A Search for Neutrino Emission from Fast Radio Bursts with Six Years of IceCube Data

Fast radio bursts (FRBs) are a new class of astrophysical phenomenon characterized by bright broadband radio emission lasting only a few milliseconds. Since the first FRB discovered in 2007 in archival data from the Parkes Radio Telescope (Lorimer et al. 2007), more than 20 FRBs have been detected by a total of five observatories (Spitler et al. 2014; Masui et al. 2015; Bannister et al. 2017; Caleb et al. 2017). This rules out the hypothesis of an instrumental or terrestrial origin of these phenomena. The number of FRBs detected together with the duration and solid angle searched implies an all-sky FRB occurrence rate of a few thousand per day (Thornton et al. 2013; Spitler et al. 2014), which is consistent with 10% of the core-collapse supernova rate (Murase et al. 2016). The burst durations suggest that FRB progenitors are very compact, with light-transit distances on the order of hundreds of kilometers. The dispersion measures—the time delay of lower frequency signal components, which is proportional to the column density of free electrons along the line of sight—of the detected FRBs are significantly greater than those the Milky Way alone could provide (Cordes et al. 2016), and the majority of sources have been detected at high Galactic latitudes, indicating extragalactic origin. The distances of the FRBs extracted from their dispersion measures, however, are only upper limits, and precise measurements are yet to be determined (most likely from multi-wavelength observations).

The nature of FRBs is still under heated debate, and a multitude of models have been proposed for the FRB progenitors, the majority of which involve strong magnetic fields and leptonic acceleration. Some models predict millisecond radio bursts from cataclysmic events such as dying stars (Falcke & Rezzolla 2014), neutron star mergers (Totani 2013), or evaporating black holes (Rees 1977). In 2015, 16 additional bursts were detected from the direction of FRB 121102 (Spitler et al. 2014; Scholz et al. 2016), spaced out non-periodically by timescales ranging from seconds to days. This indicates that the cataclysmic scenario is not true at least for this repeating FRB. A multi-wavelength follow-up campaign identified this FRB's host dwarf galaxy at a distance of ∼1 Gpc (Chatterjee et al. 2017). It is unclear whether FRB 121102 is representative of FRBs as a source class or if repetitions are possible for only a sub-class of FRBs.

While leptonic acceleration is typically the default assumption for FRB emission in most models, hadronic acceleration is also possible in the associated regions of the progenitors, which would lead to the production of high-energy cosmic rays and neutrinos (Li et al. 2014). It has been proposed that cosmological FRBs could be linked to exotic phenomena such as oscillations of superconducting cosmic strings (Ye et al. 2017), and some authors predict that such cosmic strings could also produce ultra-high-energy cosmic rays and neutrinos from super heavy particle decays (Berezinsky et al. 2009; Lunardini & Sabancilar 2012). Therefore, both multi-wavelength and multi-messenger follow-ups can provide crucial information to help decipher the origin of FRBs. Here, the IceCube telescope offers the opportunity to search for neutrinos correlated with FRBs.

The IceCube Neutrino Observatory consists of 5160 digital optical modules (DOMs) instrumenting one cubic kilometer of Antarctic ice from depths of 1450 to 2450 m at the geographic South Pole (Aartsen et al. 2017e). Charged products of neutrino interactions in the ice create Cherenkov photons, which are observed by the DOMs and allow for the reconstruction of the initial neutrino energy, direction, and interaction type. Charged-current muon neutrino interactions create muons, which travel along straight paths in the ice, resulting in events with directional resolution ≲1° at energies above 1 TeV (Maunu 2016). The detector—fully installed since 2010—collects data from the whole sky with an up-time higher than 99% per year, enabling real-time alerts to other instruments and analysis of archival data as a follow-up to interesting signals detected by other observatories.

IceCube has discovered a diffuse astrophysical neutrino flux between 10 TeV and 2.6 PeV in deposited energy (Aartsen et al. 2013a, 2013b, 2014, 2015a, 2015c, 2016a). The arrival directions of these neutrinos are consistent with an isotropic distribution, indicating that a majority of them have originated from extragalactic sources. Although tau neutrinos are yet to be identified among the observed flux (Aartsen et al. 2016b), the flavor ratio is found to be consistent with ν_e:ν_μ:ν_τ = 1:1:1 from analyses that combined multiple data sets (Aartsen et al. 2015b) and with events starting inside the detector for all flavor channels (Aartsen et al. 2015d, 2017d). Having a close-to-equal flavor ratio is another feature of astrophysical neutrinos, which have traversed astronomical distances and hence have reached full mixing (Argüelles et al. 2015; Bustamante et al. 2015). While the astrophysical neutrino flux has been detected in multiple channels with high significance, neither clustering in space or time nor cross correlations to catalogs have been found (Aartsen et al. 2017a). The once promising sources for high-energy neutrinos such as GRBs (Abbasi et al. 2012; Aartsen et al. 2015e, 2017b) and blazars (Aartsen et al. 2017c) have been disfavored as the major contributors to the observed flux. To date, the origin of the astrophysical neutrinos remains a mystery.

In Fahey et al. (2017), an analysis of four FRBs with one year of IceCube data was reported. Here, we present the results of a more sophisticated study—implementing expanding search time windows and an unbinned likelihood method with detailed background modeling—in search of high-energy neutrinos from 29 FRBs using the IceCube Neutrino Observatory. This paper is structured as follows: Section 2 describes the event sample used. We then discuss the analysis method, search strategies, and background modeling in Section 3. In Section 4, we present the sensitivities and discovery potentials based on the analysis method and search strategies established in Section 3. We then report the final results and their interpretation in Section 5. Finally, we conclude and discuss the future prospects for FRB follow-ups with IceCube in Section 6.

The data used in this analysis are assembled from muon neutrino candidate events selected in previous analyses in search of prompt neutrino coincidence with gamma-ray bursts (GRBs; Aartsen et al. 2015e, 2017b). It consists of ten data sets: five years of data from the northern hemisphere and five from the southern hemisphere (Table 1). Due to the effects of atmospheric muon contamination, which are strong in the south and negligible in the north, the data samples are constructed in two "hemispheres" separated at a decl. of δ = −5°. The northern selection extends to −5° rather than 0° decl. because there is still sufficient Earth overburden at −5° for efficient absorption of atmospheric muons.

Table 1.  IceCube Data Sets Analyzed

Northern (δ > −5°) Data	Start Date	End Date	Rate (mHz)	Events	Livetime (days)	σ90%
IC86-1	2011 May 13	2012 May 15	3.65	107,612	341.9	213
IC86-2	2012 May 15	2013 May 02	5.50	157,754	332.2	268
IC86-3	2013 May 02	2014 May 06	6.20	193,320	362.2	279
IC86-4	2014 May 06	2015 May 15	6.17	197,311	369.8	279
IC86-5	2015 May 15	2016 May 12	6.07	186,600	356.8	283
Southern (δ < −5°) Data	Start Date	End Date	Rate (mHz)	Events	Livetime (days)	σ90%
IC79	2010 May 31	2011 May 13	2.46	67,474	314.6	102
IC86-1	2011 May 13	2012 May 15	1.90	58,982	359.6	110
IC86-2	2012 May 15	2013 May 02	3.18	91,485	328.6	105
IC86-3	2013 May 02	2014 May 06	3.23	100,820	358.6	104
IC86-4	2014 May 06	2015 May 18	1.90	60,500	350.7	104

Note. Here, "IC79" indicates the first year of data used in this analysis, when the IceCube array consisted of 79 strings; "IC86-1," "IC86-2," etc. denote subsequent years of data from the completed 86-string array. The median angular uncertainty among events in each sample is given as a 90% containment radius (σ_90%), assuming each event reconstruction has a 2D Gaussian point-spread function. Each individual event is assigned a σ_90% based on characteristics of its directional and energy reconstruction, assuming an E⁻² energy spectrum, and we use these same σ_90% for all signal spectra injected (Section 4). Because the event reconstruction becomes more accurate for higher energy events (Aartsen et al. 2017a), the southern data sets have smaller σ_90% as a consequence of harder energy cuts to reduce atmospheric background. Year-to-year variations in event rate and σ_90% are the result of event selection methods aimed to maximize sensitivity independently for each data set's corresponding set of sources in a previous search for GRBs, as described in Section 2.

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2.1. Northern Data Set

The northern data samples (δ > −5°) cover five years of IceCube operation from 2011 May 13 to 2016 May 12, during which 20 northern FRBs were detected (Table 2): three each from a unique source and 17 bursts from FRB 121102. In the northern hemisphere, the Earth filters out cosmic-ray-induced atmospheric muons, so the data samples consist primarily of atmospheric muon neutrinos with a median energy on the order of 1 TeV. The event rate in the northern hemisphere increases from 3.5 mHz in the first year (Aartsen et al. 2015e) to 6 mHz in later years (Aartsen et al. 2017b), as shown in Figure 1. This year-to-year variation is due largely to two combined effects: first, the initial event selections treat each year of the IceCube data sample independently due to filter and data processing scheme updates in the early years of IceCube operation; second, each data sample was separately optimized for sensitivity to its corresponding set of GRBs.⁵³

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Table 2.  FRBs in This Analysis

Northern (δ > −5°) FRBs	Time (UTC)	Duration (ms)	R.A.	Decl.	IceCube Data Sample
FRB 110523	2011 May 23 15:06:19.738	1.73	21h 45'	−00°12'	IC86-1
FRB 110703	2011 Jul 03 18:59:40.591	<4.3	23h 30'	−02°52'	IC86-1
FRB 121102 b0	2012 Nov 02 06:47:17.117	3.3	05h 32'	33°05'	IC86-2
FRB 130628	2013 Jun 28 03:58:00.02	<0.05	09h 03'	03°26'	IC86-3
FRB 121102 b1	2015 May 17 17:42:08.712	3.8	05h 32'	33°05'	IC86-4
FRB 121102 b2	2015 May 17 17:51:40.921	3.3	05h 32'	33°05'	IC86-4
FRB 121102 b3	2015 Jun 02 16:38:07.575	4.6	05h 32'	33°05'	IC86-5
FRB 121102 b4	2015 Jun 02 16:47:36.484	8.7	05h 32'	33°05'	IC86-5
FRB 121102 b5	2015 Jun 02 17:49:18.627	2.8	05h 32'	33°05'	IC86-5
FRB 121102 b6	2015 Jun 02 17:49:41.319	6.1	05h 32'	33°05'	IC86-5
FRB 121102 b7	2015 Jun 02 17:50:39.298	6.6	05h 32'	33°05'	IC86-5
FRB 121102 b8	2015 Jun 02 17:53:45.528	6.0	05h 32'	33°05'	IC86-5
FRB 121102 b9	2015 Jun 02 17:56:34.787	8.0	05h 32'	33°05'	IC86-5
FRB 121102 b10	2015 Jun 02 17:57:32.020	3.1	05h 32'	33°05'	IC86-5
FRB 121102 b11	2015 Nov 13 08:32:42.375	6.73	05h 32'	33°05'	IC86-5
FRB 121102 b12	2015 Nov 19 10:44:40.524	6.10	05h 32'	33°05'	IC86-5
FRB 121102 b13	2015 Nov 19 10:51:34.957	6.14	05h 32'	33°05'	IC86-5
FRB 121102 b14	2015 Nov 19 10:58:56.234	4.30	05h 32'	33°05'	IC86-5
FRB 121102 b15	2015 Nov 19 11:05:52.492	5.97	05h 32'	33°05'	IC86-5
FRB 121102 b16	2015 Dec 08 04:54:40.262	2.50	05h 32'	33°05'	IC86-5
Southern (δ < −5°) FRBs	Time (UTC)	Duration (ms)	R.A.	Decl.	IceCube Data Sample
FRB 110220	2011 Feb 20 01:55:48.957	5.6	22h 34'	−12°24'	IC79
FRB 110627	2011 Jun 27 21:33:17.474	<1.4	21h 03'	−44°44'	IC86-1
FRB 120127	2012 Jan 27 08:11:21.723	<1.1	23h 15'	−18°25'	IC86-1
FRB 121002	2012 Oct 02 13:09:18.402	2.1; 3.7	18h 14'	−85°11'	IC86-2
FRB 130626	2013 Jun 26 14:56:00.06	<0.12	16h 27'	−07°27'	IC86-3
FRB 130729	2013 Jul 29 09:01:52.64	<4	13h 41'	−05°59'	IC86-3
FRB 131104	2013 Nov 04 18:04:01.2	<0.64	06h 44'	−51°17'	IC86-3
FRB 140514	2014 May 14 17:14:11.06	2.8	22h 34'	−12°18'	IC86-4
FRB 150418	2015 Apr 18 04:29:05.370	0.8	07h 16'	−19°00'	IC86-4

Note. Twenty-nine FRBs are included in this search: in the North, 20 bursts from four unique sources locations, and in the South, nine bursts each with a unique location. For each FRB, arrival time and dispersion-measure-corrected burst duration are provided with R.A. and decl. (J2000), as well as the IceCube data sample being recorded during its detection. For FRB 121102, which has been found to repeat, we label individual bursts with "b0," "b1," etc., sorted chronologically by time of detection. FRB 121002 was detected as two bursts separated by ∼1 ms. It is treated as a single burst in this analysis, but we give both burst durations for completeness.

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Within each year, a seasonal variation of the background rate can also be seen (Aartsen et al. 2013c). In the Austral summer, the warming atmosphere expands and increases the average height and mean free path of products from cosmic-ray interactions, allowing pions to more frequently decay into μ + ν_μ and⁵⁴ increasing the overall rate of atmospheric muons and neutrinos in IceCube. The phase of the seasonal variation in the northern sample is the same as that in the southern sample because the northern sample is dominated by events between +15° and −5° in decl. (Figure 2), which corresponds to production in the atmosphere at latitudes between −60° and −90°.

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2.2. Southern Data Set

The southern data samples (δ < −5°) consist of five years of data from 2010 May 31 to 2015 May 18, during which nine southern FRBs were detected. The year-to-year event rate, 2–3.5 mHz, is lower than that of the northern samples mainly due to a higher energy threshold imposed to reduce background from atmospheric muons and the asymmetric separation of hemispheres, which makes the northern hemisphere ∼20% larger in solid angle than the southern (Aartsen et al. 2017b). The southern samples are dominated by down-going atmospheric muons with median energy on the order of 10 TeV. The effective area of IceCube to neutrino events that pass the event selection can be seen in Figure 3, where the effective area has been determined for the decl. of each FRB in this analysis.

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3.1. Unbinned Likelihood Method

An unbinned maximum likelihood method is used to search for spatial and temporal coincidence of neutrino events with detected FRBs (Aartsen et al. 2015f). In a given coincidence window ΔT centered on the time of detection of each FRB, the likelihood of observing N events for an expected (n_s + n_b) events is

$$\begin{eqnarray}{\mathscr{L}}(N,\{{x}_{i}\};{n}_{s}+{n}_{b}) & = & \displaystyle \frac{{({n}_{s}+{n}_{b})}^{N}}{N!}\cdot \exp [-({n}_{s}+\,{n}_{b})]\\ & & \quad \cdot \displaystyle \prod _{i=1}^{N}\displaystyle \frac{{n}_{s}S({x}_{i})+{n}_{b}B({x}_{i})}{{n}_{s}+{n}_{b}}\end{eqnarray} \tag{ 1 }$$

where n_s and n_b are the expected number of observed signal and background events, x_i is the reconstructed direction and estimated angular uncertainty for each event i, S(x_i) is the signal PDF—taken to be a radially symmetric two-dimensional (2D) Gaussian with standard deviation σ_i—evaluated for the angular separation between event i and the FRB with which it is temporally coincident, and B(x_i) is the background PDF for the data sample to which event i belongs evaluated at the decl. of event i. The uncertainties of the FRB locations are taken into account in S(x_i), but they are significantly smaller than the median angular uncertainty of the data. In any time window ΔT, the N events are those which IceCube detected within ±ΔT/2 of any FRB detection. Before background event rates and PDFs were calculated, on-time data—data collected within±2 days of any FRB detection—were removed from the samples until all analysis procedures were determined. The remaining data (>1700 days of data per hemisphere) are considered off-time data, which we used to determine background characteristics to prevent artificial bias from affecting the results of our search. Figure 2 shows examples of off-time data distributions for both northern and southern hemispheres.

A generic test statistic (TS) is used in this analysis, defined as the logarithmic ratio of the likelihood of the alternative hypothesis ${\mathscr{L}}(N,\{{x}_{i}\};{n}_{s}+{n}_{b})$ and that of the null hypothesis ${{\mathscr{L}}}_{0}(N,\{{x}_{i}\};{n}_{b})$, which can be written as

$$\begin{eqnarray}&&{\rm{TS}}=-{n}_{s}+\displaystyle \sum _{i=1}^{N}\mathrm{ln}\left[1+\displaystyle \frac{{n}_{s}S({x}_{i})}{{n}_{b}B({x}_{i})}\right].\end{eqnarray} \tag{ 2 }$$

The TS is maximized with respect to n_s to find the most probable number of signal-like events among N temporally coincident events. n_b is calculated by multiplying the time-dependent background rate for each FRB, modeled from off-time data, by ΔT.

Two search strategies are implemented based on this TS. The stacking search tests the hypothesis that the astrophysical class of FRBs emits neutrinos. In this search, n_s and n_b are the total number of expected signal and background events contained in the time windows of an entire list of FRBs for the hemisphere. One TS value (with its corresponding n_s) is returned for an ensemble of N events that consist of on-time events from all of the bursts. This TS represents the significance of correlation between the events analyzed and the source class as a whole. The max-burst search tests the hypothesis that one or a few bright sources emit neutrinos regardless of source classification. In this search, n_s and n_b are evaluated separately for each FRB. A TS-n_s pair is calculated for each FRB considering only the events coincident with its time window. The most statistically significant of these TS (and its corresponding n_s) is returned as the max-burst TS value of the ensemble.

As neutrino emission mechanisms and potential neutrino arrival times relative to the time of radio detection are unknown, we employ a model-independent search using an expanding time window, similar to a previous search for prompt neutrino emission from GRBs by IceCube which found no correlation (Abbasi et al. 2012). Starting with ΔT = 0.01 s centered on each FRB, we search a series of time windows expanding by factors of two, i.e., ${\rm{\Delta }}T={2}^{j}\cdot (0.01\,{\rm{s}})$ for j = 0, 1, 2, ..., 24. We stop expanding at a time window size of 1.94 days (167772.16 s), where the background becomes significant. For the repeating burst FRB 121102 with burst separations less than the largest time window searched, time windows of consecutive bursts stop expanding when otherwise they would overlap. There are also FRBs for which the difference in signal transit durations between electromagnetic waves detected by the radio observatory and neutrinos detected by IceCube, assuming simultaneous emission of the two messengers, is larger than our smallest time window. This is due to the size of the Earth, which has a diameter of 42 light-milliseconds, and the geographical orientation of observatories relative to astronomical events. The largest of these differences is for FRB 121102 b0, for which hypothetically light-simultaneous signal neutrinos would be expected to pass through IceCube 32 milliseconds after its radio signal was detected by Arecibo Observatory. The method of expanding time windows addresses this effect.

In the northern max-burst search, a bright radio burst with a flux of 7.5 Jy detected by the LOFAR radio array (Stewart et al. 2016) was included. This LOFAR burst was detected on 2011 December 24 at 04:33 UTC, near the North Celestial Pole (R.A. = 22^h53^m471, decl. = +86°21'46.4'') and lasted ∼11 minutes. The burst was not consistent with an FRB, so it was not included in the stacking search, during which some degree of uniformity among the stacked source class was required.

3.2. Background Ensembles

For each search method and hemisphere, we simulate 10⁹ background-only Monte Carlo pseudo-experiments for every ΔT. This is done by first finding the seasonal variation-adjusted background rate (from Figure 1) for each FRB in the hemisphere. The product of these rates and ΔT gives a set of mean values for the Poisson distributions from which background events will be drawn. In a single trial, the number of events in the time window of each FRB is randomly drawn, and each event is assigned spatial coordinates that are uniform in detector azimuth and have decl. values drawn from the PDFs shown in Figure 2. An angular uncertainty for each event is also randomly assigned from the angular distribution of the off-time data (Maunu 2016). The TS value for the trial is maximized with respect to n_s and the process is repeated for 10⁹ trials, forming a TS distribution for the background-only hypothesis.

For example, Figure 4 shows the background-only TS distribution for the southern stacking search at ΔT = 10485.76 s. Negative TS values are rounded to zero for the purposes of calculating the significance of analysis results. Building a TS distribution in this manner implicitly factors in a trials factor for the number of bursts searched, as increasing the number of sources inflates the TS values of both the analysis result and the background-only distribution. However, there is an additional trials factor when searching in overlapping time windows, so the cross-time-window trials factor must be accounted for when calculating significance values.

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For each search, the analysis procedure returns the most optimal time window and the corresponding TS-n_s pair, as determined by the p-value of the observed TS in the background-only distribution. This p-value is trials-factor corrected by investigating additional ensembles of background-only trials. For each trial, a set of events is injected for the largest ΔT following the background-only procedure described above. Then, for each ΔT, a TS value is calculated relative to its corresponding subset of events, which are randomly selected from the total event set. The most significant of these TS values has a p-value that becomes one background-only pre-trial p-value. These trials are repeated 10⁵ times, forming a pre-trial p-value distribution. The position of the pre-trial p-value from the search on on-time data in this distribution determines its post-trial p-value.

The sensitivity and discovery potential are calculated by injecting signal events following an assumed unbroken power-law energy spectrum (E⁻², E^−2.5, and E⁻³) on top of injected background events. The injected signal fluence (time-integrated flux, denoted as F) is found, which yields a certain probability of obtaining a certain significance in the background-only TS distribution (Neyman 1937; Aartsen et al. 2017b). Specifically, sensitivity and discovery potential are defined as the minimum signal fluences required to surpass, respectively, the median in 90% of the trials and the 5σ point in 90% of the trials. Figure 5 shows the sensitivities and 5σ discovery potentials for both hemispheres and search strategies. The searches in the northern hemisphere are roughly an order of magnitude more sensitive than those in the south, because of the differences in effective area as described in Section 2.

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At ΔT = 0.01 s, we expect fewer than 0.001 background events all-hemisphere per trial in each search. As a result, the median background-only TS value is zero for all ΔT until it becomes more probable than not that a background event is injected near an FRB location, resulting in a non-zero TS value. In general, the sensitivity remains constant in a ΔT range that is relatively background-free and transitions to a monotonically increasing function in background-dominated ΔT. We still search all of these low-background ΔT because the discovery potential increases even in the small background regime (Figure 5).

As a result of our methodology, there is a point in the background transition region where the sensitivity fluence appears to improve. Where the median of the background TS distribution is zero, the 90% sensitivity threshold for signal injection remains constant. But when ΔT is growing, there are more background events in each trial, which can give rise to non-zero TS values; thus, the injected fluence necessary to meet the criteria for sensitivity is less. Once the median background TS value becomes non-zero, the sensitivity increases as expected.

After correcting for trials factors induced by 25 overlapping time windows searched, no significant correlation between neutrino events and FRBs is found (nor with the LOFAR burst). The most significant pre-trial p-value (p = 0.034) is found in the northern max-burst search at ΔT = 655.36 s, with best-fit TS and n_s of 3.90 and 0.99, respectively. The post-trial p-value for this search is p = 0.25. In the same ΔT, the northern stacking search returned a best-fit TS and n_s of 1.41 and 1.01, respectively, corresponding to a pre-trial p-value p = 0.074 and post-trial p-value p = 0.375. The most signal-like event for both searches occurred 200.806 s after FRB 121102 b3, with an angular separation of 231 and estimated angular uncertainty of 131.

In the southern hemisphere, the max-burst search returns the most significant pre-trial p-value (p = 0.412) at ΔT = 167772.16 s with TS and n_s of 0.64 and 0.78, for a post-trial p-value of p = 0.84. In the southern stacking search, no TS value greater than zero was ever obtained for all ΔT. Even for the largest ΔT, where the southern max-burst search returned a positive TS value at one FRB, the order-of-magnitude increase in background for nine FRBs stacked sufficiently diminished the significance of the events. Analysis results are summarized in Table 3, and sky maps of the events that contributed the most to the results of each hemisphere are shown in Figure 6.

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Table 3.  Analysis Results

Northern (δ > −5°)	Best-fit TS	Best-fit ns	Most Significant Event	Pre-trial p	Optimal ΔT	Coincident FRB
			(t−tFRB, ΔΨ)	(post-trial p)
max-burst test	3.90	0.99	(+200.806 s, 231)	0.034	655.36 s	FRB 121102 repeater
				$0.25$		2015 Jun 02 16:38:07.575 UTC
				0.074		FRB 121102 repeater
stacking test	1.41	1.01	(+200.806 s, 231)	(0.375)	655.36 s	2015 Jun 02 16:38:07.575 UTC
			most significant event	pre-trial p
Southern (δ < −5°)	best-fit TS	best-fit ns	(t−tFRB, ΔΨ)	(post-trial p)	optimal ΔT	coincident FRB
				0.412		FRB 140514
max-burst test	0.64	0.78	(−16.9 hr, 020)	(0.84)	167772.16 s	2014 May 14 17:14:11.06 UTC
				1.0
stacking test	0	0	⋯	(1.0)	⋯	⋯

Note. Where a most significant TS is found, the timing and directional separation of the event that contributed the most to that TS value are provided. In the southern stacking test, the TS values for all time windows are zero; there is no ΔT searched that is more signal-like than background-like.

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To set upper limits on the neutrino emission from FRBs, we use the same method that determines sensitivity, using the observed TS rather than the background-only median as a significance threshold. For most ΔT, both the background median and analysis result TS values are zero, resulting in an upper limit equal to the sensitivity (Figure 7). The northern stacking search returned the most constraining 90% confidence level upper limit for E⁻² neutrino emission from FRBs among all four searches in this analysis, E²F = 0.0021 GeV cm⁻² per burst.

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This process has been repeated for each source separately to calculate per-burst upper limits (see Table 4). E⁻² fluence upper limits were determined by running background and signal-injection trials for a source list containing only one FRB, repeated for each unique source and for each year in which FRB 121102 was detected.

In a search for muon neutrinos from 29 FRBs detected from 2010 May 31 to 2016 May 12, no significant correlation has been found. In both hemispheres, several events were found to be spatially coincident with some FRBs but also consistent with background.

Therefore, we set upper limits on neutrino emission from FRBs as a function of time window searched. For an E⁻² energy spectrum, the most stringent limit on neutrino fluence per burst is E²F = 0.0021 GeV cm⁻², obtained from the shortest time window (10 ms) in the northern stacking search. This limit is much improved in comparison to a previous search with only one year of IceCube data and using a binned likelihood method (Fahey et al. 2017). The limits set in this paper are also the most constraining ones on neutrinos from FRBs for neutrino energies above 1 TeV.

At the moment, we can set even more constraining limits on high-energy neutrino emission from FRBs using IceCube's astrophysical ν_μ flux measurement (Aartsen et al. 2016a), assuming the current catalog of detected FRBs is representative of a homogeneous source class. Using an estimated all-sky FRB occurrence rate of 3000 sky⁻¹ day⁻¹ (Macquart & Ekers 2018), the ν_μ fluence per FRB at 100 TeV cannot exceed ${E}^{2}F=1.9\cdot {10}^{-6}$ GeV cm⁻² for an emission spectrum of E⁻²; otherwise, FRBs would contribute more than the entire measured astrophysical ν_μ flux. The astrophysical flux used here is extrapolated from a fit at energies of 194 TeV–7.8 PeV, so it is only a rough estimate of the maximum neutrino emission from FRBs in the energy range this analysis concerns.

With newly operating radio observatories like CHIME (CHIME Scientific Collaboration 2017), we expect on the order of 1000 FRBs to be discovered quasi-isotropically each year, which will improve the sensitivity of IceCube to a follow-up stacking search by orders of magnitude (Figure 8). Future analyses using IceCube data may also benefit from a more inclusive data set, allowing a higher overall rate of muon-like and cascade-like events in exchange for increased sensitivity at ΔT < 1000 s. Cascade-like events do not contain muons, and as a result provide an angular resolution on the order of 10°. However, a coincident event may still provide potential for high significance in very short time windows, where background is low. Furthermore, if some sub-class of FRBs is associated with nearby supernovae, MeV-scale neutrinos can be searched in the IceCube supernova stream, which looks for a sudden increase in the overall noise rate of the detector modules (Abbasi et al. 2011).

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The ANTARES neutrino observatory is most sensitive in the southern hemisphere, where the majority of FRB sources have been detected to date. Higher FRB detection rate (due to more observation time) from the southern hemisphere also provides ANTARES the opportunities for rapid follow-up observations when FRBs are caught in real time (Petroff et al. 2017). However, we emphasize that IceCube also has excellent sensitivity in much of the southern hemisphere. In Figure 9, we provide a quantitative comparison of the effective areas of the two observatories, which can serve as a useful reference when future FRBs are detected at arbitrary decl. (ANTARES Collaboration 2017, private communication). At energies above 50 TeV, the effective area of IceCube to neutrinos is the highest of any neutrino observatory across the entire (4π) sky (Figure 9). For E_ν < 50 TeV, particularly where sin(δ) < −0.33, ANTARES complements IceCube in searches for isotropic transient sources, achieving greater effective area in one-third of the sky. As ANTARES is not located at a pole, the zenith angle of any astrophysical source changes throughout the day; thus, detector overburden and sensitivity are time-dependent. Therefore, the effective areas provided by ANTARES for a given decl. band are the day-averaged values (Adrian-Martinez et al. 2014). A joint stacking analysis between IceCube and ANTARES (Adrian-Martinez et al. 2016a, 2016b) could maximize the sensitivity of neutrino searches from FRBs across the full sky. Furthermore, with the implementation of the expanding time window techniques, IceCube can now follow up on generic fast transients rapidly, enabling monitoring of the transient sky in the neutrino sector (Aartsen et al. 2017f).

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The IceCube Collaboration designed, constructed, and now operates the IceCube Neutrino Observatory. Data processing and calibration, Monte Carlo simulations of the detector and of theoretical models, and data analyses were performed by a large number of collaboration members, who also discussed and approved the scientific results presented here. The main authors of this manuscript were S. Fahey, J. Vandenbroucke, and D. L. Xu. It was reviewed by the entire collaboration before publication, and all authors approved the final version of the manuscript.

The authors gratefully acknowledge the support from the following agencies and institutions: USA—U.S. National Science Foundation-Office of Polar Programs, U.S. National Science Foundation-Physics Division, Wisconsin Alumni Research Foundation, Center for High Throughput Computing (CHTC) at the University of WisconsinMadison, Open Science Grid (OSG), Extreme Science and Engineering Discovery Environment (XSEDE), U.S. Department of EnergyNational Energy Research Scientific Computing Center, Particle astrophysics research computing center at the University of Maryland, Institute for Cyber-Enabled Research at Michigan State University, and Astroparticle physics computational facility at Marquette University; Belgium—Funds for Scientific Research (FRS-FNRS and FWO), FWO Odysseus and Big Science programmes, and Belgian Federal Science Policy Office (Belspo); Germany—Bundesministerium für Bildung und Forschung (BMBF), Deutsche Forschungsgemeinschaft (DFG) and the German Excellence Initiative, Helmholtz Alliance for Astroparticle Physics (HAP), Initiative and Networking Fund of the Helmholtz Association, Deutsches Elektronen Synchrotron (DESY), and High Performance Computing cluster of the RWTH Aachen; Sweden—Swedish Research Council, Swedish Polar Research Secretariat, Swedish National Infrastructure for Computing (SNIC), and Knut and Alice Wallenberg Foundation; Australia—Australian Research Council; Canada—Natural Sciences and Engineering Research Council of Canada, Calcul Qubec, Compute Ontario, Canada Foundation for Innovation, WestGrid, and Compute Canada; Denmark—Villum Fonden, Danish National Research Foundation (DNRF); New Zealand—Marsden Fund; Japan—Japan Society for Promotion of Science (JSPS) and Institute for Global Prominent Research (IGPR) of Chiba University; Korea—National Research Foundation of Korea (NRF); Switzerland—Swiss National Science Foundation (SNSF).