IceCube high-energy starting event sample: Description and flux characterization with 7.5 years of data

R. Abbasi et al. (IceCube Collaboration)

Phys. Rev. D 104, 022002 – Published 8 July 2021

Abstract

The IceCube Neutrino Observatory has established the existence of a high-energy all-sky neutrino flux of astrophysical origin. This discovery was made using events interacting within a fiducial region of the detector surrounded by an active veto and with reconstructed energy above 60 TeV, commonly known as the high-energy starting event sample (HESE). We revisit the analysis of the HESE sample with an additional 4.5 years of data, newer glacial ice models, and improved systematics treatment. This paper describes the sample in detail, reports on the latest astrophysical neutrino flux measurements, and presents a source search for astrophysical neutrinos. We give the compatibility of these observations with specific isotropic flux models proposed in the literature as well as generic power-law-like scenarios. Assuming $ν_{e} : ν_{μ} : ν_{τ} = 1 : 1 : 1$ , and an equal flux of neutrinos and antineutrinos, we find that the astrophysical neutrino spectrum is compatible with an unbroken power law, with a preferred spectral index of ${2.87}_{- 0.19}^{+ 0.20}$ for the 68% confidence interval.

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Received 16 November 2020
Accepted 29 April 2021

DOI:https://doi.org/10.1103/PhysRevD.104.022002

Physics Subject Headings (PhySH)

Cosmic ray & astroparticle detectors Particle astrophysics

Gravitation, Cosmology & Astrophysics

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Measurement of the high-energy all-flavor neutrino-nucleon cross section with IceCube

R. Abbasi et al. (IceCube Collaboration)

Phys. Rev. D 104, 022001 (2021)

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Vol. 104, Iss. 2 — 15 July 2021

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Figure 1
High-energy fluxes of gamma rays, neutrinos, and cosmic rays. The segmented power-law neutrino flux, described in Sec. 6a5, obtained in the analysis described in this paper, is shown with red circles. The single power-law assumption, described in Sec. 6a1, is shown with the light red region. The high-energy gamma-ray measurements by Fermi [17] are shown in orange, while the extremely-high-energy cosmic-ray measurements by the Pierre Auger Observatory [18] are shown as purple data points. The comparable energy content of these three fluxes is of particular interest in the investigation of cosmic-ray origin.
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Figure 2
HESE veto. Diagram of the IceCube detector indicating veto DOMs. Top panel: an overhead view of the IceCube detector. Positions of strings with only veto DOMs are shown in red, while those with at least one nonveto DOM are shown in blue. Bottom panel: a side view of the IceCube detector strings and DOMs. Veto DOMs are indicated with red circles, and nonveto DOMs are shown with blue circles. Strings in front of or behind the region without veto DOMs are semitransparent.
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Figure 3
Veto charge vs total charge. The color scale shows the event density with respect to the veto charge, prior to the veto cuts and charge cuts, where the lighter color represents higher event density and darker represents lower event density. The vertical axis is the total charge, in photoelectrons, deposited in the detector, while the horizontal axis is the veto charge as defined in Sec. 2. The horizontal axis is plotted in linear scale from 0–3 PE and in log scale from 3 PE upward. The high-charge population of low-veto-charge events (between 0 and 3 PE) can be clearly seen against the background of higher-veto-charge events.
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Figure 4
Deposited energy resolution. Each line shows the median energy resolution plotted as a function of the true deposited energy in the detector for a reconstructed morphology. The error bars indicate the statistical uncertainty in the calculation of the median. At these energies, the uncertainty of the cascade deposited energy is affected by the spatial extension of the showers not modeled by the reconstruction, whereas the uncertainty in track deposited energy is dominated by the stochasticity of the losses.
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Figure 5
Distribution of expected reconstruction quantities as a function of true parameters. Transfer matrices, evaluated using simulation weighted to the single power-law best-fit parameters, are shown for all morphologies combined. The probability of a reconstructed deposited energy for a given neutrino energy (left) and the probability of a reconstructed cosine of the zenith angle for a particular cosine of the neutrino zenith angle (right) are shown. The matrices are column normalized. The asymmetry of the energy transfer matrix (left) is due to energy conservation, preventing large overfluctuations in reconstructed energy, and the wide range of visible energies possible for NC events which can lose large fractions of energy to the outgoing neutrino.
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Figure 6
Deposited energy probability distributions. Probability distribution of reconstructed deposited energies for slices of true neutrino energy for all morphologies weighted to the best-fit parameters. The lowest-energy bin in the legend does not contribute to the sample.
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Figure 7
HESE events observed in 7.5 years. Histogram of the observed events as a function of their inferred deposited energy and cosine of the reconstructed zenith angle. The dashed line indicates the low-energy threshold of 60 TeV.
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Figure 8
Muon veto passing fraction. Each line shows the fraction of muons of given energy at the detector edge, $E_{μ}$ , that pass without triggering the veto when entering the detector at a particular depth. Three depths are shown: 1500, 1950, and 2300 m from the surface, with lines of darkening color as the depth increases. The veto efficiency increases with the muon energy. Differences at various depths are due to the changing ice properties and varying acceptance as a function of depth due to the veto region’s asymmetric structure. At the top of the detector, the veto region is larger, so it is more efficient at rejecting muons. Additionally, the horizontal veto layer just above the dust region provides more rejection power for muons intersecting with it. Finally, the expected angular distribution of incident muons is dominated by vertical events which are more easily rejected by the upper veto region. Above approximately 10 TeV, limited simulation samples are available to assess the response, and above approximately 100 TeV, the function is entirely extrapolated. At all depths, the sum of a sigmoid function and a Gaussian distribution is fit to the results of muon simulation.
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Figure 9
Conventional and prompt atmospheric component passing fraction. The top row of plots shows the atmospheric neutrino passing fraction as a function of the neutrino energy for a flux of neutrinos originating from pions and kaons, assuming the Hillas-Gaisser H3a [123, 124, 125] cosmic-ray model and sibyll2.3c [126] hadronic interaction model. The bottom row of plots shows the atmospheric neutrino passing fraction for a flux of neutrinos originating from charmed hadrons under the same assumptions. Solid lines correspond to muon neutrinos, and dashed lines correspond to electron neutrinos. The different colors, from darkest to lightest, are for three different detector depths: 1350, 1950, and 2550 m below the surface. The left, center, and right panels correspond to cosine of the zenith angles 0.1, 0.3, and 0.9, respectively (or zenith angles of 84.3°, 72.5°, and 25.8°).
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Figure 10
Expected distribution of atmospheric neutrinos produced by pions and kaons in the sample. Distribution of neutrinos that pass the veto as a function of the deposited energy and the cosine of the zenith angle assuming nominal values for the nuisance parameters. The dashed line at 60 TeV marks the low-energy cut of the analysis. Suppression in the down-going region is due to the veto. Suppression in the up-going region is due to absorption of neutrinos in the Earth.
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Figure 11
Expected distribution of atmospheric neutrinos produced by charmed hadrons in the sample. Displays the same information as Fig. 10 but for the BERSS flux calculation for neutrinos from charmed hadrons [103].
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Figure 12
All-sky average astrophysical neutrino flux and atmospheric neutrino fluxes in the vertical direction compared at $\cos θ_{z} = 1$ before and after the veto. The atmospheric neutrino fluxes considered in this analysis are shown as dashed lines. The solid lines show the product of the atmospheric flux with the passing fraction averaged over depth at a zenith angle of 0°. The frequentist segmented power-law fit of the astrophysical flux assumes isotropy, as described in Sec. 6a5, is shown in black. This comparison demonstrates the effect of the veto in the down-going region, where it is strongest. The atmospheric flux suppression becomes weaker toward the horizon and is not present in the up-going region. The dashed lines labeled “before veto” are equivalent to the up-going atmospheric fluxes, with or without the veto, neglecting Earth absorption effects.
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Figure 13
Expected distribution of atmospheric muons in the sample. Distribution of muons that pass the veto as calculated with muongun as a function of the deposited energy and the cosine of the zenith angle. The normalization is set to match the data driven subdetector study. The dashed line at 60 TeV marks the low-energy cut of the analysis.
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Figure 14
Deposited energy and reconstructed $\cos θ_{z}$ distributions. In these panels, the data are shown as crosses, and the best-fit expectation is shown as a stacked histogram with each color specifying a given flux component: astrophysical neutrinos (golden), conventional atmospheric neutrinos (red), and penetrating atmospheric muons (purple). Left: distributions of events and expected event count assuming best-fit parameters as a function of the deposited energy; events below 60 TeV (light blue vertical line) are ignored in the fit. Right: distribution of events with energy greater than 60 TeV in the cosine of their reconstructed zenith angle. Up-going events are on the left side of this panel, and down-going events are on the right. The expected number of events is split by components and displayed as a stacked histogram. The normalization of the prompt atmospheric neutrino component fits to zero, and so is not shown in the stacked histogram. The distribution of data events appears to be largely flat as a function of cosine zenith with a small decline toward the up-going region. The lower event rate in the up-going region is expected as a result of the Earth’s absorption of the neutrino flux and appears to be compatible with the Monte Carlo expectation.
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Figure 15
Single power-law profile likelihood. Diagonal panels show the TS, as a function of different model parameters, and the one sigma intervals assuming Wilks’s theorem. Other panels show the best-fit point and two-dimensional contours. The pair of solid contours represent the 68% and 95% confidence regions assuming Wilks’s theorem. The parameter $γ_{astro}$ is the single power-law spectral index, $Φ_{astro}$ is a scaling factor of the astrophysical flux at 100 TeV, and $Φ_{prompt}$ is a scaling factor of the BERSS prompt neutrino flux calculation [103]; further descriptions of these parameters are provided in Sec. 5, Eq. (1), and Eq. (9).
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Figure 16
Comparison of single power-law parameters from different analyses. Assuming an unbroken single power-law model for the astrophysical neutrino flux, results from different IceCube samples are shown. The horizontal axis is the spectral index of the model, and the vertical axis is the six-neutrino flux normalization at 100 TeV given as a dimensionless multiplicative factor relative to $10^{- 18} {GeV}^{- 1} {sr}^{- 1} s^{- 1} {cm}^{- 2}$ . The stars denote the different best-fit points, solid contours show the 68% confidence region using the asymptotic approximation given by Wilks’s theorem, and dashed contours show the 95% confidence regions. Blue represents results from this work, while the purple shows results from IceCube’s 5 year inelasticity measurement [170], salmon shows results from IceCube’s 6 year cascade sample [67], and orange shows IceCube’s 9.5 year Northern track sample preliminary result [96]. The differing preferred regions of parameter space for the astrophysical flux between the samples suggest a level of discrepancy; however, a small region of parameter space is compatible with all samples at the 95% level. Many checks have been performed for possible explanations of the discrepancy without definitive conclusions.
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Figure 17
Impact of systematic uncertainties on the single power-law parameters. Each panel shows the impact of the systematic on the astrophysical spectral index (left panel) and normalization (right panel). The impact, horizontal axis, is defined as the change in the parameter of interest relative to its uncertainty when modifying one systematic nuisance parameter. Orange bars indicate the effect of increasing the value of the nuisance parameter from its MAP value by $1 σ$ as defined by the nuisance parameter’s 68% highest posterior density region, while purple bars indicate the corresponding reduction of the parameter. Systematic parameter values are given in Table 10. The prompt normalization ( $Φ_{prompt}$ ) and DOM efficiency ( $ε_{DOM}$ ) have the largest effect on the astrophysical parameters. All other systematics pull the astrophysical parameters by significantly less than $0.5 σ$ .
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Figure 18
Astrophysical parameter sensitivity to injected spectra. The three colors from blue to salmon show the expected astrophysical parameter 68% (solid lines) and 95% (dashed lines) uncertainty for three injected astrophysical spectra $γ_{astro} \in {2.3, 2.6, 2.9}$ . In each of these cases, the expected number of events for 7.5 years of live time is injected as data using nominal values for nuisance parameters and holding the number of injected astrophysical events to be equal between the spectra. As expected, the spectral index uncertainty grows with softer spectra from approximately 0.14 to 0.21 when changing $γ_{astro}$ from 2.3 to 2.9.
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Figure 19
Single power-law parameters posteriors. Diagonal panels show the one-dimensional posterior distribution of the parameters (joint distribution integrated over all other parameters), where the horizontal axis of the panel is the same as the horizontal axis at the bottom of the column, and the vertical axis of the panel is the probability density in an arbitrary scale. The solid blue lines denote the MAP estimator for each parameter, and the dashed lines denote the bounds of the one-dimensional 68% HPD region; these numbers are also listed above the diagonal panels. Nondiagonal panels show the two-dimensional posterior distribution of the parameters, where the horizontal and vertical axes of the panel correspond to the horizontal axis at the bottom of the column and the vertical axis at the far left of the row, respectively. The innermost contours show the two-dimensional 68% HPD region, and the outermost contours show the 95% HPD region. The grayscale of the histogram within the contours shows the probability density in an arbitrary scale. The points outside the contours show individual points from the MCMC.
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Figure 20
Double power-law model hard/soft parameters posterior distribution. Results derived from the posterior distribution of the double-power-law model are shown in the same style as Fig. 19. The figure shows the one- and two-dimensional posterior distributions for the parameters of the hard and soft components of the astrophysical neutrino flux. The diagonal panels show the one-dimensional posterior with the parameter MAP estimation and 68% HPD region indicated, while the nondiagonal panels show the two-dimensional posterior with 68% and 95% regions indicated.
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Figure 21
Spectral cutoff Bayes factors and regions of exclusion. The inverse of the Bayes factor, $B$ , is plotted in the blue curve as a function of the cutoff energy assumed in the alternative hypothesis. Regions of the cutoff energy shown by the shaded regions are disfavored with respect to the null hypothesis with varying degrees of certainty according to Jeffreys’s scale. The Bayes factor is computed for each value of the cutoff energy with the single power law as a null hypothesis. The gray dashed line indicates where the evidence of the cutoff model and the single power-law model are equal.
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Figure 22
Cutoff model comparison using frequentist test statistic. The test statistic comparing the cutoff hypothesis and the single power-law hypothesis is plotted as the black curve. The gray dashed line indicates where the cutoff model’s test statistic and the single power-law model are equal; there is a slight preference for the cutoff scenario in the several PeV region, although this is not statistically significant. We also report the results of parameter estimation for the cutoff model in this plot. The best-fit value for the cutoff energy, $E_{cutoff}$ , is shown as the solid blue line, and the dashed blue line indicates the boundary of the 68% confidence interval.
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Figure 23
Log-parabola astrophysical model parameters posterior distribution. Results derived from the posterior distribution of the model are shown in the same style as Fig. 19. The figure shows the one- and two-dimensional posterior distributions for the astrophysical flux normalization, $Φ_{astro}$ ; the spectral index at 100 TeV, $α$ ; and the change in spectral index, $β$ . The diagonal panels show the one-dimensional posterior with the parameter MAP estimation and 68% HPD region indicated, while the nondiagonal panels show the two-dimensional posterior with 68% and 95% regions indicated. As we can see from the posterior distribution, $β$ is compatible with zero, which implies that an unbroken power law is a good fit to the data under these model constraints.
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Figure 24
Segmented power-law fit. The differential flux as obtained by fitting the normalizations of independent $E^{- 2}$ segments defined in true neutrino energy. The segmented power-law model extends below the 60 TeV reconstructed energy cutoff to cover lower-energy neutrinos that misreconstruct to higher energies. Left: in this plot, each error bar shows the region in which $Δ L \leq 0.5$ while holding all other parameters fixed, providing an approximate 68% confidence level interval for the astrophysical normalization in that particular segment. Right: in this plot, each error bar shows the 68% highest probability density credible interval for the astrophysical normalization in that particular segment, assuming a uniform prior on the normalizations. The width of the turquoise bands is proportional to the posterior density of the normalization in that segment, and the horizontal scales of these bands are arbitrary.
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Figure 25
Atmospheric-background-only fit to the data. In these diagrams, we present the best-fit distribution from simulation in the absence of an astrophysical component as stacked histograms. The left panel shows the deposited energy distribution, and the right panel shows the angular distribution. As can be seen in the right panel, the angular distribution is in tension with the expectation in several bins. This amounts to a greater than $5 σ$ difference with respect to the best-fit astrophysical model. The colors of the stacked histogram are the same as in Fig. 14, and the data are shown as black crosses.
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Figure 26
Prompt neutrino normalization constraints. The horizontal axis shows the size of the prompt normalization with respect to the baseline BERSS model discussed in Sec. 4 with passing fractions given in Ref. [122]. The vertical axis gives the reciprocal of the Bayes factor; decreasing Bayes factors implies a more disfavored prompt normalization. The shaded regions denote exclusions of the prompt normalization according to Jeffreys’s scale from substantial to decisive.
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Figure 27
Source-specific model energy distributions. Different panels show the predicted energy distribution compared to the data for a subset of the models considered in Table 12. In the cases shown above, there are two astrophysical components: a specific source model and an additional single power-law component. All the components are shown as a stacked histogram at the best-fit value of the components normalizations. Left: the Stecker [197] model is shown as an example of a case where the Bayes factor assuming equally likely alternatives indicates significant preference for the single power-law model over the two-component scenario. Right: the Kimura et al. (B4) [199] model is shown as an example of a case where an additional single power law is needed to explain the distribution of events.
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Figure 28
Source-specific models tested in this work together with the segmented-fit outcome. Models discussed in Sec. 6c and listed in Table 12 are shown as lines. The HESE segmented power-law model, described in Sec. 6a5, best-fit normalizations are shown as black crosses. Models are ordered in the color scale from largest (darkest color) to smallest (lightest color) evidence as reported in Table 12.
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Figure 29
Right ascension distribution ( $ϕ_{R A}$ ). Events above 60 TeV are shown together with the stacked expectation of the astrophysical (Astro.) and atmospheric (Atmo.) components using simulation weighted with the best-fit parameters for the single power-law astrophysical model. This figure has the same format as Fig. 14.
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Figure 30
Effect of changing the DOM efficiency on the sample. Left and center panels show the ratio of the systematic expectation with respect to the nominal as a function of the deposited energy and the cosine of the zenith angle for decreasing and increasing the efficiency by one sigma, respectively. The color scale is proportional to the change, and less saturated colors correspond to lesser change. The rightmost panel shows the ratio of energy distributions, when decreasing and increasing the efficiency, as dark and light lines as a function of the deposited energy. In these three panels, all morphologies are considered.
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Figure 31
Effect of changing the hole ice on the sample. The layout and colors have the same meaning as in Fig. 30 and show the effect of decreasing and increasing the head-on efficiency. Since this effect is predominantly an effect in the angular distribution, the rightmost panel shows the ratio to nominal as a function of the cosine of the zenith angle. In these three panels, all morphologies are considered.
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Figure 32
Effect of changing ice anisotropy on length distribution in the sample. The layout and colors have the same meaning as in Fig. 30 and show the change relative the baseline to ice model anisotropy. The rightmost panel shows the ratio of length distributions, when decreasing and increasing the anisotropy, as dark and light lines as a function of the reconstructed length. In these three panels, all morphologies are considered.
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Figure 33
All-sky energy dependent astrophysical neutrino effective area. The sum of neutrino and antineutrino direction averaged effective areas is shown as a function of the neutrino energy incident on Earth for the three neutrino flavors. This effective area takes into account the effects of absorption in the Earth. To obtain the expected number of astrophysical neutrinos, this effective area can be multiplied by the average of the neutrino and antineutrino all-sky astrophysical fluxes. On the other hand, to obtain the expected number of atmospheric events, the atmospheric passing fraction must be included in the calculation of the effective area.
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Figure 34
Point source TS map. The TS at each point on the sky is indicated by the blue color scale. The Galactic center and Galactic plane are indicated by the gray dot and gray curve, respectively. Unlike in previous analyses [62, 63, 64, 65], the most significant position is well separated from the Galactic plane, at $(α, δ) = (342.1 °, 1.3 °)$ , indicated by the white $\times$ .
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