Joint Constraints on Galactic Diffuse Neutrino Emission from the ANTARES and IceCube Neutrino Telescopes

A diffuse Galactic neutrino emission is expected from cosmic-ray (CR) interactions with interstellar gas and radiation fields. These interactions are also the dominant production mechanism of the diffuse high-energy γ-rays in the Galactic plane, which have been measured by the Fermi-Large Area Telescope (Fermi-LAT; Ackermann et al. 2012).

In the GALPROP-based (Vladimirov et al. 2011) conventional model of Galactic diffuse γ-ray production, CRs are accelerated in a distribution of sources such as supernova remnants. They propagate diffusively in the interstellar medium producing γ-rays and neutrinos via interactions with the interstellar radiation field and interstellar gas. The interstellar radiation field is weakly constrained by Fermi-LAT γ-ray data and interstellar gas is constrained by both Fermi-LAT γ-ray data and radio measurements of CO and H i line intensities. The CR population model itself is normalized to local measurements taken at Earth. The GALPROP model parameters are tuned to achieve optimal agreement between Fermi-LAT (Ackermann et al. 2012) data and the direction-dependent prediction given by integrating expected γ-ray yields along the line of sight from Earth. The neutral pion decay component estimated by the conventional model should be accompanied by a neutrino flux from charged pion decay.

The conventional model, however, underpredicts the γ-ray flux above 10 GeV in the inner Galaxy (Ackermann et al. 2012). The KRA${}_{\gamma }$ models (Gaggero et al. 2015a, 2015b, 2017) address this issue using a radially dependent model for the CR diffusion coefficient and the advective wind. The primary CR spectrum assumed within the KRA${}_{\gamma }$ models has an exponential cutoff at a certain energy. In order to bracket measurements by KASCADE (Antoni et al. 2005) and KASCADE-Grande (Apel et al. 2013) in the [100 TeV, 100 PeV] and [10 PeV, 2000 PeV] energy ranges, respectively, while maintaining agreement with proton and helium measurements by CREAM (Ahn et al. 2010), cutoffs at 5 and 50 PeV per nucleon are considered. The resulting models are referred to as KRA${}_{\gamma }^{5}$ and KRA${}_{\gamma }^{50}$, respectively. The direction dependence of the energy-integrated KRA${}_{\gamma }^{5}$ neutrino flux prediction is shown in Figure 1. Compared to the conventional model of the Galactic diffuse emission, the KRA${}_{\gamma }$ models predict modified spectra and enhanced overall γ-ray and neutrino fluxes in the southern sky, especially in the central ridge where a hardening of the CR spectra is reproduced. Hence, neutrinos offer a unique opportunity to independently test the model assumptions of Galactic CR production and transport, accessing energies far beyond the reach of current γ-ray experiments.

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The KRA${}_{\gamma }$ predictions have already been tested separately with Astronomy with a Neutrino Telescope and Abyss environmental RESearch (ANTARES; Albert et al. 2017) and IceCube (Aartsen et al. 2017a) data. ANTARES and IceCube achieved sensitivities of $1.05\times {{\rm{\Phi }}}_{{\mathrm{KRA}}_{\gamma }^{50}}$ and $0.79\times {{\rm{\Phi }}}_{{\mathrm{KRA}}_{\gamma }^{50}}$, respectively; both analyses obtained 90% confidence level (CL) upper limits of $1.2\times {{\rm{\Phi }}}_{{\mathrm{KRA}}_{\gamma }^{50}}$. ANTARES additionally examined the 5 PeV cutoff model, obtaining a sensitivity of $1.4\times {{\rm{\Phi }}}_{{\mathrm{KRA}}_{\gamma }^{5}}$ and an upper limit of $1.1\times {{\rm{\Phi }}}_{{\mathrm{KRA}}_{\gamma }^{5}}$ due to an underfluctuation of the fitted signal flux in the track channel.

This Letter presents a combination of these two maximum-likelihood analyses exploiting the advantageous field of view of ANTARES as well as the high statistics of IceCube.

The IceCube Neutrino Observatory (Aartsen et al. 2017b) is located at the South Pole between 1.45 and 2.45 km below the surface of the ice. It consists of 5160 photomultiplier tubes (PMTs) instrumenting one cubic kilometer of ice. The ANTARES neutrino telescope (Ageron et al. 2011) consists of 885 PMTs deployed in the Mediterranean sea, 40 km off the coast of Toulon, France. It is installed at depths between 2.01 km and 2.47 km below sea level, instrumenting a volume of ∼0.01 km³.

Neutrinos interacting with matter produce charged particles that generate Cerenkov light in the detectors. From the collected Cerenkov light, the energy and direction of the incoming neutrinos are reconstructed. A muon neutrino¹⁰¹ undergoing a charged current interaction produces a muon that can travel large distances through the medium, leading to a track event topology in the detector. Most other interactions produce a nearly spherical shower event topology. In this analysis, ANTARES events of both topologies are used, while only track events are taken from IceCube data.

The ANTARES event sample used in this Letter includes the one used in  Albert et al. (2017) extended by the data collected in 2016. These data use the most recent offline-reconstructed data set, incorporating dedicated calibrations of positioning, timing, and efficiency (Adrián-Martínez et al. 2012). The sample is taken from a total of 2780 days of detector livetime, over a total of 10 calendar years. Part of the sample was collected with partially completed detector configurations. Here, 218 shower(-like) events are selected, while 2.6 signal events are expected from the KRA${}_{\gamma }^{5}$ model. For these signal events we have a median angular resolution of $2\buildrel{\circ}\over{.} 4$. The track selection includes 7,850 events, with 10.2 signal events expected to have an angular resolution of $0\buildrel{\circ}\over{.} 5$. The energy ranges including 90% of signal events are [2.1 TeV, 150 TeV] for showers and [360 GeV, 130 TeV] for tracks.

The IceCube seven-year track selection used in this analysis is detailed by Aartsen et al. (2017c). It results in a total of 730,130 events with 191 events expected from the KRA${}_{\gamma }^{5}$ model. The data set was collected over a total of 2431 days of detector livetime, some of which took place during the construction phase of the detector. The IceCube signal events are expected to have median angular resolution of $0.8^\circ$. The energy range containing 90% of the expected signal events is [390 GeV, 110 TeV].

The energy range in which the combined analysis is valid is [90 GeV, 300 TeV]. This range is defined as containing 90% of the sensitivity. It is calculated by finding the low- and high-energy thresholds where removing simulated signal events outside of these values worsens the sensitivity by 5% each.

The present analysis uses an unbinned likelihood ratio test. The likelihood functions for each sample—ANTARES tracks, ANTARES showers, and IceCube tracks—are defined as

$$\begin{eqnarray}\begin{array}{rcl}{{ \mathcal L }}_{\mathrm{sig}+\mathrm{bkg}}({n}_{\mathrm{sig}}) & = & \displaystyle \prod _{i}\left[\displaystyle \frac{{n}_{\mathrm{sig}}}{N}\cdot { \mathcal S }({E}_{i},{\alpha }_{i},{\delta }_{i})\right.\\ & & \left.+\left(1-\displaystyle \frac{{n}_{\mathrm{sig}}}{N}\right)\cdot { \mathcal B }({E}_{i},{\delta }_{i})\right],\end{array}\end{eqnarray} \tag{ 1 }$$

where N is the total number of events, ${n}_{\mathrm{sig}}$ is the number of signal events, and ${ \mathcal S }$ is the signal probability density function (PDF) for an event i at the equatorial coordinates $({\alpha }_{i},{\delta }_{i})$ with energy E_i. It is obtained from Monte Carlo simulations of the detectors with the model flux as input, and is proportional to the expected signal rate at a given reconstructed energy and direction. ${ \mathcal B }$ is the PDF of the background.

Minor differences in the original, separate ANTARES and IceCube PDF constructions are preserved in this Letter. For IceCube tracks, the background term ${ \mathcal B }$ comes from the data with a correction for the signal contamination expected for ${n}_{\mathrm{sig}}$ signal events (Aartsen et al. 2017a). For the ANTARES samples, this is approximated by ignoring the signal correction term (Albert et al. 2017). In addition, the IceCube signal PDF accounts for the estimated point-spread function of each event, while average point-spread functions are used for track and shower ANTARES events.

In order to account for the different acceptances of each sample as well as any bias in the fitted signal normalization, we forward-fold the signal flux ${{\rm{\Phi }}}_{\mathrm{sig}}$ into the individual likelihoods using a response function obtained from simulated pseudo-experiments.

Then the combined likelihood is simply the product over the per-sample likelihoods. The combined test statistic is the log-likelihood ratio evaluated for that ${{\rm{\Phi }}}_{\mathrm{sig}}$, which maximizes the combined likelihood

$$\begin{eqnarray}&&{\mathrm{TS}}_{\mathrm{comb}}=\mathop{\max }\limits_{{{\rm{\Phi }}}_{\mathrm{sig}}}\left\{\displaystyle \sum _{\mathrm{sample}}\mathrm{ln}\left[\displaystyle \frac{{{ \mathcal L }}_{\mathrm{sig}+\mathrm{bkg}}({{\rm{\Phi }}}_{\mathrm{sig}})}{{{ \mathcal L }}_{\mathrm{bkg}}}\right]\right\},\end{eqnarray} \tag{ 2 }$$

where TS${}_{\mathrm{comb}}$ is the combined test statistic, and ${{ \mathcal L }}_{\mathrm{bkg}}={{ \mathcal L }}_{\mathrm{sig}+\mathrm{bkg}}({{\rm{\Phi }}}_{\mathrm{sig}}=0)$ is the likelihood to have only background and the sum runs over the event samples. This is illustrated in Figure 2 with the combined log-likelihood ratio and ${\mathrm{TS}}_{\mathrm{comb}}$ fit for the KRA${}_{\gamma }^{5}$ model.

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The combined and independent sensitivities are summarized in Table 1. They are defined as the median upper limit.¹⁰² The combination is not only a way to exploit more data with different systematics, but also an opportunity to benefit from the complementarity of the two detectors. While IceCube has much higher statistics than ANTARES, we show in Figure 3(a) that ANTARES offers enhanced sensitivity in the southern sky where a larger flux is expected. This favorable view is coupled with relatively better angular resolution for ANTARES than IceCube. In Figure 3(b) we show that while IceCube can in principle detect higher energy events compared to ANTARES, the direction-dependent model spectra studied here result in similar energy ranges being tested by both detectors. Overall, the relative contribution of IceCube to the sensitivity is 61%; for ANTARES tracks and showers the relative contributions are 25% and 14%, respectively.

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Table 1.  Sensitivities and Results of the Analysis on the KRA${}_{\gamma }$ Models with the 5 and 50 PeV Cutoffs

Energy Cutoff	Sensitivity $[{{\rm{\Phi }}}_{{\mathrm{KRA}}_{\gamma }}]$			Fitted Flux	${\text{}}p$-value	Upper Limit (UL) at 90% CL
	Combined	ANTARES	IceCube	$[{{\rm{\Phi }}}_{{\mathrm{KRA}}_{\gamma }}]$	[%]	$[{{\rm{\Phi }}}_{{\mathrm{KRA}}_{\gamma }}]$
5 PeV	0.81	1.21	1.14	0.47	29	1.19
50 PeV	0.57	0.94	0.82	0.37	26	0.90

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This analysis combines seven years of IceCube tracks and ten years of ANTARES tracks and showers using a likelihood ratio test. The results are summarized in Table 1. Systematic uncertainties on the ANTARES detection efficiency (due to the uncertainty on the acceptance of the ANTARES PMTs) are included in the analysis as in the paper by Albert et al. (2017). As described by Aartsen et al. (2017c), systematic uncertainties in the modeling of the Antarctic ice and the optical module efficiency lead to an uncertainty on the IceCube detection efficiency of at most 11%, which is not included here.

The maximum-likelihood estimate yields a non-zero diffuse Galactic neutrino flux for both models with a p-value of 29% for KRA${}_{\gamma }^{5}$ and 26% for KRA${}_{\gamma }^{50}$. As neither of these results is statistically significant, we place upper limits on both model normalizations. The KRA${}_{\gamma }^{50}$ model is constrained at the 90% CL (with an upper limit of $0.9\times {{\rm{\Phi }}}_{{\mathrm{KRA}}_{\gamma }^{50}}$), while the KRA${}_{\gamma }^{5}$ model is not yet constrained by our analysis. This was expected as the 50 PeV cutoff represents an extreme tuning of the acceleration parameters for the Galactic CRs, while the 5 PeV cutoff in light CR can be considered a more reliable case for the Galactic accelerators.

Figure 4 represents the combined upper limits in comparison to the all-flavor full-sky energy spectrum of the KRA${}_{\gamma }$ models as well as the previous IceCube and ANTARES upper limits. The present upper limit on the 5 PeV model is higher than the previously published upper limit for ANTARES alone, although the sensitivity is much better. This is due to the overfluctuation observed in the IceCube data sample as well as the difference in the definition of the test statistic. In the ANTARES stand-alone analysis it was the sum of the shower and track test statistics, computed independently, instead of computing one test statistic from the combined log-likelihood ratio curve (Equation (2)).

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The results presented here provide for the first time a combined constraint on diffuse Galactic neutrino emission by IceCube and ANTARES. The limit on the KRA${}_{\gamma }$ model with 50 PeV cutoff extends the energy range of the constraint on the model from 10 GeV with Fermi-LAT up to hundreds of TeV. Based on the limit on the KRA${}_{\gamma }^{5}$-model, this analysis limits the total flux contribution of diffuse Galactic neutrino emission to the total astrophysical signal reported by Aartsen et al. (2015) to 8.5%. In the future, the sensitivity of this analysis can be further improved by including IceCube showers (Aartsen et al. 2017d). This will allow for a powerful test of the KRA${}_{\gamma }^{5}$ model, thereby constraining the diffusion mechanisms, the maximal energy injected by supernova remnants and the Galactic gas distributions considered in the model.

ANTARES acknowledges the financial support of the funding agencies: Centre National de la Recherche Scientifique (CNRS), Commissariat à l'énergie atomique et aux énergies alternatives (CEA), Commission Européenne (FEDER fund and Marie Curie Program), Institut Universitaire de France (IUF), IdEx program and UnivEarthS Labex program at Sorbonne Paris Cité (ANR-10-LABX-0023 and ANR-11-IDEX-0005-02), Labex OCEVU (ANR-11-LABX-0060) and the A*MIDEX project (ANR-11-IDEX-0001-02), Région Île-de-France (DIM-ACAV), Région Alsace (contrat CPER), Région Provence-Alpes-Côte d'Azur, Département du Var and Ville de La Seyne-sur-Mer, France; Bundesministerium für Bildung und Forschung (BMBF), Germany; Istituto Nazionale di Fisica Nucleare (INFN), Italy; Nederlandse organisatie voor Wetenschappelijk Onderzoek (NWO), the Netherlands; Council of the President of the Russian Federation for young scientists and leading scientific schools supporting grants, Russia; National Authority for Scientific Research (ANCS), Romania; Ministerio de Economía y Competitividad (MINECO): Plan Estatal de Investigación (refs. FPA2015-65150-C3-1-P, -2-P, and -3-P, (MINECO/FEDER)), Severo Ochoa Centre of Excellence and MultiDark Consolider (MINECO), and Prometeo and Grisolía programs (Generalitat Valenciana), Spain; Ministry of Higher Education, Scientific Research and Professional Training, Morocco. We also acknowledge the technical support of Ifremer, AIM, and Foselev Marine for the sea operation and the CC-IN2P3 for the computing facilities.

The IceCube Neutrino Observatory acknowledges support from the following agencies: 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 Wisconsin-Madison, Open Science Grid (OSG), Extreme Science and Engineering Discovery Environment (XSEDE), U.S. Department of Energy-National 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), 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 Québec, 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).

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. It was reviewed by the entire collaboration before publication, and all authors approved the final version of the manuscript.

The main authors of this manuscript were Jon Dumm, Timothée Grégoire, Christian Haack, and Michael Richman.