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

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 neutral-current 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° (IceCube Collaboration 2021).

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 a ${ \mathcal O }({10}^{9})$ higher rate than signal neutrinos at the 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.

Figure 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 they will become the most sensitive at even softer spectra.

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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, i.e., 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 Figure 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 (Cao et al. 2021; Cristofari 2021; Bustamante 2023; Cardillo & Giuliani 2023). Thus, the enhancement in neutrino flare sensitivities in the southern sky opens a new phase space in Galactic neutrino flare searches. Some models on neutrino emission from from PeVatrons, such as Galactic gamma-ray binaries (Bykov et al. 2021), show fluxes in the TeV range and beyond that are compatible with IceCube's sensitivity ranges.

A previous IceCube search for a neutrino flares yielded no statistically significant observation (Abbasi et al. 2021a). This analysis also scanned the entire sky for the most statistically significant neutrino flares in the northern and southern skies, and it 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 ${ \mathcal O }({10}^{2})$ 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.

The cascade data set contains 59,592 cascade-like events detected with IceCube's complete 86-string configuration from 2011 May 13 to 2021 May 27 with energies between 500 GeV and 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 it uses novel event-reconstruction and event-selection techniques with neural networks and boosted decision trees (Abbasi et al. 2021b). Approximately 87% of the cascade events are estimated to be atmospheric neutrinos, 7% are astrophysical neutrinos, and the remainder are 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 and 100 TeV, atmospheric neutrinos become the subdominant component of the cascade data set (Abbasi et al. 2023).

We use 10 yr 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. 2021a). The likelihood,

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

runs over every ith event in the data set that includes N events. Here, S_i and B_i are probability density functions (PDFs) that are products of individual spatial, energy, and temporal PDFs. To search for neutrino emission, the sky is partitioned into 12,288 pixels of equal solid angle using HEALPix ⁶⁸ (Gorski et al. 2005). The spatial PDF accounts for the angular distance between the center of each pixel and the reconstructed arrival direction of each cascade event. Due to the rotation of the Earth, the angular distribution of background events is assumed to be uniform in R.A. We also assume a Gaussian PDF to test for temporal clustering between given cascade events and treat IceCube's background event rate as uniform in time while also accounting for detector livetime. IceCube's previous searches have been performed with both a Gaussian and a "box-shaped" temporal PDF that follows a Heaviside step function. Here, we use the Gaussian PDF, since it is less computationally intensive. The energy PDFs account for the astrophysical spectra and the energy distribution of the cascade events as a function of decl. We assume that, for the signal hypothesis, the neutrino flux follows an unbroken power law, E^−γ , where γ is the spectral index.

In this analysis, we define the null hypothesis such that there is no spatial and temporal neutrino clustering for a given area of the sky. The alternative hypothesis fits for the following four parameters at every pixel: number of signal events (n_s ), which is constrained to be n_s ≥ 0, signal spectral index (γ), allowed to fit within the range 1.0 ≤ γ ≤ 4.0, mean time of the flare (T₀ [Modified Julian Date (MJD)]), allowed to fit to any time during the livetime of the data set, and half-width flare duration (σ_t [days]), constrained to σ_t ≥ 10⁻¹¹ and maximally to half of the duration of the livetime of the data set, in order to search for neutrinos that are spatially and temporally clustered. The alternative hypothesis indicates an excess of signal-like events that surpass the expected background. To test the null and alternate hypotheses, we use the likelihood ratio test, as described in Wilks (1938), to construct a test statistic (TS):

$\begin{eqnarray}&&{\rm{TS}}=-2\mathrm{log}\left[\displaystyle \frac{{T}_{\max }-{T}_{\min }}{{\sigma }_{t}}\times \displaystyle \frac{{ \mathcal L }({n}_{s}=0)}{{ \mathcal L }({n}_{s},\gamma ,{T}_{0},{\sigma }_{t})}\right].\end{eqnarray} \tag{ 2 }$

In Equation (2), T_max and T_min refer to the livetime bounds of the cascade data set. The TS includes a marginalization term for the flare duration in addition to the likelihood ratio; this prevents a bias that arises from overfitting for σ_t with shorter durations. IceCube's previous untriggered flare searches have searched for flares by imposing a signal-over-background (S/B) threshold to reduce the computational complexity of the analysis. The S/B threshold is used to seed potential flares with events that have a high probability of being a signal, based off their reconstructed direction and energy. Thus, S/B only accounts for the spatial and energy PDFs of a given event. Previous all-sky track analyses had data sets with high data rates; these analyses used thresholds of S/B > 1000 to efficiently search for flares. Since the cascade data set has an order of magnitude fewer events than IceCube's track data set, we relax this threshold to S/B >1 .

To calculate the TS, the events' arrival directions are uniformly randomized in R.A.; the time of the event is also randomized. A TS is then calculated for each pixel in the all-sky search. This process is repeated ${ \mathcal O }({10}^{4})$–${ \mathcal O }({10}^{5})$ times in order to obtain an ensemble of TS that follows the null hypothesis of no spatial or temporal clustering. Each TS in the ensemble represents a different realization of background data. To minimize the computational expense of building an ensemble of TS for each pixel, and to account for the decl. dependence of the data, we build an ensemble of TS in 81 decl. bins and one R.A. bin. The decl. bins range from [−80°, 80°] and are evenly spaced in 2° increments. The TS for the data, TS_data, is then calculated for every pixel and compared to the corresponding ensemble of TS in order to calculate a local p-value (p_local), which is the probability of getting a TS ≥ TS_data from a random background realization of our data. We report two local p-values, p_local, for the data that correspond to the most statistically significant pixels in the northern and the southern sky, respectively. Since we test many pixels on the sky, the two local p-values, p_local, for the northern and southern skies are corrected for statistical trials to report global p-values (p_global). We construct p_global by considering ${ \mathcal O }({10}^{2})$ randomized sky scans that correspond to different realizations of background data, and then taking the most statistically significant pixels in the northern and southern sky from each sky scan in order to obtain respective distributions of the most statistically significant p_local. Finally, the two values of p_global are reported as the trial-corrected significances.

The sensitivity and discovery potential fluences at the hottest spot, along with two benchmark declinations of ±60o, 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.

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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 power law 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.