All-sky Search for Transient Astrophysical Neutrino Emission with 10 Years of IceCube Cascade Events

Neutrino flares in the sky are searched for in data collected by IceCube between 2011 and 2021 May. This data set contains cascade-like events originating from charged-current electron neutrino and tau neutrino interactions and all-flavor neutral-current interactions. IceCube’s previous all-sky searches for neutrino flares used data sets consisting of track-like events originating from charged-current muon neutrino interactions. The cascade data set is statistically independent of the track data sets, and while inferior in angular resolution, the low-background nature makes it competitive and complementary to previous searches. No statistically significant flare of neutrino emission was observed in an all-sky scan. Upper limits are calculated on neutrino flares of varying duration from 1 hr to 100 days. Furthermore, constraints on the contribution of these flares to the diffuse astrophysical neutrino flux are presented, showing that multiple unresolved transient sources may contribute to the diffuse astrophysical neutrino flux.


INTRODUCTION
The astrophysical processes responsible for producing, accelerating, and propagating high-energy cosmic rays have not been resolved.High-energy neutrinos can provide insights into the origins of cosmic rays.In 2013, IceCube reported observations of the diffuse astrophysical neutrino flux (Aartsen et al. 2013a).However, the majority of the diffuse astrophysical neutrino flux still has unresolved origins.Since then, IceCube has observed evidence of time-dependent and steady-state neutrino emission from astrophysical objects.In 2017, IceCube detected a 290 TeV neutrino (IceCube-170922A) in spatial coincidence with the blazar TXS 0506+056; IceCube-170922A was also temporally coincident with enhanced multi-wavelength activity in the blazar (Aartsen et al. 2018a).The statistical significance of this spatial and temporal coincidence was reported at 3σ.An archival search of 9.5 years of IceCube data found further evidence at a statistical significance of 3.5σ for a neutrino flare that occurred between September 2014 and March 2015 that was not coincident with gamma-ray emission (Aartsen et al. 2018b).Since then, further searches (Allakhverdyan et al. 2023;Albert et al. 2023) have hinted at the possible connection of neutrino flares and blazars.IceCube observed evidence for continuous neutrino emission from the Seyfert galaxy NGC 1068 with a significance of 4.2σ (Abbasi et al. 2022).Recently, IceCube has also observed steady diffuse neutrino emission from the Milky Way at a significance of 4.5σ (Abbasi et al. 2023).In the past decade, time-domain multi-messenger astronomy has observed multiple breakthroughs that serve potential insight into which sources are capable of contributing to the diffuse astrophysical neutrino flux.Not all astrophysical transient events are expected to produce a neutrino flux; however, hadronic astrophysical transient events are primary candidates for contributing to the diffuse neutrino flux (Murase & Bartos 2019).In order to remain model-independent, this analysis excludes multi-messenger information and solely uses 10 years of IceCube's cascade data to perform a time-dependent search for neutrino flares across the entire sky.
The IceCube Neutrino Observatory is located at the geographic South Pole and occupies a cubic kilometer of ice instrumented with 5,160 digital optical modules (DOMs).The DOMs are situated on 86 readout and support cables that have been frozen into the Antarctic glacier at depths between 1450 m -2450 m (Abbasi et al. 2009;Aartsen et al. 2017).The primary in-ice DOMs array is composed of 78 readout and support cables; the DOMs have a vertical spacing of 17 m and a horizontal spacing of 125 m.This design allows IceCube to detect the Cherenkov radiation from charged particles that are created by neutrinos with energies from 100 GeV -10 PeV interacting with the Antarctic ice.The remaining 8 cables were used to create a higher density sub-volume of IceCube in order to detect neutrinos down to 10 GeV (Abbasi et al. 2012).Since 2011, IceCube has been fully operational and taking data with > 99% uptime (Aartsen et al. 2017).

SEARCH FOR NEUTRINO FLARES
2.1.Cascade events: A new avuenue to search for flares IceCube detects electron neutrinos (ν e ), muon neutrinos (ν µ ), and tau neutrinos (ν τ ), as well as their antiparticles.At Earth, we expect a flavor ratio (ν e : ν µ : ν τ ) of approximately 1:1:1 due to neutrino oscillations occurring over astronomical distances (Learned & Pakvasa 1995).Depending on the interaction type, a neutrino will primarily produce two event topologies: cascades and tracks (Aartsen et al. 2014).Cascade events are produced by all-flavor neutralcurrent interactions, as well as charged-current ν e and ν τ interactions, which can produce hadronic and electromagnetic showers (Aartsen et al. 2014).Due to the spatial extent of the showers and the scattering length of light within the Antarctic ice, which is shorter compared to the DOM spacing, cascade events appear nearly symmetric and have reconstructed angular resolutions of ∼5 • -15 • depending on the energy of the neutrino (Aartsen et al. 2013b;Abbasi et al. 2023).Conversely, tracks are produced when ν µ interact with the ice through the charged-current channel and produce a muon that can travel for several kilometers while emitting Cherenkov light.At high energies, tracks have reconstructed angular resolutions ≲ 1 • (Abbasi et al. 2021a).
However, a major disadvantage of the track data set is the much higher background rates compared to the cascade data set.Atmospheric muons are detected at O(10 9 ) higher rate than signal neutrinos at trigger level, and most of the atmospheric neutrinos that reach the IceCube detector are muon neutrinos.Thus atmospheric backgrounds overwhelmingly produce track events.By using cascade events, the background contamination of the data set is greatly reduced (Abbasi et al. 2023).This has a large effect on sensitivities in the Southern Sky, where IceCube does not have the Earth to shield the detector from atmospheric muons.Because the atmospheric background fluxes are expected to be a softer spectrum of E −3.7 compared to the neutrino spectrum from astrophysical flares at E −2 to E −3 , the reduction in background effectively lowers the energy threshold of the cascade analysis relative to the track analysis.
Fig. 1 compares the 90% confidence level (C.L.) sensitivity fluxes of neutrino flares as detected in a track data set and the cascade data set.While track events have better sensitivity in the Northern Sky, the sensitivity deteriorates rapidly in the Southern Sky as Earth shielding of atmospheric muons disappears.The cascade data set remains flat in sensitivity flux since atmospheric muons are not the main background in this data set.Even in the Northern Sky, the sensitivity fluxes remain relatively close when a soft emission of E −2.7 flare is assumed, and will become the most sensitive at even softer spectra.
A region of particular interest to neutrino flare searches is the Galactic Center.The Galactic Center region hosts a supermassive black hole (SMBH) at the position of Sgr A* which is the nearest object capable of strong flare activity.SMBHs can be sources of flare-like emission of cosmic rays and their secondaries, neutrinos and gamma-rays.By using cascade events, we lower the sensitivity flux to such flares by more than an order of magnitude for the emission duration and spectral index assumed in Fig. 1.Astrophysical sources of PeV-scale cosmic ray production, dubbed PeVatrons, are hypothesized along the Galactic Plane, with most of the population in the Southern Sky (Cristofari A previous IceCube search for a neutrino flares yielded no statistically significant observation (Abbasi et al. 2021b).This analysis also scanned the entire sky for the most statistically significant neutrino flares in the Northern and Southern Skies, and did not utilize external triggers, such as alerts from gamma-ray telescopes.Such an "untriggered" search can detect astrophysical phenomena that solely produce neutrinos or produce neutrinos and other astrophysical messengers at times offset from the detection of optical, X-ray, or gamma-ray flares.In IceCube, when searching for neutrino flares that have durations of O(10 2 ) days or less, this method becomes more sensitive than time-integrated searches (Braun et al. 2010).IceCube's previous untriggered analyses only used track events due to their high event rate and small angular uncertainties.The analysis of cascade events provides a new opportunity to use a statistically independent data set to observe the transient sky.This is the first such all-sky search utilizing a cascade data set.

Cascade Data set
The cascade data set contains 59,592 cascade-like events detected with IceCube's complete 86-string configuration from May 13, 2011 to May 27, 2021 with energies between 500 GeV -5.35 PeV.The angular resolution of the data set is energy-dependent.At 1 TeV, the median angular resolution is > 15 • ; at 100 TeV, the median angular resolution is ≲ 10 • and improves to ∼ 5 • at PeV energies.The data set was designed to search for time-integrated all-sky and Galactic diffuse emission (Abbasi et al. 2023), and uses novel event reconstruction and event selection techniques with neural networks and boosted decision trees (Abbasi et al. 2021c).Approximately 87% of the cascade events are estimated to be atmospheric neutrinos, 7% are astrophysical neutrinos, and the remainder being atmospheric muons (Abbasi et al. 2023).The atmospheric neutrino spectrum is comparatively softer than that of astrophysical neutrinos (Aartsen et al. 2015).Thus, at energies between 10 TeV -100 TeV, atmospheric neutrinos become the subdominant component of the cascade data set (Abbasi et al. 2023).

Analysis Methods
We use 10 years of cascade events to search for the most statistically significant spatial and temporal clustering of events in IceCube's Northern (δ > -5 • ) and Southern (δ < -5 • ) Sky, which were predefined in a blind analysis.The north/south split was chosen to be consistent with previous IceCube analyses using track events.The points within 10 • of the celestial poles are excluded due to their low statistics and limited background estimation.The clustering search uses a maximum likelihood method to identify time-dependent neutrino emission from point sources, similar to IceCube's previous analyses (Braun et al. 2010;Abbasi et al. 2021b).The likelihood,

RESULTS & IMPLICATIONS
No significant spatial and temporal clustering of astrophysical neutrinos was observed in this analysis.In the Northern Sky, the most significant point is located at (α, δ) = (322.03• , −4.78 • ) with a corresponding p local = 2.45 × 10 −3 and a pre-trials significance of 2.81σ.The most significant point in the Southern Sky is located at (α, δ) = (320.63• , −5.98 • ) with a respective p local = 2.12 × 10 −3 and a pre-trials significance of 2.86σ.The "hottest" spots are separated by < 2 • in declination and are located in the same extended "warm" spot.This is due in part to the angular resolution of the cascade events.Since cascade events are correlated with different pixels, the statistical fluctuations near the hottest spot have similar p local .After correcting trials, we report the final p-values of p global = 0.71 in the Northern Sky, and p global = 0.51 in the Southern Sky.The results of this all-sky search for transient astrophysical neutrino emission are consistent with the background-only hypothesis.

Diffuse Flux Constraints
Figure 2. Left: Fluences of neutrino flares at the 90% sensitivity and 5σ discovery potential of this analysis, assuming flare durations between 0.1 days and 100 days.An energy spectrum of E −2.53 is assumed in these flares to match that of the measured diffuse neutrino emission in cascades (Aartsen et al. 2020).Simulated flares are placed at the declination of the hottest spot found, and also at a benchmark declination of ±60 o .Right: Comparison of the time-averaged upper limit and sensitivity fluxes, at the declination of the hottest spot, to the previously measured steady-state diffuse neutrino flux (Aartsen et al. 2020).As the flare duration increases, the maximum possible contribution to the diffuse cascade flux increases.For each possible flare duration shown, hundreds or thousands of independent neutrino flares are needed to equal the entire diffuse astrophysical flux.At the longest flare duration (100 days), at least 100 neutrino flares are needed to account for the observed diffuse flux.
The sensitivity and discovery potential fluences at the hottest spot, along with two benchmark declinations of ±60 o , are shown as a function of σ t in Figure 2 -left.IceCube has previously measured a time-integrated diffuse astrophysical neutrino flux with cascade events (Aartsen et al. 2020).This plot assumes the flare emission has a power law of E −2.53 taken from the best fit spectral index of the measured diffuse cascade flux.
As no significant flare was observed, we calculated the 90% upper limits (U.L.) on neutrino fluxes (Figure 2 -right) for the all-sky hottest spot and we discuss implications for the observed diffuse astrophysical flux.Assuming a powerlaw of E −2.53 taken from the measured diffuse cascade flux, we calculate the time-averaged fluxes at the sensitivity of this analysis and the resulting U.L. from data, each at the 90% C.L., at the location of the most significant point.The energy range used for each flux corresponds to the energy range of the neutrino events contributing to 90% of the flux.Fluxes are converted to time-averaged fluxes by distributing them over the entire livetime of the data set in order to compare to the measured diffuse cascade flux.As the flare duration increases, the maximum possible contribution from a single neutrino flare to the diffuse astrophysical neutrino flux increases.However, at least 100 neutrino flares of σ t = 100 days are needed to account for the diffuse astrophysical flux.

CONCLUSIONS
In the all-sky search for transient neutrino emission, no significant spatial and temporal clustering was observed.We provide upper limits on the time-averaged neutrino flux at the 90% confidence level for various assumed flare durations, as shown in Figure 2 -left.These all-sky upper limits show that depending on the flare duration hundreds or thousands of individual neutrino flares are needed in order to comprise the diffuse astrophysical neutrino flux.These all-sky upper limits are not dependent on a specified class of astrophysical transient objects; thus, multiple unresolved transient objects may contribute to the diffuse neutrino flux.
Cascades provide upper limits that can help constrain future searches for transient neutrino emission.Cascade data sets are considered to be independent of IceCube's track data sets, and future searches for transient neutrino emission could combine tracks and cascades.In addition, the next generation of IceCube, IceCube-Gen2, will have the capability to conduct a more sensitive search for transient neutrino emission across the entire sky (Aartsen et al. 2021).This will provide us with the opportunity to observe the origin of high-energy astrophysical neutrinos and further motivate time-domain multi-messenger astronomy.

Figure 1 .
Figure 1.The 90% C.L. sensitivity flux to an E −2.7 neutrino flare emission with a duration of 10 days at various declinations.Using IceCube's track data set (IceCube Collaboration 2021), the sensitivity deteriorates rapidly in the Southern Sky as the Earth shielding to atmospheric muons disappears, while cascade data set remains flat.Even in the Northern Sky, the sensitivity fluxes remain relatively close because of the soft emission of E−2.7 flare that is assumed here.This is due to the low background nature of the cascade data set, which effectively lowers the energy threshold of the analysis as described in the main text.