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Search for Gravitational Waves Associated with Gamma-Ray Bursts Detected by Fermi and Swift during the LIGO–Virgo Run O3a

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Published 2021 July 9 © 2021. The Author(s). Published by the American Astronomical Society.
, , Citation R. Abbott et al 2021 ApJ 915 86 DOI 10.3847/1538-4357/abee15

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Abstract

We search for gravitational-wave transients associated with gamma-ray bursts (GRBs) detected by the Fermi and Swift satellites during the first part of the third observing run of Advanced LIGO and Advanced Virgo (2019 April 1 15:00 UTC–2019 October 1 15:00 UTC). A total of 105 GRBs were analyzed using a search for generic gravitational-wave transients; 32 GRBs were analyzed with a search that specifically targets neutron star binary mergers as short GRB progenitors. We find no significant evidence for gravitational-wave signals associated with the GRBs that we followed up, nor for a population of unidentified subthreshold signals. We consider several source types and signal morphologies, and report for these lower bounds on the distance to each GRB.

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1. Introduction

Gamma-ray bursts (GRBs) are transient flashes of gamma radiation of cosmological origin observed at a rate of ≳1 per day (Nakar 2007). The interaction of matter with a compact central object, e.g., an accreting black hole (BH; Woosley 1993; Popham et al. 1999) or a magnetar (Usov 1992; Zhang & Meszaros 2001), is believed to drive highly relativistic jets which power the prompt emission of these astrophysical events. GRBs are broadly grouped into two classes—long and short GRBs—depending on the duration and spectral hardness of their prompt emission (Mazets et al. 1981; Norris et al. 1984; Kouveliotou et al. 1993).

Long, soft GRBs have durations ≳2 s and are firmly associated by optical observations to the collapse of massive stars (Galama et al. 1998; Hjorth et al. 2003; Stanek et al. 2003; Hjorth & Bloom 2012). Gravitational waves (GWs) will be radiated by the core-collapse process, (e.g., Fryer & New 2011). Several models of this process do not yield radiation that is detectable by the current generation of GW interferometers beyond Galactic distances (Abbott et al. 2020c). However, rotational instabilities and instabilities induced by the additional presence of an accretion disk as part of the GRB engine may enhance the GW emission, making it detectable even for extragalactic sources (van Putten 2001; 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; Abbott et al. 2020c).

The unambiguous association (Abbott et al. 2017a) of neutron star (NS) binary merger GW170817 (Abbott et al. 2017b, 2019d) and short GRB 170817A (Goldstein et al. 2017; Savchenko et al. 2017) has confirmed that compact binary mergers of this kind can produce short GRBs. This milestone in multimessenger astronomy corroborated the idea first proposed in the 1980s (Blinnikov et al. 1984; Paczynski 1986; Eichler et al. 1989; Paczynski 1991; Narayan et al. 1992) that the progenitors of short GRBs are compact binaries containing NSs (for a review of proposed progenitors, see Lee & Ramirez-Ruiz 2007; Nakar 2007). Indirect evidence that had previously reinforced this idea was due to the observation of a possible kilonova associated with GRB 130603B (Berger et al. 2013; Tanvir et al. 2013), and to numerous studies of the environments of short GRBs (for reviews see Berger 2011, 2014), starting with the afterglow observation and host-galaxy association of GRB 050509B (Castro-Tirado et al. 2005; Gehrels et al. 2005; Bloom et al. 2006).

In addition to confirming the origin of some short GRBs, combining data from observations of GW170817 and GRB 170817A allowed for the inference of basic properties of short GRB jets. These include the isotropic equivalent luminosity of the jet, determined through a redshift measurement made possible by the optical follow-up of the GW localization (Abbott et al. 2017a; Goldstein et al. 2017), and the geometry of the GRB jets (Williams et al. 2018; Farah et al. 2020; Mogushi et al. 2019). The precise mechanism by which the jet is launched is still unknown, although it is typically believed to be either neutrino-driven or magnetically driven (Nakar 2007, but see also Liu et al. 2015 and references therein). Indeed, the scientific debate about the emission profile of the jet and the subsequent gamma-ray production mechanism of GRB 170817A is still ongoing (Hallinan et al. 2017; Kasliwal et al. 2017; Lamb & Kobayashi 2017; Troja et al. 2017; Gottlieb et al. 2018b; Lazzati et al. 2018; Gill & Granot 2018; Mooley et al. 2018; Zhang et al. 2018; Ghirlanda et al. 2019). It is generally believed that there are symmetric polar outflows of highly relativistic material that travel parallel to the total angular momentum of the binary system (Aloy et al. 2005; Kumar & Zhang 2014; Murguia-Berthier et al. 2017). These jets are thought to be collimated and roughly axisymmetric, emitting preferentially in a narrow opening angle due to a combination of outflow geometry and relativistic beaming. The data from extensive multi-wavelength observation campaigns that ran for nearly 20 months following the merger (Fong et al. 2019; Makhathini et al. 2020; Troja et al. 2020) are in agreement with a structured jet model, in which the energy and bulk Lorentz factor gradually decrease with angular distance from the jet symmetry axis (e.g., Dai & Gou 2001; Lipunov et al. 2001; Rossi et al. 2002; Zhang & Mészáros 2002; Ghirlanda et al. 2019; Beniamini et al. 2020). Further, according to one of the models proposed, as the jet drills through the surrounding merger ejecta it inflates a mildly relativistic cocoon due to interactions between the material at the edge of the jet and the ejecta (Lazzati et al. 2017; Gottlieb et al. 2018a). In this case, it is possible that the cocoon alone could produce the gamma-rays observed from GRB 170817A (Gottlieb et al. 2018b). Additional joint detections of GRBs and GWs will significantly aid our understanding of the underlying energetics (Lamb & Kobayashi 2017; Wu & MacFadyen 2018; Burns et al. 2019), jet geometry (Farah et al. 2020; Mogushi et al. 2019; Biscoveanu et al. 2020; Hayes et al. 2020), and jet ignition mechanisms (Veres et al. 2018; Ciolfi et al. 2019; Zhang 2019) of binary neutron star (BNS) coalescences.

A targeted search for GWs in sky and time coincidence with GRBs enhances our potential of achieving such joint detections. In this paper we present our results for the targeted GW follow-up of GRBs reported during the first part of the third observing run of Advanced LIGO and Advanced Virgo (O3a) by the Fermi (Meegan et al. 2009) and Swift (Gehrels et al. 2004; Barthelmy et al. 2005) satellites. As in the first (Abbott et al. 2017c) and second (Abbott et al. 2017a, 2019b) observing runs, two searches with different assumptions about signal morphology are applied to the GW data: we process all GRBs with a search for generic GW transients (X-Pipeline; Sutton et al. 2010; Was et al. 2012, see Section 3.2 for details) and we follow up short GRBs with an additional, modeled search for BNS and neutron star–black hole (NSBH) GW inspiral signals (PyGRB; Harry & Fairhurst 2011; Williamson et al. 2014, see Section 3.1 for details). These searches were able to process 105 and 32 GRBs in O3a, respectively.

The scope of these targeted searches is to enhance our ability to detect GW signals in coincidence with GRBs with respect to all-sky searches for transient GW signals carried out by the LIGO Scientific & Virgo Collaboration (Abbott et al. 2019c, 2021). These may lead to joint GW–GRB detections in the case of loud GW events, as for GW170817 and GRB 170817A, but the targeted searches we report on here aim at uncovering subthreshold GW signals by exploiting the time and localization information of the GRBs themselves. The Fermi Gamma-ray Burst Monitor (GBM) team conducts an analogous effort when searching through GBM data for gamma-ray transients coincident with confirmed events and low-significance candidates reported by LIGO–Virgo offline analyses (Hamburg et al. 2020). Similarly, the Swift/Burst Alert Telescope (BAT) team has developed their own autonomous pipeline to enable subthreshold GRB searches for externally triggered events (Tohuvavohu et al. 2020).

This first part of the third observing run took place between 2019 April 1 15:00 UTC and 2019 October 1 15:00 UTC. Setting the false-alarm-rate threshold to two per year, 39 compact binary coalescence events were identified in O3a (Abbott et al. 2021). The majority of these have been classified as signals emitted by binary BH mergers; however, three events have the possibility of coming from a binary with at least one NS, that is, a potential short GRB progenitor.

  • 1.  
    GW190425 (Abbott et al. 2020a) was a compact binary coalescence with primary mass ${2.0}_{0.3}^{0.6}$ and secondary mass ${1.4}_{-0.3}^{+0.3}$ (all measurements quoted at the 90% credible level) and is therefore consistent with being the result of a BNS merger (Abbott et al. 2020a, 2021).
  • 2.  
    GW190426 was the GW candidate event with the highest false-alarm rate in Abbott et al. (2021); assuming it is a real signal, its inferred component masses of ${5.7}_{-2.3}^{+3.9}$ and ${1.5}_{-0.5}^{+0.8}$ indicate that it may have originated from an NSBH, or a binary BH merger.
  • 3.  
    GW190814 (Abbott et al. 2020b) could have originated from an NSBH, or a binary BH merger, as it has a primary mass measurement of ${23.2}_{-1.0}^{+1.1}$ and posterior support for a secondary mass ${2.59}_{-0.09}^{+0.08}$. This makes the secondary compact object either the lightest BH or the heaviest NS known to be in a compact binary system.

While there is considerable uncertainty in source type for all three of these events, GW190425 is the one for which the prospects of observing an associated GRB were most promising, as it is consistent with a BNS merger, rather than a binary BH merger or an NSBH merger with high or moderately high mass ratio. However, no confirmed electromagnetic or neutrino counterparts were observed in association with this event (Hosseinzadeh et al. 2019; Lundquist et al. 2019; Abbott et al. 2020a; Coughlin et al. 2020, 2020; see also Pozanenko et al. 2020, 2020) despite extensive searches, which are logged in the Gamma-ray Coordinates Network (GCN) Circular archive. 204 There are a number of reasons for which an electromagnetic counterpart associated with GW190425 may not have been detected. First, the large area covered by the localization region of GW190425 determined from GW data ( > 8000 deg2) posed a considerable challenge for electromagnetic follow-up. 45.4% of this localization region was occulted by the Earth for the Fermi satellite so, if gamma-rays were emitted from the source, it is possible they were not detectable. Other gamma-ray observatories with lower sensitivities to short GRBs, such as INTEGRAL and KONUS-Wind, were covering relevant fractions of the localization region, however (Martin-Carrillo et al. 2019; Svinkin et al. 2019). Second, GRB jets are expected to be aligned with the total angular momentum of the binary system, and thus more easily detectable at small viewing angles. The binary inclination angle of GW190425 was poorly constrained, so it is possible that a jet from this system was formed but was oriented away from our line of sight. Additionally, the luminosity distance inferred for GW190425 (∼160 Mpc) was significantly larger than that for GW170817 (∼40 Mpc). GRB 170817A, which followed GW170817, was such an exceptionally faint short GRB (Abbott et al. 2017a) that its prompt emission photon flux would have dipped below the detection threshold for Fermi-GBM, had the source been farther than ∼75 Mpc (Abbott et al. 2017a; Goldstein et al. 2017), and by ∼100 Mpc it would become undetectable by Swift/BAT (Tohuvavohu et al. 2020). Thus, if emission from the system that produced GW190425 was similarly faint, it would not have been detectable by Swift/BAT or Fermi-GBM. Therefore, we do not necessarily expect a GRB detection to be associated with GW190425 due to its almost unconstrained inclination angle, large localization region, and distance, even if gamma-rays were emitted from this system. Scenarios like this one further motivate the need for GW follow-up analyses of GRB events which, by definition, constrain the sky localization and inclination angle of the progenitor.

In Section 2 we discuss the set of GRBs analyzed in this paper. In Section 3, we summarize the two targeted search methods used to follow up GRBs. Section 4 presents the results obtained with these two methods. We also consider each of the two sets of results collectively and quantify its consistency with the no-signal hypothesis. Finally, in Section 5 we provide our concluding remarks.

2. GRB Sample

The sample of GRBs analyzed in this paper includes events circulated by the GCN, 205 complemented with information from the Swift/BAT catalog (Lien et al. 2016), 206 the online Swift GRB Archive, 207 and the Fermi-GBM Catalog. 208 (Gruber et al. 2014; von Kienlin et al. 2014; Narayana Bhat et al. 2016) Once an alert detailing an event has been received via the GCN, the dedicated Vetting Automation and Literature Informed Database (Coyne 2015) is applied to find the latest GRB results by comparing the time and localization parameters with those in tables relating to each satellite, the published catalogs, and an automatic literature search. The GCN notices provide a set of 141 GRBs during the O3a data-taking period (2019 April 1 15:00 UTC–2019 October 1 15:00 UTC).

As mentioned in the Introduction, we carry out two searches with distinct assumptions about signal morphology (see Section 3 for details on both methods): a search for generic GW transients and a modeled search for GW signals from NS binary inspirals, i.e., BNSs and NSBHs. We do this because GRBs of different durations are expected to have different origins and therefore different GW signal morphologies. In particular, if a compact binary merger were to produce a GRB it would be expected to have a short duration. In order to specifically target such phenomena with the modeled search, we classify each GRB as long, short, or ambiguous. This classification relies on the measurement of the time interval over which 90% of the total background-subtracted photon counts are observed (T90, with error ∣δ T90∣). When T90 + ∣δ T90∣ < 2 s the GRBs are labeled as short, when T90 − ∣δ T90∣ > 4 s the GRBs are labeled as long, and the rest are labeled as ambiguous. The unmodeled search for generic transients is applied to GRBs of all classifications. All of the short and ambiguous GRBs are additionally analyzed with the modeled search in order to maximize the chances of uncovering any potential binary coalescence candidate.

The classification process results in 20 short GRBs, 108 long GRBs, and 13 ambiguous GRBs. As in Abbott et al. (2019b), we require a minimum amount of coincident data from at least two GW detectors around the time of a GRB for the generic unmodeled GW transient search to assess the significance of a GW candidate with sub-percent level accuracy (see Section 3.2 for technical details). This requirement is applied to GRBs of all classifications and results in 105 GRBs being analyzed with this method, out of the 141 GRBs recorded by Fermi and Swift during O3a. This amounts to 74.5%, a percentage of events that is compatible with the fraction of observing time during which at least two interferometers in the network were operating in observing mode (81.9 %; Abbott et al. 2021). Similarly, requirements from the modeled search (see Section 3.1 for technical details) set the minimum amount of data needed from at least one detector around the time of the GRBs. It leads to 32 short and ambiguous GRBs being analyzed with this method, 209 that is, 97.0% of the 33 possible ones. This value matches the fraction of observing time during which at least one interferometer in the network was operating in observing mode during O3a (96.9 %; Abbott et al. 2021).

Of the 141 Fermi and Swift GRBs in our sample, the vast majority do not have redshift measurements. Those that do are the ambiguous GRB 190627A at z = 1.942 (Japelj et al. 2019), and the two long GRBs 190719C and 190829A at z = 2.469 and z = 0.0785, respectively (Rossi et al. 2019; Valeev et al. 2019). All three fall beyond the detection range of our interferometers, and are not expected to produce measurable GW results. Regardless of availability of redshift information, however, we followed up as many GRBs as we could and we were indeed able to analyze these three cases.

3. Search Methods

We now provide a description of the two targeted search methods used in this paper. These are the same methods applied to GW data coincident with GRBs that occurred during the first (Abbott et al. 2017c) and second (Abbott et al. 2017a, 2019b) Advanced LIGO and Virgo observing runs. In Section 3.1 we summarize the modeled search method that aims at uncovering subthreshold GW signals emitted by BNS and NSBH binaries (PyGRB; Harry & Fairhurst 2011; Williamson et al. 2014). In Section 3.2 we discuss the search for generic GW transients (X-Pipeline; Sutton et al. 2010; Was et al. 2012). Results from these two searches are presented in Section 4.

3.1. Modeled Search for Binary Mergers

This analysis searches for a GW signal compatible with the inspiral of a BNS or NSBH binary—collectively NS binaries—within 6 s of data associated with an observed short GRB. This stretch of data is the on-source window and runs from −5 s to +1 s around the start of the GRB emission (i.e., the GRB trigger time). The surrounding ∼30–90 minutes of data are split into 6 s off-source trials which are also analyzed in order to build a background. Around 30 minutes allows the modeled search to accurately estimate the power spectral density of the available instruments and ensures that it can assess at sub-percent level accuracy the significance of any candidate events found in the on-source window. All the data are processed using PyGRB (Harry & Fairhurst 2011; Williamson et al. 2014), a coherent matched filtering pipeline that is part of the general open-source software PyCBC (Nitz et al. 2020) and has core elements in the LALSuite software library (LIGO Scientific Collaboration 2018). We scan each trial of data and the on-source window in the 30–1000 Hz frequency band using a predefined bank of waveform templates (Owen & Sathyaprakash 1999) created with a hybrid geometric–stochastic method (Capano et al. 2016; Dal Canton & Harry 2017) and using a phenomenological inspiral-merger-ringdown waveform model for non-precessing point-particle binaries (IMRPhenomD; Husa et al. 2016; Khan et al. 2016). 210 The waveform template bank includes waveforms corresponding to a range of masses ([1.0, 2.8]M for NSs, [1.0, 25.0]M for BHs) and dimensionless spin magnitudes ([0, 0.05] for NSs, [0, 0.998] for BHs) for aligned-spin, zero-eccentricity BNS or NSBH systems that may produce an electromagnetic counterpart via the tidal disruption of the NS (Pannarale & Ohme 2014). Aside from the updated sensitivity of our detectors, the only difference with respect to the second LIGO–Virgo observing run (Abbott et al. 2019b) is that the generation of the bank has been updated to apply more accurate physics to determine whether an NSBH system could produce an accretion disk from this disruption (Foucart et al. 2018). We only search for circularly polarized GWs, which may be emitted by binaries with inclinations of 0° or 180°: such systems have GW amplitudes that are consistent (Williamson et al. 2014) with those of binary progenitors with inclination angles over the full range of viewing angles that we expect for typical brightness GRBs (≲30°; Fong et al. 2015), such as those in our sample.

The strength of any potential signal is ranked via a coherent matched filter signal-to-noise ratio (S/N; Harry & Fairhurst 2011; Williamson et al. 2014) which is re-weighted according to a χ2 goodness-of-fit between the template that identified it and the signal itself. The significance of the latter is quantified as the probability of background alone producing such an event. This is evaluated by comparing the re-weighted S/N of the loudest trigger within the 6 s on-source to the distribution of the re-weighted S/Ns of the loudest triggers in the 6 s off-source trials. When data from more than one detector are available, this background S/N distribution is extended by generating additional off-source trials via time slides, that is, by combining data from detectors after introducing time shifts longer than the light-travel time across the network. Specifically, our time shifts are 6 s long, in order to match the width of the on-source window and the off-source trials.

In order to derive the sensitivity of this search to potential GRB sources, simulated signals are injected in software into the off-source data. The 90% exclusion distances, D90, are defined as the distances within which 90% of the injected simulated signals are recovered with a greater ranking statistic than the loudest on-source event. Three different astrophysical populations are considered: BNS binaries with generically oriented—i.e., precessing—spins, aligned-spin NSBH binaries, and NSBH binaries with generically oriented spins. These simulated signals cover a portion of parameter space that extends beyond that covered by the template bank, as they include NS dimensionless spin values up to 0.4 and, for two families of injected signals, admit precession. As stated previously, the templates used to filter the data are produced using IMRPhenomD. In order to factor into the sensitivity assessment any potential loss due to uncertainties in GW signal modeling, the injected signals are not produced with the same model used for the templates. Precessing BNS signals are simulated using the TaylorT2 time-domain, post-Newtonian inspiral approximant (SpinTaylorT2; Sathyaprakash & Dhurandhar 1991; Blanchet et al. 1996; Mikoczi et al. 2005; Arun et al. 2009; Bohé et al. 2013, 2015; Mishra et al. 2016), while NSBH-injected waveforms are generated assuming a point-particle effective-one-body model tuned to numerical simulations which can allow for precession effects from misaligned spins (SEOBNRv3; Pan et al. 2014; Taracchini et al. 2014; Babak et al. 2017). The three populations used to build the injected signals are defined as in the first two LIGO–Virgo observing runs, to allow for direct comparisons (Abbott et al. 2017c, 2019b). NS masses for the injections are taken between 1 M and 3 M from a normal distribution centered at 1.4 M with a standard deviation of 0.2 M (Kiziltan et al. 2013) and 0.4 M for BNS and NSBH systems, respectively. BH masses are taken to be between 3 M and 15 M from a normal distribution centered at 10 M with a standard deviation of 6 M. Spins are drawn uniformly in magnitude and, when applicable, with random orientation; the maximum allowed NS spin magnitude is 0.4, from the fastest observed pulsar spin (Hessels et al. 2006), while the maximum BH spin magnitude is set to 0.98, motivated by X-ray binary observations (e.g., Özel et al. 2010; Kreidberg et al. 2012; Miller & Miller 2014). Injected signals have a range of total inclinations from 0°–30° and 150°–180° while removing any systems which could not feasibly produce a short GRB (Pannarale & Ohme 2014).

3.2. Unmodelled Search for Generic Transients

X-Pipeline looks for excess power that is coherent across the network of GW detectors and consistent with the sky localization and time window for each GRB. As in the first two observing runs, we use a search time window that begins 600 s before the GRB trigger time and ends 60 s after it, or at the T90 time itself (whichever is larger). This window is long enough to encapsulate the time delay between GW emission from a progenitor and the GRB prompt emission (Koshut et al. 1995; Aloy et al. 2000; MacFadyen et al. 2001; Zhang et al. 2003; Lazzati 2005; Wang & Meszaros 2007; Burlon et al. 2008, 2009; Lazzati et al. 2009; Vedrenne & Atteia 2009). Our frequency range is restricted to the most sensitive band of the GW detectors, namely 20–500 Hz. While gravitational radiation from core-collapse supernovae is expected to contain frequency content above this band (Radice et al. 2019), detection of bursts above a few hundred hertz is not energetically favorable (see, e.g., Figure 4 in Abbott et al. 2019a) and increasing the frequency upper limit also increases the computational cost.

The generic transient search pipeline coherently combines data from all detectors and produces time–frequency maps of this GW data stream. The maps are scanned for clusters of pixels with excess energy, referred to as events. The events obtained this way are first ranked according to a detection statistic based on energy and then subject to coherent consistency tests. These are based on correlations between data in different detectors and reject events associated with noise transients. The surviving event with the largest ranking statistic is taken to be the best candidate for a GW detection. Its significance is evaluated in the same way as in the modeled analysis, but with 660 s long off-source trials. In order to ensure that the significance is assessed at a sub-percent level, we require at least ∼1.5 hr of coincident data from at least two detectors around the time of a GRB. Non-Gaussian noise transients, or glitches, are handled as described in Abbott et al. (2019b).

Similarly to the modeled search, we quantify the sensitivity of the generic transient search by injecting simulated signals into off-source data in software and recovering them. Calibration errors are accounted for by jittering the amplitude and arrival time of the injections according to a Gaussian distribution representative of the calibration uncertainties in O3a (Abbott et al. 2017c). We report results obtained for four distinct sets of circular sine-Gaussian (CSG) waveforms, with fixed quality factor Q = 9 and with central frequencies of 70, 100, 150, and 300 Hz (see Equation (1) and Section 3.2 of Abbott et al. 2017c). These models are intended to represent the GWs from stellar collapses. In all four cases, we set the total radiated energy to EGW = 10−2 M c2, a choice that is about an order of magnitude higher than the results presented in Abbott et al. (2020c) for the detectability of core-collapse supernovae. As optimistic representatives (Ott & Santamaría 2013) of longer-duration GW signals detectable by the unmodeled search, we use accretion disk instability (ADI) waveforms (van Putten 2001; van Putten et al. 2014). In these ADI models, instabilities form in a magnetically suspended torus around a rapidly spinning BH, causing GWs to be emitted. The model specifics and parameters used to generate the five families of ADI signals that we consider are the same as in Table 1 and Section 3.2 of Abbott et al. (2017c).

4. Results

During O3a we used the generic transient method to follow up a total of 105 GRBs, whereas the modeled search was applied to the 32 GRB triggers classified as short or ambiguous. For all of the most GW-signal-like triggers associated with the examined GRBs, the searches returned no significant probability of incompatibility with background alone (p-value). This indicates that no GW signal was uncovered in association with any of these GRBs. This is consistent with the estimated GW–GRB joint detection rate with Fermi-GBM of 0.07–1.80 per year reported in Abbott et al. (2019b) for the 2019–2020 LIGO–Virgo observing run. The most significant events found by the generic transient method and by the modeled search had p-values of 5.5 × 10−3 (GRB 190804058) and 2.7 × 10−2 (GRB 190601325), respectively.

Figures 1 and 2 show the cumulative distributions of p-values returned by the modeled search and the generic transient search, respectively. For cases in which no associated on-source trigger survived the analysis cuts of the modeled search, the associated p-value ranges between 1—i.e., an upper bound on a probability—and the fraction of background trials for the GRB that also yielded no associated GW trigger. In both figures, the expected background distribution under the no-signal hypothesis is shown by the dashed line, and its 2σ limits are indicated by the two dotted lines. Both cumulative distributions are within the 2σ lines and therefore compatible with the no-signal hypothesis. These figures indicate that the lowest p-value found by each search is compatible with the no-signal hypothesis.

Figure 1.

Figure 1. Cumulative distribution of loudest on-source event p-values for the neutron star binary modeled search in O3a. If the search reports no trigger in the on-source, we plot an upper limit on the p-value of 1 (open circles), and a lower limit equal to the fraction of off-source trials that contained no trigger (full circles). The dashed line indicates the expected distribution of p-values under the no-signal hypothesis, with the corresponding 2σ envelope marked by dotted lines.

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Figure 2.

Figure 2. Cumulative distribution of p-values from the unmodelled search for transient gravitational waves associated with 105 gamma-ray bursts. The dashed line represents the expected distribution under the no-signal hypothesis, with dotted lines indicating a 2σ deviation from this distribution.

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Having found no GW signal associated with the GRBs followed up by our searches, we consider the set of modeled search results and the set of generic transient search results, collectively. We apply a weighted binomial test described in Abadie et al. (2012) to evaluate how consistent each set of results is collectively with the no-signal hypothesis. This test is conducted using the most significant 5% of p-values in the sample weighted by a prior probability of detection estimated using the network detector sensitivity at the time and location of each GRB. This final probability of observing this distribution of p-values given background alone, i.e., under the no-signal hypothesis, was 0.43 (0.31) for the modeled (generic transient) search method. Therefore, both searches gave no significant evidence for a population of unidentified subthreshold GW signals. For the analyses carried out in the first observing run of Advanced LIGO and Advanced Virgo, the combined p-values were 0.57 and 0.75 for the modeled and generic transient search, respectively (Abbott et al. 2017c); in the second observing run of Advanced LIGO and Advanced Virgo, they were 0.30 and 0.75 (Abbott et al. 2019b).

In Figure 3, we show the cumulative 90% exclusion distances for the 32 short and ambiguous GRBs followed up with the modeled search. The lowest exclusion distance values (∼20 Mpc) were obtained for ambiguous GRB 190409901. This is due to the fact that only Virgo data were available for this GRB and that the sky location of this event was in a direction in which Virgo had ∼30% sensitivity with respect to an optimal sky location. For each of the three simulated signal classes, we quote the median of the 32 D90 results in the top part of Table 1. All three values are 40%–60% times higher than those reported in Abbott et al. (2019b) for the previous LIGO–Virgo observing run. The individual D90 values for each class of simulated signals are reported in Table 2. As a term of comparison, during the six month duration of O3a, the Hanford and Livingston Advanced LIGO instruments, and the Virgo interferometer had BNS ranges of 108 Mpc, 135 Mpc, and 45 Mpc, respectively. 211 We also place a 90% confidence level lower limit on the distance for each of the 105 GRBs analyzed by the generic transient search, assuming the various emission models discussed in Section 3.2 (see also Abbott et al. 2017c). Figure 4 shows the distribution of D90 values for the ADI model A (van Putten 2001; van Putten et al. 2014) and for a CSG with central frequency of 150 Hz (Abbott et al. 2017c). These limits depend on the sensitivity of the detector network which, in turn, varies over time and with sky location, and have been marginalized over errors introduced by detector calibration. For the ADI and the CSG models mentioned above, as well as for the other seven models used in the generic transient method search (see Section 3.2), we provide population median exclusion limits, D90, in Table 1. These vary roughly over one order of magnitude, which reflects the wide range of models used in the analysis. We report the D90 values found for each GRB in the case of ADI model A simulated signals and CSG simulated signals with central frequency of 150 Hz in Table 2.

Figure 3.

Figure 3. Cumulative histograms of the 90% confidence exclusion distances, D90, for the binary neutron star (blue, thin line) and generically spinning neutron star–black hole (orange, thick line) signal models, shown for the sample of 32 short and ambiguous gamma-ray bursts (GRBs) that were followed up by the NS binary modeled search during O3a, none of which had an identified gravitational wave counterpart. For a given GRB event and signal model, D90 is the distance within which 90% of simulated signals inserted into off-source data are recovered with greater significance than the most significant on-source trigger. These simulated signals have inclinations θJN —the angle between the total angular momentum and the line of sight—drawn uniformly in $\sin {\theta }_{{JN}}$ with θJN restricted to [0°, 30°] ∪ [150°, 180°].

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Figure 4.

Figure 4. Cumulative histograms of the 90% confidence exclusion distances, D90, for accretion disk instability (ADI; van Putten 2001; van Putten et al. 2014) signal model A (orange, thin line) and circular sine-Gaussian (CSG) 150 Hz (Abbott et al. 2017c) model (green, thick line). For a given GRB and signal model this is the distance within which 90% of simulated signals inserted into off-source data are successfully recovered with a significance greater than the loudest on-source trigger. The median values for ADI-A and CSG-150 waveforms are 23 Mpc and 73 Mpc, respectively.

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Table 1. Median 90% Confidence Level Exclusion Distances, D90, for the Searches during O3a

Modelled Search  NSBHNSBH
(Short GRBs)BNS Generic SpinsAligned Spins
D90 [Mpc]119 160231
Unmodelled searchCSGCSGCSGCSG
(All GRBs)70 Hz100 Hz150 Hz300 Hz
D90 (Mpc)1461047328
Unmodelled searchADIADIADIADIADI
(All GRBs)ABCDE
D90 (Mpc)23123281133

Note. Modeled search results are shown for three classes of NS binary progenitor model, and unmodeled search results are shown for CSG (Abbott et al. 2017c) and ADI (van Putten 2001; van Putten et al. 2014) models.

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Table 2. Information and Limits on Associated GW Emission for Each of the Fermi and Swift GRBs Followed Up during the LIGO–Virgo Run O3a

        D90 (Mpc)
GRB NameUTC TimeR.A.Decl.SatelliteTypeNetworkBNSGeneric NSBHAligned NSBHADI-ACSG 150 Hz
19040429307:01:218h 05m 33s 55° 25'FermiLongH1L135152
19040645010:47:2023h 46m 21s 20° 23'FermiLongH1L1V12115
19040646511:09:4719h 05m 21s 61° 30'FermiLongH1L1V169186
19040757513:48:366h 02m 07s −64° 08'FermiLongH1L1V1 61171
19040767216:07:2612h 07m 16s 40° 37'FermiLongL1V13249
19040778818:54:4113h 30m 57s −7° 57'FermiAmbiguousL1V11693113953454
19040990121:38:0515h19m53s −33°52'FermiAmbiguousV1192234
19041157913:53:583h 02m 31s 48° 38'FermiLongH1L1V1 10108
19041517304:09:491h 50m 50s 17° 26'FermiLongH1V125
19041941409:55:377h 05m 48s −40° 08'FermiLongH1V1 3454
19042098123:32:2421h 17m 09s −66° 25'FermiAmbiguousL1V11752153153552
19042228406:48:1720h 26m 38s −73° 01'FermiLongH1L1 14127
19042267016:05:0412h 36m 55s −54° 57'FermiLongH1L1V12167
19042508902:07:4321h 01m 43s −15° 13'FermiAmbiguousL1V1(H1L1)2042474402338
190427A04:34:1518h 40m 52s 40° 19'SwiftShortL1V11381992533392
19042878318:48:121h 55m 45s 15° 51'FermiLongL1V12938
19042974317:49:5013h 20m 12s −7° 60'FermiLongH1L1V170126
19050179419:03:4210h 25m 09s −22° 00'FermiLongL1V1 1835
19050216804:01:306h 16m 43s 3° 17'FermiLongH1L1V13492
19050441509:57:344h 41m 57s 39° 34'FermiLongH1L1V1 1650
19050467816:16:289h 09m 43s 33° 01'FermiShortL1V1931241891768
19050505101:14:0922h 21m 33s 42° 11'FermiShortL1V11001492062436
19050727006:28:2310h 23m 50s −12° 48'FermiLongH1L1 39111
19050771217:05:1605h44m53s −61°7'FermiShortV1425870
19050797023:16:2919h 11m 16s −22° 49'FermiLongH1L1V132231
19050898723:41:246h 54m 02s 27° 02'FermiLongH1L1V1 30178
19051012002:52:138h 18m 09s −53° 04'FermiLongH1V1 853
19051043010:19:168h 32m 31s 33° 33'FermiShortH1L112819625348116
190511A07:14:488h 25m 46s −20° 15'SwiftLongH1L150142
190512A14:40:095h 29m 35s −7° 35'SwiftLongL1V12056
19051519004:33:039h 10m 45s 29° 17'FermiShortL1V11221481942242
19051781319:30:1018h 00m04s 25° 46'FermiLongH1L13074
190519A07:25:397h 39m 01s −38° 49'SwiftLongH1L1V110190
19052503200:45:4722h 32m 04s 5° 27'FermiShortH1L1V112824838522165
19053131207:29:111h 24m 28s 16° 21'FermiLongL1V12173
19053156813:38:0318h 16m 40s 38° 52'FermiShortH1V186150187329
19060132507:47:2410h 51m 55s 54° 35'FermiShortH1V1(H1L1V1)1361692481734
19060379519:04:251h 20m 19s 40° 55'FermiLongH1L13156
19060444610:42:3722h 50m 12s 46° 22'FermiLongH1L172174
19060608001:55:075h 06m 09s −0° 41'FermiShortH1V1526881837
19060800900:12:1815h 02m 57s −31° 25'FermiLongL1V1 1530
19061075017:59:4921h 49m 31s 42° 25'FermiLongL1V1140
19061083420:00:2320h 59m 19s −15° 56'FermiAmbiguousL1V11492023063458
190610A11:27:453h 04m 57s −7° 40'SwiftShortH1L163821142358
19061216503:57:2414h 55m 48s 62° 06'FermiLongH1L1V1 48178
190613A04:07:1812h 10m 12s 67° 15'SwiftLongH1L1V170200
190613B10:47:0220h 21m 45s −4° 39'SwiftLongH1L1 54160
19061563615:16:2712h 45m 36s 49° 23'FermiLongH1L1V1445
19061901800:26:0123h 17m 14s 12° 52'FermiLongH1L1V1 6132
19061959514:16:2519h24m 16s 20° 10'FermiLongH1L1V1 247
19062050712:10:1010h 48m 19s 30° 29'FermiLongH1L1594
19062346111:03:2722h 21m 57s −23° 20'FermiLongH1L1V11095
19062748111:31:5923h 29m 02s −8° 53'FermiLongH1L116116
190627A11:18:3116h 19m 29s −5° 18'SwiftAmbiguousH1L11151392112177
19062852112:30:559h 36m 19s −77° 04'FermiLongH1L147164
19063025706:09:5820h 27m 55s −1° 20'FermiShortH1V147911211625
190630B06:02:0814h 54m 55s 41° 32'SwiftLongH1V11012
190630C23:52:5919h 35m 33s −32° 46'SwiftLongH1L1V147118
190701A09:45:201h 52m 31s 58° 54'SwiftLongH1L1V112157
19070728506:50:0510h 11m 28s −30° 59'FermiLongH1L1V149163
19070730807:23:0112h 17m 19s −9° 31'FermiLongH1L13475
19070836508:45:1113h 59m 24s −1° 18'FermiLongH1L1V11858
19071201800:25:2022h44m14s −38°35'FermiAmbiguousH1L168204357
19071209502:16:4119h 13m 33s 56° 09'FermiLongH1L1V138159
19071601900:27:594h 41m 40s 16° 28'FermiLongH1L1 512
190718A04:41:1522h 26m 25s −41° 11'SwiftLongH1L1 1293
19071949911:57:516h 34m 26s 6° 42'FermiLongH1L1V13394
190719C14:58:3416h 00m 49s 13° 00'SwiftLongH1L1V1 4157
19072061314:42:0913h 30m 52s 41° 47'FermiLongH1L1V11038
19072096423:08:389h 15m 28s −55° 35'FermiLongH1L11034
19072403100:43:5611h21m24s 15°9'FermiShortH1L1197286329
19072664215:24:5320h 41m 02s 34° 17'FermiLongH1L1V1 3485
19072684320:14:3022h 50m 43s −55° 59'FermiLongH1L1V1 72180
19072766816:01:5214h 57m 57s 19° 26'FermiLongH1L124109
190727B20:18:178h 25m 59s −13° 16'SwiftLongL1V13468
19072827106:30:3623h 46m 45s 5° 26'FermiShortH1L1V11602042723279
19080405801:23:277h 12m 04s −64° 52'FermiAmbiguousH1V11321842403474
19080510602:32:3011h 10m 36s −23° 46'FermiLongH1L1V135121
19080519904:46:0013h 59m 00s 19° 28'FermiLongH1V13375
19080653512:50:0220h 22m 14s 0° 33'FermiLongH1L1V12052
19080875218:03:1711h 12m 12s 39° 43'FermiLongL1V13262
19081067516:12:0112h 55m 07s −37° 34'FermiShortH1L1V185159222250
19081352012:29:097h 05m 31s −23° 16'FermiShortH1L1841211612356
190816A14:42:2422h 44m 43s −29° 45'SwiftLongL1V1 3475
19081795322:52:2518h 20m 40s −31° 08'FermiAmbiguousH1L161102109130
19082270516:55:298h 49m 04s −8° 05'FermiShortL1V1148181278217
190824A14:46:3914h 21m 17s −41° 54'SwiftLongH1L1V1 24160
19082517104:06:5614h 03m 26s −74° 08'FermiLongL1V11738
19082746711:12:4811h 43m 14s 46° 27'FermiLongH1L1726
190828B12:59:5916h 47m 21s 27° 17'SwiftLongH1V1 2252
190829A19:56:442h 58m 10s −8° 57'SwiftLongL1V1 3351
19083002300:32:487h 27m 36s −23° 46'FermiLongL1V13359
19083026406:20:4610h 36m 48s −54° 43'FermiAmbiguousH1V1(H1L1V1)2423314783145
19083133207:57:314h 22m 31s 14° 53'FermiLongL1V12240
19083169316:38:3711h 19m 31s −22° 21'FermiLongH1L1V12886
19090189021:21:4914h 41m 12s 0° 56'FermiLongL1V1 2229
19090372217:19:3604h09m43s −64°8'FermiShortV16687133
19090417404:11:002h 23m 40s −25° 02'FermiAmbiguousL1V1(H1V1)84109154712
19090598523:38:2815h37m55s 3°7'FermiShortV1425477
19090676718:25:0911h 27m 21s −71° 34'FermiLongH1L1V136111
19091002800:39:3715h 18m 00s 9° 04'FermiLongH1V13354
19091315503:43:0916h 53m 21s 44° 58'FermiShortH1V1(H1L1V1)201250382915
19091434508:16:341h 13m 45s 21° 27'FermiLongL1V1 2336
19091524005:44:573h 13m 19s 3° 59'FermiLongL1V12542
19091659014:10:1421h 25m 04s −48° 54'FermiLongH1L1V123170
19091976418:20:0223h 49m 26s −21° 49'FermiLongH1L1V173234
19092169916:45:5522h 33m 31s −63° 25'FermiLongH1V13246
19092361714:48:020h 32m 48s −11° 01'FermiAmbiguousH1L11331622393280
190926A09:52:166h 42m 27s 59° 32'SwiftLongH1L1 72186
19093040009:36:0615h 52m 52s −6° 05'FermiLongL1V1 2230
19100127906:41:5020h 20m 47s 15° 05'FermiLongH1V11241

Note. The Satellite column lists the instrument the sky localization of which was used for GW analysis purposes. The Network column lists the GW detector network used in the analysis of each GRB: H1 = LIGO Hanford, L1 = LIGO Livingston, V1 = Virgo. A denotes cases in which T90 > 60 s, so the on-source window of the generic transient search was extended to cover the GRB duration. For cases in which the generic transient search (Section 3.2) and the neutron star binary search (Section 3.1) used a different network, we report the network used by the latter in parentheses. Columns 8–12 display the 90% confidence exclusion distances to the GRB (D90) for several emission scenarios: BNS, generic and aligned-spin NSBH, ADI-A, and CSG GW burst at 150 Hz with total radiated energy EGW = 10−2 M c2. The first three are determined with the neutron star binary search, while the last two are calculated with the generic transient search.

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4.1. GRB 190610A

For each event in the O3a sample that was localized with an error radius smaller than 0fdg5, we searched GLADE (Dálya et al. 2018) for galaxies within 200 Mpc. We then compared the angular separation between each GRB and galaxy, and recorded all separations less than or equal to twice the error radius for each GRB. Of the 141 events in our sample, four had nearby galaxies according to the definition above: GRB 190530430, GRB 190531840, GRB 190610A, and GRB 190731943. Data for our GW follow-up analysis were available only in the case of the short GRB 190610A, first observed by Swift/BAT (Evans et al. 2019) and localized to within a 90% error radius of $1\buildrel{\,\prime}\over{.} 9$ (Lien et al. 2016; Palmer et al. 2019). On the edge of its localization region, there is a nearby galaxy at a luminosity distance of approximately 165 Mpc (z = 0.037), as reported in GLADE (see Figure 5). 212 The angular separation between the center of the localization region and the nearby galaxy is at the 2.21σ level relative to the formal fit error, which is slightly less conservative than the quoted 90% localization derived from the S/N, and is consistent with expectations of angular offsets from a host galaxy at that distance (Fong & Berger 2013).

Figure 5.

Figure 5. Overlay of the estimated 90% Swift/BAT error radius for GRB 190610A (orange circle) on the sky. A galaxy at around 165 Mpc (Dálya et al. 2018) compatible with this localization is indicated by the blue crosshair.

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We did not find any GW signal associated with GRB 190610A in the data available from the two LIGO detectors (Virgo data were not in observing mode at that particular time). Our modeled search described in Section 3.1, which uses an on-source window from −5 s to +1 s around the GRB trigger time, placed 90% confidence exclusion distances of 63 Mpc, 82 Mpc, and 114 Mpc for BNS binaries with generically oriented spins, NSBH binaries with generically oriented spins, and aligned-spin NSBH binaries (see Section 3.1 for more details on these three populations). In general, a distance of 165 Mpc can be within the reach of our modeled search, but GRB 190610A was in a sky location such that the sensitivity of both detectors was less than 30% of what it would have been in an optimal sky location.

5. Conclusions

We carried out targeted analyses for GWs associated with Fermi and Swift GRBs reported during the O3a LIGO–Virgo observing run. In the case of short and ambiguous GRBs events (see Section 2), we ran a modeled search for NS binary merger signals (Harry & Fairhurst 2011; Williamson et al. 2014), while an unmodeled search for GW transient signals was performed for all GRBs (Sutton et al. 2010; Was et al. 2012). As a result of our analyses, we found no GW signal in association with the GRBs that we followed up. This is consistent with the previously predicted rate of coincident detections of 0.1–1.4 per year for the third observing run of Advanced LIGO and Advanced Virgo (Abbott et al. 2017a). Additionally, by carrying out a weighted binomial test, we found no strong evidence for a population of unidentified subthreshold GW signals in our results. We set lower bounds on the distances to the progenitors of all GRBs we analyzed for a number of emission models. These D90 values are reported in Table 2, along with other information about each GRB that we considered; this includes timing, sky location, observing instrument, and GW detectors with available data. The 90% confidence level exclusion distances achieved in this run include the largest values published so far for some individual GRBs (see Abbott et al. 2017c, 2019b). Among the GRBs we analyzed is GRB 190610A, the sky localization of which included a nearby galaxy at a luminosity distance of 165 Mpc. We placed 90% confidence level exclusion distances lower than this value for NS binary merger GW signals and are therefore unable to rule out the possibility that GRB 190610A occurred in such galaxy.

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 Netherlands Organization 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'Innovació Universitats, Ciència i Societat Digital de la Generalitat Valenciana and the CERCA Programme Generalitat de Catalunya, Spain, the National Science Centre of Poland and the Foundation for Polish Science (FNP), 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 French Lyon Institute of Origins (LIO), the Belgian Fonds de la Recherche Scientifique (FRS-FNRS), Actions de Recherche Concertées (ARC) and Fonds Wetenschappelijk Onderzoek–Vlaanderen (FWO), Belgium, the Paris Île-de-France Region, the National Research, Development and Innovation Office Hungary (NKFIH), the National Research Foundation of Korea, the Natural Science and Engineering Research Council Canada, Canadian Foundation for Innovation (CFI), 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.

We would like to thank all of the essential workers who put their health at risk during the COVID-19 pandemic, without whom we would not have been able to complete this work.

We would also like to thank Christian Malacaria and Aaron Tohuvavohu for providing useful comments that helped improve this paper.

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

Software: LALSuite software library (LIGO Scientific Collaboration 2018), Matplotlib (Hunter 2007; Caswell et al. 2018), PyCBC (Nitz et al. 2020), X-Pipeline (Sutton et al. 2010; Was et al. 2012).

Footnotes

  • 204  

    All GCN Circulars related to this event are archived at https://gcn.gsfc.nasa.gov/other/S190425z.gcn3.

  • 205  
  • 206  
  • 207  
  • 208  
  • 209  

    The single GRB we were unable to follow up with the modeled search is GRB 190605974. The GRBs we were unable to analyze with either of the searches are: GRB 190401139, GRB 190406745, GRB 190411407, GRB 190422A, GRB 190424A, GRB 190508808, GRB 190515B, GRB 190530430, GRB 190531840, GRB 190604B, GRB 190605974, GRB 190607071, GRB 190609315, GRB 190611A, GRB 190611950, GRB 190622368, GRB 190626254, GRB 190706B, GRB 190714573, GRB 190716917, GRB 190719113, GRB 190723309, GRB 190731943, GRB 190804792, GRB 190806675, GRB 190808498, GRB 190814837, GRB 190821A, GRB 190821716, GRB 190828614 .

  • 210  

    All waveforms mentioned in this section are generated with the LALSimulation package that is part of the LALSuite software library (LIGO Scientific Collaboration 2018).

  • 211  

    The BNS inspiral range is defined as the distance at which the coalescence of two 1.4 M NSs can be detected with an S/N of 8, averaged over all directions in the sky, source orientation, and polarization (Finn & Chernoff 1993; Allen et al. 2012; Chen et al. 2021).

  • 212  

    This galaxy can be found in the HyperLeda database (http://leda.univ-lyon1.fr/) under the identifier PGC 1015066 (Makarov et al. 2014), as well as the Sloan Digital Sky Survey under the identifier J030449.65-073956.6 (Alam et al. 2015).

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10.3847/1538-4357/abee15