib (Hunter 2007; Caswell et al. 2018), LALInference (Veitch et al. 2015), PyCBC (Nitz et al. 2018), X-Pipeline (Sutton et al. 2010; Was et al. 2012).