A Search for IceCube Sub-TeV Neutrinos Correlated with Gravitational-wave Events Detected By LIGO/Virgo

The LIGO / Virgo collaboration published the catalogs GWTC-1, GWTC-2.1, and GWTC-3 containing candidate gravitational-wave ( GW ) events detected during its runs O1, O2, and O3. These GW events can be possible sites of neutrino emission. In this paper, we present a search for neutrino counterparts of 90 GW candidates using IceCube DeepCore, the low-energy in ﬁ ll array of the IceCube Neutrino Observatory. The search is conducted using an unbinned maximum likelihood method, within a time window of 1000 s, and uses the spatial and timing information from the GW events. The neutrinos used for the search have energies ranging from a few GeV to several tens of TeV. We do not ﬁ nd any signi ﬁ cant emission of neutrinos, and place upper limits on the ﬂ ux and the isotropic-equivalent energy emitted in low-energy neutrinos. We also conduct a binomial test to search for source populations potentially contributing to neutrino emission. We report a nondetection of a signi ﬁ cant neutrino-source population with this test.

1. INTRODUCTION * also at Institute of Physics, Sachivalaya Marg, Sainik School Post, Bhubaneswar 751005, India † also at Department of Space, Earth and Environment, Chalmers University of Technology, 412 96 Gothenburg, Sweden ‡ also at Earthquake Research Institute, University of Tokyo, Bunkyo, Tokyo 113-0032, Japan Multi-messenger astronomy is a growing field, where combined observations with different types of observatories are used to gain more information about the various astrophysical sources.In particular, it is an excellent tool to help us nail down the sources of astrophysical neutrinos.The observation of neutrinos with the Ice-Cube Neutrino Observatory (Aartsen et al. 2017) from the direction of a blazar (IceCube Collaboration et al. 2018), TXS 0506+056, followed by electromagnetic detections of the same source (Aartsen et al. 2018), which thereby boosted its significance, is an excellent example that illustrates the importance of multi-messenger observations to identify neutrino sources.While TXS 0506+056 was detected initially in the realtime stream of IceCube, NGC 1068, an obscured active galaxy, was identified as a neutrino source with the help of a catalog of known gamma-ray emitters (Abbasi et al. 2022).The identification of both of these sources demonstrate the power of multi-messenger observations.Binary mergers of black holes (BBH), neutron stars (BNS), and neutron star-black hole (NSBH) are known to produce gravitational waves (GW).These systems are also considered as possible sites of neutrino production.In particular, relativistic outflows resulting from the merger of BNS and NSBH systems can produce neutrinos in the TeV-PeV energy range.The relativistic protons can also scatter off the slower neutrons within the ejecta and produce GeV neutrinos (Murase et al. 2013;Bartos et al. 2013;Murase & Bartos 2019).The expected neutrino emissivity from a structured jet can vary depending on the jet angle and can be much larger than that from a uniform jet (Ahlers & Halser 2019).It is predicted that the flux of neutrinos (mainly in the few 10-100s of GeV regime) can be enhanced in an off-axis observation scenario, especially when sub-photospheric emission of the gamma-ray burst (GRB) is considered (Biehl et al. 2018).The time scale of neutrino emission from gamma-ray bursts, which is set as the reference scale for observing neutrinos from binary mergers, is predicted to be t neutrino − t GW ≈ ± 500 s (Baret et al. 2011).Some models also predict longer timescales for the neutrino emission, in particular from BNS and NSBH mergers (Fang & Metzger 2017).
Several searches in the past have looked for neutrinos correlated with gravitational-wave detections, with no emission detected so far with high significance.Previous searches from IceCube focused on high-energy neutrinos with energies above several 100s of GeV that can be coincident with the observed gravitational-wave events (Aartsen et al. 2020;Abbasi et al. 2023).During the O3 run of LIGO and Virgo, these searches were conducted both in realtime -when public alerts of GW events were sent by the LIGO/Virgo Collaboration (LVC) -and offline, once the GW catalogs were published after LVC performed its offline analyses.The archival searches were performed on the GW events from GWTC-1 (Abbott et al. 2019), GWTC-2.1 (Abbott et al. 2021a), and GWTC-3 (Abbott et al. 2021b).No significant emission was found in any of these searches using high-energy neutrinos (Aartsen et al. 2020;Abbasi et al. 2023).IceCube's search for neutrinos in the MeV-GeV energy range did not return any significant observa-tion and has constrained the neutrino emission from GW sources at these energies (Abbasi et al. 2021).Searches from other detectors like ANTARES (Albert et al. 2020), KamLAND (Abe et al. 2021), SuperKamiokande (Abe et al. 2021), andBorexino (Agostini et al. 2017) did not yield any significant detection either.
While the emission of neutrinos coincident with GW events has not been detected so far, a counterpart in the electromagnetic (EM) regime has been confidently observed.GRB170817A, which is the EM counterpart of GW170817, the first BNS event detected by LVC, was observed with gamma-ray telescopes (Abbott et al. 2017) and was later confirmed by optical telescopes to be originating from the host galaxy NGC4993 (Coulter et al. 2017).Spectroscopic observations in the UV, IR and optical regimes confirmed the EM counterpart to be a kilonova (Coulter et al. 2017;Smartt et al. 2017).Further campaigns established x-ray (Troja et al. 2017) and radio counterparts (Hallinan et al. 2017;Alexander et al. 2017) to GW170817.Neutrinos, however, were not observed in searches conducted by IceCube, ANTARES, and the Pierre Auger Observatory neither within a period of ± 500 s nor within a 14-day period after the merger (Albert et al. 2017).Further searches for coincident observation of GW events and EM/neutrino counterparts have been unsuccessful in obtaining a significant observation, which can mainly be attributed to the relatively large luminosity distances of these GW events (Abbott et al. 2020).
Although previous searches for joint emission from merger events with both IceCube and other neutrino detectors did not return any significant observations, it is worthwhile to search for low-energy neutrinos detected by IceCube that are potentially coming from such a merger.In particular, the different exposure to these class of neutrinos detected with IceCube proves useful.
Here, we present the results of our search for lowenergy neutrinos coincident with the candidate GW events published in the LVC catalogs GWTC-1, GWTC-2.1 and GWTC-3 (Abbott et al. 2019(Abbott et al. , 2021a,b),b).In Section 2 we describe the IceCube neutrino observatory and its infill array IceCube DeepCore, which detects the lowenergy dataset used in this analysis.We describe the GW observations used for this follow-up study in Section 3 and the analysis method in Section 4. We show the obtained results in Section 5. Finally, we present the conclusions in Section 6. into ice.These strings hold 5160 digital optical modules (DOMS) hosting photomultiplier tubes at depths ranging from 1450 m to 2450 m from the surface.The array has a horizontal spacing of 125 m between the strings and a vertical spacing of 17 m between the DOMs.The DOMs are designed to detect signals from Cherenkov photons emitted by charged leptons that are produced by neutrinos interacting with the surrounding medium of ice.
IceCube is also equipped with an infill array, known as DeepCore, which features 8 strings with DOMs located at depths of 2100 m to 2450 m from the surface (Abbasi et al. 2012).These DOMs have a higher quantum efficiency than those in the main array.This, along with the shorter spacing between the DeepCore strings (72 m) and the individual DOMs on each string (7 m) allows for the detection of lower energy neutrinos.While the main array of IceCube detects neutrinos with energies above hundreds of GeV, IceCube DeepCore has the capability to detect neutrinos with energies of a few GeV and above.
There are two main types of event signatures observed in IceCube data.Tracks are formed when muon neutrinos undergo charged-current interactions in ice, producing secondary muons that travel in a straight line.Cascades, on the other hand, are event types that involve the charged-current interactions of electron neutrinos resulting in the production of electrons, which in turn produce electromagnetic showers in ice.Cascades are also produced by neutral-current interactions of muon, electron and tau neutrinos in ice.A special class of events appears among cascades and tracks: starting events in which the neutrino interaction occurs inside the detector volume resulting in light detected from an initial hadronic cascade as well as the outgoing lepton.
In this paper, we use a dataset with a selection of low-energy neutrinos detected by IceCube DeepCore.This dataset, hereby named the GRECO (GeV Reconstructed Events with Containment for Oscillation) Astronomy dataset Abbasi et al. (2022), is optimised for low-energy searches of astrophysical transients and contains neutrinos of all flavours with cascade and track event topologies.It consists of starting events observed in IceCube DeepCore, with energies ranging from a few GeV to several tens of TeV.These neutrinos are selected from the entire sky, resulting in similar effective areas for the dataset in both the Northern and the Southern hemispheres.A majority of the events within the dataset are either atmospheric neutrinos or atmospheric muons.The dataset, however, is suited for searches of transient sources of astrophysical neutrinos since the background is suppressed on short time scales.
Unlike the high-energy neutrino datasets, the neutrinos in the GRECO Astronomy dataset have worse angular resolution.The angular uncertainties of these events are energy dependent and the median value can be as large as ∼ 50 • at a few GeV, but can also as small as ∼ 5 • at a few hundreds of GeV, especially for starting tracks.The sensitive energy range of the neutrinos in the dataset starts at ∼ 3 GeV and goes up to ∼ 50 TeV.Other datasets have demonstrated better sensitivities for neutrino-source searches than the GRECO Astronomy dataset at energies starting from ∼ 200 GeV in the Northern hemisphere and ∼ 10 TeV in the Southern Hemisphere.The average rate of the dataset is 4.5 mHz.
For more details about the GRECO Astronomy dataset, see the appendix in Abbasi et al. (2022).

GRAVITATIONAL WAVE DETECTIONS FROM LIGO/VIRGO
The Advanced LIGO detectors (LIGO Scientific Collaboration et al. 2015) had their first observing run (O1) from 12 September 2015 to 19 January 2016, followed by their second run (O2) from 30 November 2016 to 25 August 2017.On 1 August 2017 Virgo (Acernese et al. 2015) also joined the observing run, forming a global three-detector system which resulted in better sky localizations than before (Abbott et al. 2019).The LIGO/Virgo collaboration (LVC) published the catalog GWTC-1, containing 11 confident detections of GW events from its O1 and O2 observing runs.These events consisted of 10 binary black hole (BBH) and 1 binary neutron star (BNS) mergers (Abbott et al. 2019).LVC resumed its third observing run (O3) on 1 April 2019.The first half of O3 (known as O3a) ended on 1 October 2019, and the second half (O3b) was conducted from 1 November 2019 to 27 March 2020.The candidate GW events from O3a were published initially in GWTC-2 (Abbott et al. 2021c), which was later updated to GWTC-2.1 catalog (Abbott et al. 2021a), containing 44 GW events (42 BBH, 1 BNS and 1 NSBH).Following this, LVC also published GWTC-3, a catalog containing the candidate events from O3b (Abbott et al. 2021b).This catalog reported 35 GW events (32 BBH events and 3 NSBH events) with high astrophysical probability (p astro > 0.5) and 7 marginal events (p astro < 0.5).For these GW events from the catalogs mentioned above, we see that the sky coverage goes down to ∼ 20 deg 2 in the case of well localized GW events, and up to ∼ 20000 deg 2 for badly localized events.For more details, see Table 1.
In this paper, we follow up all 11 GW events from GWTC-1, 44 events from GWTC-2.1, and 34 GW events with high p astro along with 1 marginal GW event (GW200105 162426, previously published as a public alert and an interesting candidate NSBH event) from GWTC-3.GW191222 033537 from GWTC-3 is omitted in this study due to an absence of data within the GRECO Astronomy dataset during the period of this merger.

ANALYSIS METHOD
An unbinned maximum likelihood method forms the core of the analysis.For each gravitational wave event, we search for neutrinos within a time window of ± 500 s.The method is similar to those used in previous highenergy neutrino follow-up searches (Aartsen et al. 2020;Veske et al. 2022).
We define a likelihood of the form (1) Here, n s is the number of signal events, n b is the number of background events, N is the observed number of events, S i represents the signal PDF, and B i represents the background PDF.The first term in the likelihood is a Poisson term which accounts for fluctuations in the short time window considered here, and the product term accounts for the probabilities for each event.
The Poisson term along with the ±500 s time window results in the likelihood being specialised for transientsource searches.There is no further optimization done on the transient likelihood.That is, a box profile is considered for the time window and we do not consider any particular shape for the time profile of the emission to avoid any model dependence.Moreover, the low event rate of the dataset implies that we expect only ≈ 4-5 events on the sky within the 1000 s time window.The signal PDF depends on the energy and the spatial location of the neutrino event, and is derived from Monte Carlo simulations.The energy term is dependent on the spectral index, assuming a simple power law flux.The background PDF is derived from data by randomizing the events with respect to time.For this, we randomly choose the events within a ± 5 day time window with respect to the GW time.This procedure is equivalent to randomizing in right ascension, and preserves the seasonal time structure of the data at the same time.
The likelihood defined in Equation 1is used to formulate the test statistic (TS), which compares a signal and background hypothesis to a background-only hypothesis.The TS is defined as where γ is the spectral index, which is allowed to float in the fit.The entire sky is divided into 49152 pixels as a HEALpix grid (Górski et al. 2005) (with nside = 64) for this procedure.Here w k is a spatial weighting term applied to each pixel k in the sky, and is calculated as the ratio of the GW probability in each pixel and the area of the pixel, normalized across the whole sky.The term 2ln(w k ) has a maximum value of 0 corresponding to the maximum probability pixel in the sky and has negative values at other pixels.The probabilities are obtained from the HEALpix skymap of the GW event.
The likelihood ratio is evaluated at each pixel covering 99.99% of the GW probability map and the TS value is taken as the maximum from such a scan over the pixels (Balagopal V. et al. 2022).
The procedure is used to evaluate the TS distribution of the background-only hypothesis, and also the distributions for pseudo experiments with signal injections.The background TS distribution is also used to compute the observed one-sided p-values reported in Section 5.The sensitivity is calculated from these TS distributions.We define the sensitivity as the flux level at which 90% or more of the signal-injected pseudo experiments return a TS value greater than the median TS of the background distribution.For more details of the sensitivity calculations see Balagopal V. et al. (2022).
Figure 1 shows the sensitivities obtained with this analysis.The sensitivities for each GW event in the GWTC-1 catalog is shown in Figure 1(a).These are the sensitivities where spatial constraints are also included for each GW event.The corresponding declinations covered by the GW events are shown on the x-axis.We define the time-integrated flux (per-flavour, neutrino and anti neutrino summed), shown in Figure 1 (a) and (b), as (3) where N is the number of events, E is the energy, t is the time, A is the area, and ∆t = 1000 s is the time window considered for the neutrino search.ϕ 0 is the flux normalization at the reference energy E 0 = 1 GeV.We fix the spectral index γ to 2 for the reported sensitivities and upper limits in this paper, although we allow γ to float within the fit during the likelihood maximization.A detailed study where we fix γ to several choices of values in the likelihood demonstrated that the chosen γ does not affect the reported flux values, since this is a short time window search and therefore behaves close to a counting experiment where the choice of spectral index does not affect the analysis.The Northern and the Southern-sky behaviour of the sensitivities of the GRECO Astronomy dataset is evident from Figure 1(a).While the Southern-sky sensitivity is worse than that of the Northern sky (which is expected, due to the higher atmospheric background in the Southern sky), they remain within the same order of magnitude.It is seen that for events with large coverage across the sky, shown as large error bars on the declination in Figure 1(a), an averaging of the point-source sensitivities at the declination range it spans occurs.For smaller skymaps the sensitivity becomes identical to the point-source sensitivity at that declination.
A comparison of the sensitivities of the different datasets within IceCube, which cover different energy ranges, used to search for neutrinos correlated to GW events is shown in Figure 1(b).The differential sensitivities shown in the figure are calculated within each decadal energy bin using the same method as that for the integral sensitivities, by restricting the the energy to the corresponding ranges.A spectral index of 2 is assumed within each energy bin.While the sensitivity for high-energy neutrinos (GFU dataset; IceCube Collaboration et al. ( 2016); Kintscher & IceCube Collaboration ( 2016)) is better within IceCube, it is evident from the figure that the GRECO Astronomy dataset provides complementary information at lower energies, which is otherwise inaccessible.Also noticeable are the similar sensitivities (differential) of the lowest energy bin of the GFU dataset and the highest energy bin of the GRECO Astronomy dataset.The differential sensitivity for the GRECO Astronomy dataset shown in the figure corresponds to δ = −23.38• .The differential sensitivities for positive declinations and at the horizon follow similar trends to what is shown in the figure.This is unlike the differential sensitivities for the GFU dataset, which vary a lot between the Northern and Southern hemisphere.For a comparison of the differential sensitivities of the two dataset at various declinations see the appendix of Abbasi et al. (2022).The upper limit obtained with ELOWEN, an extremely low energy search with IceCube (Abbasi et al. 2021), is also shown in the figure and is seen to be orders of magnitude above the sensitivity of the GRECO Astronomy dataset.
Model predictions for possible emission of low-energy neutrinos from binary neutron star mergers from Biehl et al. (2018) are also shown in Figure 1 10 1 10 0 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 10 11 Energy (GeV)  3. The sensitivities for events in the Northern and Southern hemispheres are within an order of magnitude.(b) The differential sensitivities of the GRECO Astronomy dataset (in blue squares) compared to the differential sensitivities of the high-energy dataset (GFU).The differential sensitivity curves are constructed by dividing the entire energy range into decadal bins.The GRECO Astronomy dataset contains neutrinos of all flavours while GFU contains only muon neutrinos.Also shown are the integral sensitivities to a declination corresponding to that of the host galaxy of GW170817, NGC4993 (Coulter et al. 2017).The grey marker shows the flux upperlimit on GW170817 obtained with the follow-up analysis using extremely low energy neutrinos detected with IceCube (Abbasi et al. 2021).The green curves represent model predictions showing low-energy neutrino emission from a GRB like 170817A (Biehl et al. 2018).All sensitivities shown in (a) and (b) assume a spectral index of 2 for the flux.
edge of the jet and the observation axis.Here, only the curves for the sub-photospheric emission from the original paper are shown (Biehl et al. 2018).For comparison, the observation angle for GRB170817A is estimated to be ∼ 28 • (Troja et al. 2017).Although the model relates to the specific case of GW170817, this is relevant for other GWs also, since off-axis observations are more likely than on-axis observations.The flux of neutrinos from such sources can also scale up or down depending on the Lorentz factor, as shown in Biehl et al. (2018).These model predictions are shown only to depict the relative scales of IceCube sensitivities and expected emission from such sources.There are several other possible emission scenarios discussed in other papers (Ahlers & Halser 2019;Carpio & Murase 2020;Gottlieb & Globus 2021).From the figure, it is evident that such model predictions are ∼ 3 orders of magnitude below the sensitivities of IceCube.Even in the large observation angle scenario, the GRECO Astronomy sensitivities (assuming a source-spectral shape of E −2 ) are well above the model predictions.Conducting searches as described in this analysis could help test such models.A significant detection of neutrinos could hint towards an incomplete understanding of the physics of neutrino production in such sources.

Population test
In addition to conducting individual follow-ups for each GW event, we also perform a binomial test to search for a source population.This test is conducted only on the GW events with high astrophysical probability reported by LVC (89 out of 90 events).To conduct the binomial test, we first order the observed p-values for the 89 GW events in their ascending order.After choosing the first k GW events out of these, we then calculate the binomial probability to obtain m successes given by Once we repeat this for k = 1 to k = 89, we choose the lowest value of P (k) and this is the final binomial probability (pre-trial).
To account for the trials factor for this test, we perform the binomial test on the background-only scenario.We randomly pick TS values from the background-only TS distributions of the 89 GW events and calculate the corresponding binomial p-value.This is repeated multiple times to construct a background distribution of the binomial p-values.The observed binomial p-value can be compared to this background distribution to correct for the trials.

RESULTS
The search for neutrinos within the 1000 s time window is conducted for 90 GW events from GWTC-1, GWTC-2.1 and GWTC-3.No significant emission is seen for any GW event.The GW event with the lowest pre-trial p-value is found to be GW151226, which is a BBH event.The GW events are treated as three separate groups of BBH, BNS and NSBH for trialscorrection purposes.The pre-trial p-value of GW151226 is 7.83 × 10 −3 (2.4 σ), which becomes 4.83 × 10 −1 after correcting for trials run for 83 BBH events.Out of the BNS candidate events, GW190425 has the smallest pretrial p-value of 9.08 × 10 −2 .Table 1 shows the p-values and the flux upper limits obtained for all 90 GW events followed up in this analysis.).These limits are for a flux with a spectral index of 2. The energy ranges shown here are the central 90% energies contributing to the flux limits at the declinations spanning the 90% probability regions of the GW skymap.These energy ranges are computed for each declination bin by calculating the upper and lower energy limits of the dataset at which the sensitivity degrades by 90%.Three GW events are highlighted here.These are GW151226 (the event with the lowest pre-trial p-value in this analysis), GW190425 (the only BNS event with a pre-trial p-value < 0.1) and GW170817 (first and only BNS event for which the electromagnetic counterpart has been observed).
Figure 2 shows the 90% C.L. flux upper limits obtained with the GRECO Astronomy dataset for the 90 GW events, assuming a spectral index of 2. These upper limits are compared to those obtained with the highenergy neutrino dataset of IceCube.From the figure, it is evident that while the GRECO Astronomy dataset can probe energies lower than the GFU dataset, its resulting flux upper limits are less constraining, which is primarily due to its worse sensitivities.There are certain GW events with some overlap in the energy ranges probed by the two datasets.These are the GW events that lie mainly in the Northern sky, where the central energy range is lower for the GFU dataset when compared to that at the Southern sky.On the other hand, the extent of energies covered by the GRECO dataset does not vary a lot between the Northern and the Southern hemispheres.The flux upper limits with the GFU dataset were reported in Aartsen et al. (2020) and Abbasi et al. (2023).
The figure also highlights three GW events: GW151226 is the event with the lowest pre-trial p-value obtained with the GRECO Astronomy dataset.Therefore, its flux upper limit is the highest among the 90 tested GW events.GW190425 is the BNS event with the lowest pre-trial p-value, and GW170817 is the only BNS event, observed during the O1 run, which also had electromagnetic counterparts.There are no observed neutrino counterparts to GW170817 in both the highenergy and low-energy follow-ups.

Background expectation Observed
Figure 3. Pre-trial p-value distribution of the 90 GW events followed up in this analysis (orange solid).This is compared to the background expectation of p-values (blue dashed).
The observed p-value distribution is consistent with the background expectation.
The distribution of pre-trial p-values obtained with the GRECO Astronomy dataset is shown in Figure 3.These are the observed p-values for 90 GW events from GWTC-1, GWTC-2 and GWTC-3.The background expectation of the p-values for these GW events are also shown in the figure.The background expectation is derived by randomly choosing entries from the background TS distribution of each GW event.The observed p-value distribution is consistent with the background expectation.It is bimodal in nature, a characteristic resulting from the discrete behaviour of the TS distribution.This discreteness arises due to the counting experiment done here in a low background regime.A binomial test is conducted on 89 GW events with high astrophysical probabilities.The top panel shows the evolution of the binomial p-value as we add k GW events (x-axis), sorted according to their pre-trial p-values.The minimum value, pmin = 0.028, is the resultant binomial pvalue of this population test and is obtained from 18 GW events.The bottom panel shows the trials-correction procedure for the binomial test.pmin (dashed vertical line) is compared to the background distribution of binomial p-values (blue histogram) and corrected for, based on its probability of occurrence.This results in the final, trial-corrected, pvalue of 0.215 (dashed horizontal line).
We perform a binomial test on the collection of GW events with high astrophysical probability followed up in this analysis in order to test the existence of a population of a combined GW and neutrino source, as described in detail in Section 3. We obtain a binomial p-value of 2.8 × 10 −2 corresponding to a population of 18 GW .Upper limits to the isotropic equivalent energy emitted in low-energy neutrinos of all flavours.The orange squares show the BBH events, the blue triangles the NSBH events and the black stars the BNS events.Also shown is the median expectation of the Eiso upper limits, derived from the background sensitivities of the GRECO Astronomy dataset (grey band).The events that lie above the band are those with p-values < 0.1 seen in this analysis.Also note that the observed isotropic energy in gamma rays from GRB170817A is 1.36×10 46 ergs, which is several orders of magnitude below the scale of this figure.The corresponding event GW170817 is the bottom-left star in this figure .events.The observed binomial p-value is compared to the background distribution of binomial p-values to obtain a post-trials p-value of 2.15 × 10 −1 .Figure 4 shows the results of the binomial test.
The observed TS values for each GW event is used to place an upper limit on the isotropic equivalent energy (E iso ) emitted in neutrinos of all flavours.For each GW event, we determine the required E iso to produce the observed TS value in 90% of the injected pseudo experiments.The E iso is related to the flux of neutrinos by the equation where Φ(E) is the flux of neutrinos and r is the distance from the source.We compute E 1 as 3 GeV and E 2 as 50 TeV for the GRECO Astronomy dataset, which is the sensitive energy range of the dataset for a sourcespectrum of the shape E −2 and is calculated in the same manner as the energy ranges depicted in Figure 2.With this, a given E iso is converted to neutrinos detected at IceCube after convolving with the 3D location of the source, which is marginalized, and the declination-dependent effective areas of the dataset.For more details of the method see Aartsen et al. (2020).The source-location information was obtained from the data release from LVC (LIGO Scientific Collaboration and Virgo Collaboration 2019, 2021; LIGO Scientific Collaboration, Virgo Collaboration and KAGRA Collaboration 2021).
The E iso upper limits obtained with this analysis are shown in Figure 5.The figure shows 90 GW events from GWTC-1, GWTC-2 and GWTC-3.The trend of increasing upper limits on E iso as the luminosity distance increases is to be expected based on a 4πr 2 sphericallysymmetric emission.Most of the events lie within the bounds for the median E iso expectation, shown as a band in the figure.It is seen that some observed E iso upper limits lie above the grey band.These events correspond to the events with pre-trial p-values < 0.1 and therefore have a high TS, which is expected to occur when many experiments are conducted.An observed higher TS, in turn, leads to less stringent upper bounds on the E iso .These events are consistent with 3σ expectations from the background and therefore they do not indicate a significant population.The reported E iso upper limits assume a source spectrum of the form E −2 .

CONCLUSION
We have presented the results of a search for lowenergy neutrinos detected with IceCube DeepCore, that are coincident with GW events detected by LVC.The dataset used here includes neutrinos of all flavours.The search was conducted for 90 GW events in a 1000 s time window centered around the time of each GW event, and did not result in any significant detection.We have also performed a binomial test to search for the existence of an underlying population of neutrinos associated with GW events.We report a post-trial p-value of 2.15×10 −1 for this test.Further, we set flux upper limits and E iso upper limits for each GW event used in this study.
The results presented here complement those from the high-energy neutrino follow-up (Aartsen et al. 2020;Abbasi et al. 2023) and the extremely low energy neutrino search (Abbasi et al. 2021) previously published by Ice-Cube.We note that some of the GW events have an observed pre-trial p-value ≤ 0.1 in the analysis presented here as well as the previously published IceCube search with high-energy neutrinos.However, it is not appropriate to simply multiply the p-values obtained from the two searches.There are some neutrino events that are common in both datasets.Also, due to the large spatial localizations of the GW events it is natural that accidental coincidence of the GW skymap with the neutrino events from both datasets occur, sometimes at dis-joint locations in the sky.An analysis that addresses all of these factors and does a combined search including both datasets will be performed to understand the possible emission across a wide energy range from these GW events in a robust manner.
With the expected increase in GW detection rate from the next run of the LIGO/Virgo/KAGRA (LVK) collaboration, more GW events will be available for searches like that presented in this paper, allowing us to probe more possibilities of joint emission.A better localization of the GW sources will also enhance such a search.The GRECO Astronomy dataset is expected to exhibit improved reconstruction with the use of more advanced methods like those including neural-networks.This can further improve the significance of a possible joint emission.
In addition to this, IceCube Upgrade -the upcoming enhancement to the infill array -will provide a higher exposure at low energies and is expected to improve the localization and energy determination capabilities of the detector at lower energies.This is also expected to improve the capabilities of the analysis presented in this paper.
Table 1.The obtained results for the 90 GW events followed up in this analysis.The obtained p-values and flux upper limits assuming a spectral index γ = 2 are shown.The events are ordered with respect to their obtained p-values.The table also shows the upper limits on the total isotropic equivalent energy emitted in neutrinos with energies between 3 GeV and 50 TeV in this analysis.The distances reported in this table are the mean distances to the GW source marginalized across the whole sky, and is also used in Figure 5.The areas of the GW events are obtained from the sky localizations of the 90% probability regions of the GW skymaps.
(b).This model was formulated based on GRB170817A, which is the observed gamma-ray counterpart to GW170817.The curves depict off-axis emission for a fixed assumption of the Lorentz factor (Γ = 30) and baryonic loading (ξ = 100).The various curves represent different observation angles (2 • , 4 • , 6 • , 8 • and 10 • from right to left), where the observation angle is the angle between the 90

Figure 1 .
Figure 1.(a)  Sensitivities of the GRECO Astronomy dataset to the 11 GW events in the GWTC-1 catalog.The x-axis represents the declinations of the corresponding GW events (declination with maximum probability shown by the squares and the declinations covering the 68% probability region shown as error bars).Fν + ν represents the timeintegrated flux as defined in Equation3.The sensitivities for events in the Northern and Southern hemispheres are within an order of magnitude.(b) The differential sensitivities of the GRECO Astronomy dataset (in blue squares) compared to the differential sensitivities of the high-energy dataset (GFU).The differential sensitivity curves are constructed by dividing the entire energy range into decadal bins.The GRECO Astronomy dataset contains neutrinos of all flavours while GFU contains only muon neutrinos.Also shown are the integral sensitivities to a declination corresponding to that of the host galaxy of GW170817, NGC4993(Coulter et al. 2017).The grey marker shows the flux upperlimit on GW170817 obtained with the follow-up analysis using extremely low energy neutrinos detected with IceCube(Abbasi et al. 2021).The green curves represent model predictions showing low-energy neutrino emission from a GRB like 170817A(Biehl et al. 2018).All sensitivities shown in (a) and (b) assume a spectral index of 2 for the flux.

Figure 2 .
Figure2.Flux upper limits obtained for the 90 GW events obtained in this analysis (blue dashed).The corresponding flux upper limits obtained with the high energy muon neutrino follow-up analysis are also shown (orange solid)(Aartsen et al. 2020; Abbasi et al. 2023).These limits are for a flux with a spectral index of 2. The energy ranges shown here are the central 90% energies contributing to the flux limits at the declinations spanning the 90% probability regions of the GW skymap.These energy ranges are computed for each declination bin by calculating the upper and lower energy limits of the dataset at which the sensitivity degrades by 90%.Three GW events are highlighted here.These are GW151226 (the event with the lowest pre-trial p-value in this analysis), GW190425 (the only BNS event with a pre-trial p-value < 0.1) and GW170817 (first and only BNS event for which the electromagnetic counterpart has been observed).
Figure4.A binomial test is conducted on 89 GW events with high astrophysical probabilities.The top panel shows the evolution of the binomial p-value as we add k GW events (x-axis), sorted according to their pre-trial p-values.The minimum value, pmin = 0.028, is the resultant binomial pvalue of this population test and is obtained from 18 GW events.The bottom panel shows the trials-correction procedure for the binomial test.pmin (dashed vertical line) is compared to the background distribution of binomial p-values (blue histogram) and corrected for, based on its probability of occurrence.This results in the final, trial-corrected, pvalue of 0.215 (dashed horizontal line).
Figure5.Upper limits to the isotropic equivalent energy emitted in low-energy neutrinos of all flavours.The orange squares show the BBH events, the blue triangles the NSBH events and the black stars the BNS events.Also shown is the median expectation of the Eiso upper limits, derived from the background sensitivities of the GRECO Astronomy dataset (grey band).The events that lie above the band are those with p-values < 0.1 seen in this analysis.Also note that the observed isotropic energy in gamma rays from GRB170817A is 1.36×10 46 ergs, which is several orders of magnitude below the scale of this figure.The corresponding event GW170817 is the bottom-left star in this figure.