IceCube Search for Neutrinos Coincident with Compact Binary Mergers from LIGO-Virgo's First Gravitational-wave Transient Catalog

During the first and second observing runs of the advanced GW detector network (Aasi et al. 2015; Virgo Collaboration 2015), the LIGO and Virgo Collaborations (LVC) searched the collected data and discovered signals from compact binary mergers. Three binary black hole (BBH) mergers were detected during O1 (2015 September 12–2016 January 19), and an additional seven BBH events were detected during O2 (2016 November 30–2017 August 25). The LVC also discovered the very first binary neutron star (BNS) inspiral signal during O2, on 2017 August 17 (GW170817). A GW transient catalog of compact binary mergers observed by LIGO and Virgo during the first and second observing runs, GWTC-1, provides information on source properties and localization on the aforementioned 11 GW events (Abbott et al. 2019).

The observed masses of BBH components span a wide range from ${7.7}_{-2.5}^{+2.2}$ to ${50.2}_{-10.2}^{+16.2}$ ${M}_{\odot }$, while for the BNS event, GW170817, the NS masses are ${1.27}_{-0.09}^{+0.09}$ and ${1.46}_{-0.10}^{+0.12}$ ${M}_{\odot }$. The O1 and O2 GW events range in distance between ${40}_{-15}^{+8}$ Mpc for GW170817 and ${2840}_{-1360}^{+1400}$ Mpc for GW170729 (Abbott et al. 2019). All references to distance refer to the luminosity distance, D_L.

The time difference between the signals observed at the different interferometers in the GW detector network, together with the phase and amplitude of the detected GW events, enables sky localization of the source (Singer & Price 2016; Veitch et al. 2015). The 90% credible regions of the sky localizations for the GWTC-1 events span 16–1666 deg². Most events were observed only with the two LIGO detectors; thus, the corresponding sky localization regions for these events are rather large. The presence of the Virgo detector, especially for closer and/or higher-mass events, significantly improves the localization (see Table 1), though in all cases, the GW localization is poor with respect to the angular uncertainty of high-energy neutrino events, which tend to be less than a few square degrees.

Table 1.  Results for Every Detected GW from the O1 and O2 Observing Runs

O1 and O2 Detections
						Maximum Likelihood			LLAMA
Event	Type	Detectors	Ω	DL	UL Range	p-value	UL	${E}_{\mathrm{iso}}$ UL	p-value	UL
			(${\deg }^{2}$)	(Mpc)	(GeV cm−2)		(GeV cm−2)	(erg)		(GeV cm−2)
GW150914	BBH	LH	182	${440}_{-170}^{+150}$	0.0296–1.03	0.51	0.66	5.10 × 1053	0.29	0.70
GW151012	BBH	LH	1523	${1080}_{-490}^{+550}$	0.0286–0.821	0.83	0.16	7.50 × 1053	0.82	0.18
GW151226	BBH	LH	1033	${450}_{-190}^{+180}$	0.0286–0.904	0.74	0.22	1.74 × 1053	0.26	0.21
GW170104	BBH	LH	921	${990}_{-430}^{+440}$	0.0286–0.667	0.54	0.044	1.81 × 1053	0.16	0.055
GW170608	BBH	LH	392	${320}_{-110}^{+120}$	0.0309–0.0821	0.61	0.037	1.37 × 1052	0.97	0.038
GW170729	BBH	LHV	1041	${2840}_{-1360}^{+1400}$	0.0286–1.02	0.21	0.62	1.80 × 1055	0.17	0.62
GW170809	BBH	LHV	308	${1030}_{-390}^{+320}$	0.0568–0.758	0.60	0.27	1.02 × 1054	0.83	0.26
GW170814	BBH	LHV	87	${600}_{-220}^{+150}$	0.488–0.711	0.83	0.45	5.47 × 1053	1.0	0.43
GW170817	BNS	LHV	16	${40}_{-15}^{+7}$	0.180–0.429	0.19	0.27	1.67 × 1051	0.94	0.25
GW170818	BBH	LHV	39	${1060}_{-380}^{+420}$	0.0364–0.0431	0.58	0.028	1.17 × 1053	0.40	0.028
GW170823	BBH	LH	1666	${1940}_{-900}^{+970}$	0.0286–0.796	0.75	0.18	2.33 × 1054	0.25	0.18

Note. Here Ω is the area of the 90% credible region of the GW and D_L is the reported median luminosity distance. These values are taken from GWTC-1 (Abbott et al. 2019). The Detectors column indicates which of the three LIGO-Virgo detectors detected the GW. We also report 90% ULs on the energy-scaled time-integrated flux, ${E}^{2}F$, from both analyses. The UL Range column shows the minimum and maximum 90% ULs assuming a point-source hypothesis within the 90% credible region of the GW skymap. Here E_iso is the UL on the isotropic equivalent energy emitted in neutrinos during 1000 s. Note that error bars on derived energy quantities are not shown for clarity but are dominated by the error in the distance measurements of each GW.

Download table as:  ASCIITypeset image

IceCube and LIGO-Virgo have previously reported on the search for high-energy neutrino counterparts for four of the 11 GWTC-1 catalog events (GW150914, GW151012, and GW151226 from O1 and GW170817 from O2; Adrián-Martínez et al. 2016; Albert et al. 2017a, 2017b). Moreover, during O2, the LLAMA disseminated joint search results (Countryman et al. 2019) to electromagnetic follow-up partners for six events (GW170104, GW170608, GW170809, GW170814, GW170817, and GW170823), as well as for additional candidate events that were distributed to LVC partners (Abbott et al. 2019). In this paper, we present the results for all 11 GW events in the GWTC-1 catalog from a model-independent unbinned maximum-likelihood search, as well as an updated version of the previous LLAMA search.

Both searches presented below search for prompt neutrino emission within a 1000 s time window centered around the GW event time. This search window is chosen based on a range of neutrino emission mechanisms from gamma-ray bursts and is a conservative estimate of the difference in arrival times of the GW and neutrinos (Baret et al. 2011). Searches for longer-timescale neutrino emission are in development but are not considered here.

IceCube is a cubic-kilometer neutrino observatory located at the geographic South Pole (Aartsen et al. 2017a). IceCube consists of 86 strings, each of which holds 60 digital optical modules (DOMs) that are located at depths between 1.5 and 2.5 km in the Antarctic ice. These DOMs contain photomultiplier tubes that detect the Cerenkov light radiated by charged secondaries of neutrino charged-current and neutral-current interactions.

IceCube's sensitivity to a point source is strongly dependent on the decl. of the source. Figure 1 shows IceCube's sensitivity to a transient point source in a 1000 s time window as a function of decl. The predominant background in the northern sky consists of atmospheric neutrinos that can travel large column depths through the Earth, while any atmospheric muons will be absorbed in the Earth (Formaggio & Zeller 2012). This is not the case in the southern sky, where atmospheric muons have enough energy to travel from the atmosphere to the detector, resulting in a much higher total background rate. Therefore, IceCube is much more sensitive to sources in the northern sky.

Zoom In Zoom Out Reset image size

IceCube's nearly 100% uptime and continuous 4π sr field of view make it an ideal observatory for multimessenger programs, both to trigger other observatories and to perform follow-ups (Aartsen et al. 2017b). In the case of multimessenger follow-ups of GW events, IceCube is able to search for neutrinos within the full GW localization region for all reported GW events.

Both analyses described in this paper use the same neutrino data, which come from the IceCube Gamma-ray Follow Up (GFU) sample (Kintscher 2016), but they use different statistical methods and test different hypotheses. This sample is used for low-latency as well as offline analyses in IceCube. It consists of throughgoing muon tracks primarily induced by cosmic-ray interactions in the atmosphere. These backgrounds consist of downgoing muons as well as upgoing muons from atmospheric muon–neutrino interactions. The rate of background events in the sample is roughly 3 orders of magnitude larger than the rate of astrophysical neutrinos. Overall, the sample has a 6.7 mHz all-sky event rate, and the events in the sample have a median angular resolution of ≲1° for energies above 1 TeV. The GFU sample is ideal for real-time multimessenger follow-ups due to its low latency (∼30 s) and good angular resolution.

The unbinned maximum-likelihood analysis tests for a pointlike neutrino source that is consistent with the localization of the GW source detected by LVC. The method uses the GW skymap as a spatial weight in a neutrino point-source likelihood (Schumacher 2019). The likelihood has the form

$$\begin{eqnarray}&&{ \mathcal L }=\displaystyle \frac{{e}^{-({n}_{s}+{n}_{b})}{\left({n}_{s}+{n}_{b}\right)}^{N}}{N!}\displaystyle \prod _{i=1}^{N}\displaystyle \frac{{n}_{s}{{ \mathcal S }}_{i}+{n}_{b}{{ \mathcal B }}_{i}}{{n}_{s}+{n}_{b}},\end{eqnarray} \tag{ 1 }$$

where n_s is the number of signal events, n_b is the number of background events, and N is the total number of events in the sky. Here S_i and B_i are the signal and background probability distribution functions, respectively.

The sky is divided into equal-area bins using HEALPix (Górski et al. 2005). The pixels are roughly 0.01 deg², which is about the order of magnitude of the best angular resolution of the neutrino events in the GFU sample. In each pixel, the likelihood is maximized with respect to n_s and the source spectral index, γ.

The maximized likelihood, which represents the hypothesis most compatible with our data, is then multiplied by the spatial weight, which is a penalty at every pixel derived from the probability distribution of the GW event over the sky. This yields a weighted test statistic (TS)

$$\begin{eqnarray}&&{\rm{\Lambda }}=2\mathrm{ln}\left(\displaystyle \frac{L(\hat{{n}_{{\rm{s}}}},\hat{\gamma })\cdot w}{L({n}_{{\rm{s}}}=0)}\right),\end{eqnarray} \tag{ 2 }$$

where w is the weight derived from the GW localization, w = ${P}_{\mathrm{GW}}({\rm{\Omega }})/{A}_{\mathrm{pix}}$, where ${P}_{\mathrm{GW}}({\rm{\Omega }})$ is the GW localization probability as a function of position on the sky and A_pix is the area of the pixels on the sky. A full, detailed description of this method can be found in Hussain et al. (2019).

For a given GW event, we test for coincident neutrinos by considering a ±500 s time window centered on the GW event time. To keep the analysis model-independent, neutrinos are assumed to be emitted uniformly within the ±500 s time window. An example of a GW event overlaid with IceCube neutrinos within ±500 s of the GW event is shown in Figure 2. For a gallery of all 11 skymaps with overlaid neutrinos, see Figure A4 in the Appendix.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

We quantify the significance of a given observation by comparing our maximum observed Λ over the full sky to a background-only distribution and computing the resulting p-value. The background distribution is built from 30,000 trials using randomized neutrino events from the data themselves. To randomize the neutrino events used in each trial, the event arrival times are randomly shuffled while keeping the local coordinates of the events. This procedure preserves the time structure of the data set while assigning a random R.A. to each neutrino event, thus producing a unique sample for each trial. For more details on this scrambling method, see Alexandreas et al. (1993) and Cassiday et al. (1989). An example of a background-only TS distribution for GW170729 is shown in Figure A1 in the Appendix. We fix the GW skymap for these trials so each GW event in the catalog has a unique background distribution. The associated p-value for a given GW event quantifies the chance probability of a set of background neutrinos having a significant correlation with the localization of the GW event. Thirty thousand trials per GW event yield enough statistics to compute accurate p-values while still being computationally feasible.

The LLAMA search calculates the odds ratio of having a multimessenger counterpart for a GW event versus the GW originating from noise or not having a counterpart (see Countryman et al. 2019; Keivani et al. 2019 for more information). This odds ratio is used as the TS for the search. The calculation of the odds ratio is based on a Bayesian framework by assuming a model for the multimessenger sources (Bartos et al. 2019). The method uses a distribution for the astrophysical high-energy neutrinos' total emission energies, a spectrum for individual neutrinos' differential energy density, IceCube's detector response, and the spatial position reconstruction of the GW detection to estimate the expected number of neutrinos to be detected from the GW event. More neutrinos are expected to be detected from closer and otherwise identical events; thus, closer events are favored. A log-uniform distribution between 10⁴⁶ and 10⁵¹ erg is used for the distribution of the total high-energy neutrino emission energy. The assumed neutrino emission spectrum is a power law with exponent γ = −2. The method's input parameters are the detection times and localizations of candidate neutrinos and the GW, the reconstructed energies of the candidate neutrinos, the reconstructed distance of the GW, and the signal-to-noise ratio (S/N) of the GW. For GW events that have confirmed detections, as is the case with the 11 events considered here, the probability of the GW event arising from background is assumed to be zero, and the S/N information from the GW is not used. The method assumes neutrinos and GWs are emitted uniformly in ±250 s around the joint astrophysical event time (Baret et al. 2011). This results in a triangular distribution for the time difference between neutrinos and GWs with a maximum of ±500 s time difference, where neutrinos temporally closer to the GW are favored. The p-value for each event is found by comparing the observed TS value for the event to a background distribution. The background distribution is built by running the analysis on injected GWs that are distributed uniformly in the comoving volume and detected with the sensitivity of the GW detectors during the O1 and O2 runs, which have similar sensitivities. The background distributions for BBH and BNS events are kept separate due to the significantly different distance distributions of their detections. Figure A3 in the Appendix shows the background TS distribution for BBH mergers detected with three GW detectors: aLIGO Hanford, aLIGO Livingston, and AdVirgo.

Figure A1 shows the background distribution for the unbinned maximum-likelihood analysis. Here 30,000 trials are performed for GW170729. Neutrino arrival times are randomly assigned, which has the effect of assigning a random R.A. value to each neutrino while preserving the decl. and temporal distribution of our data. Since IceCube's sensitivity does not depend on R.A., we can randomize neutrinos in R.A. to produce different realizations on the sky.

For each trial and random realization of the sky, the likelihood is maximized in each pixel on the sky, and the maximum resulting TS on the sky is taken as the TS for that trial. Shown in Figure A1 are the maximum TS values on the sky for 30,000 unique trials.

Zoom In Zoom Out Reset image size

Figure A2 shows the method used to compute sensitivity and ULs in the unbinned maximum-likelihood analysis. We perform signal injection trials with neutrinos from Monte Carlo. For each trial, we choose a random location on the sky weighted by the GW localization and inject signal. We compute a passing fraction that refers to how many trials yielded a TS larger than the background median for a given injected flux. We increase the injected flux and perform trials again. We repeat this procedure for multiple injected flux values and fit a χ² cumulative distribution function (CDF) to the passing fraction versus injected flux, as shown in Figure A2. In the case of computing ULs, the passing fraction refers to how many trials yielded a TS larger than the observed TS for the GW. We fix the lower bound of the UL to the sensitivity to be conservative.

Zoom In Zoom Out Reset image size

The fluence ULs of the LLAMA search in Table 1 are calculated as follows. Three sets of neutrino lists are prepared for each GW event. In the first set, the lists consist of only background neutrinos whose count is drawn from a Poisson distribution with the mean background neutrino count in 1000 s. The neutrinos are chosen from the archival GFU data set. Neutrinos' R.A.s and detection times are randomized and other properties are kept the same. The detection times of these neutrinos are uniformly chosen around the ±500 s of the GW event time. The R.A.s are uniformly randomized between $[0,2\pi ]$. The second set of lists has one signal neutrino in addition to the first set of lists. The emission locations of the signal neutrinos are randomized according to the GW sky localization. The detection times of the neutrinos are chosen from a symmetric triangular distribution whose mode is the GW event time and extent is ±500 s around the GW event time. The neutrinos are chosen from a Monte Carlo signal simulation list with an E⁻² energy spectrum. The Monte Carlo list consists of neutrinos detected all over the sky. For choosing neutrinos from this list, only the neutrinos in the $\pm 1^\circ$ decl. band around the emission location are considered. The Monte Carlo list has an actual injection location, simulated detection location and simulated detection error on the localization for each simulated signal neutrino. Maintaining the difference between the actual injection and simulated detection location, chosen neutrinos' actual injection locations are shifted to emission points that have been chosen on the sky according to the GW's sky localization distribution. The third set of lists is similar to the second set of lists except for having two signal neutrinos emitted from the same point in each list. Then the analysis is run on these sets of lists. Finally, we find the fluence value for which 90% of the detected lists of neutrinos will have a higher TS than the TS of the actual detection. The fluence affects the expected number of signal neutrinos. The expected number of signal neutrinos for a fluence is found by using the effective area of the detector and assuming an E⁻² spectrum. By using the TS values from the three sets of lists, we can calculate the fraction of events that would have a higher TS than the actual detection's TS for a fluence value. When doing this, we assume that the events that have three or more signal neutrinos will always have a higher TS than the actual detection's TS, since such a detection would be extremely significant. Moreover, we put a lower bound to the actual detection's TS that is equal to the median of the TS distribution of only background neutrinos (sensitivity). See Veske et al. (2020) for the limits obtained based on maximum-likelihood estimators without the sensitivity lower bound for the first three GW events.

Figure A3 shows the background TS distribution of the LLAMA search used for the analysis of joint GW high-energy neutrino events that have GWs detected by the three-detector network of two aLIGO detectors and the AdVirgo detector. In order to create background pairs of GWs and high-energy neutrino events, GWs were first injected and detected at O1/O2 sensitivity with the three GW detectors. The injections were made uniform in comoving volume. The injection volume is as large as the detectors' maximum reach. Then each detected GW injection was paired with a set of neutrinos whose count was drawn from a Poisson distribution whose mean was the mean count of the neutrino detections from the GFU stream in 1000 s. According to the Poisson draws, that many neutrinos were chosen from the archival GFU data set. Before the selection, the R.A. coordinates of the neutrinos in the data set were scrambled. Finally, those neutrinos were distributed uniformly in the ±500 s window around the GW injections, which created the background joint GW high-energy neutrino event. The search was run on a set of ∼10⁴ such events.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size