# Neutrino astronomy

Post-publication activity

Curator: Markus Ahlers

For centuries, optical telescopes proved an accessible means for exploring the skies with visible light. In the 19th century, as scientists discovered more forms of light invisible to the naked eye, technology advanced to produce more and more sophisticated instruments, like the Hubble Space Telescope, for space exploration. With the recent discovery of an astrophysical flux of neutrinos by the IceCube Neutrino Observatory, the advent of neutrino astronomy has arrived, bringing forth the possibility of viewing the cosmos through the lens of the neutrino.

## High-energy neutrino astronomy

Soon after the 1956 observation of the neutrino, the idea emerged that it represented the ideal astronomical messenger. Neutrinos travel from the edge of the Universe without absorption and with no deflection by magnetic fields. Having essentially no mass and no electric charge, the neutrino is similar to the photon as an astronomical messenger, except for one important attribute: its interactions with matter are extremely feeble. So, high-energy neutrinos may reach us unscathed from cosmic distances: from the close neighborhood of black holes and from the nuclear furnaces where cosmic rays (CRs) are born. But, their weak interactions also make cosmic neutrinos very difficult to detect. It was already realized in the early 1970s that immense particle detectors are required to collect cosmic neutrinos in statistically significant numbers.

Given the detector’s required size, early efforts concentrated on transforming large volumes of natural water into Cherenkov detectors that collect the light produced when neutrinos interact with nuclei in or near the detector. After a two-decade-long effort, building the Deep Underwater Muon and Neutrino Detector (DUMAND) in the sea off the main island of Hawaii unfortunately failed. However, DUMAND paved the way for later efforts by pioneering many of the detector technologies in use today, and by inspiring the deployment of a smaller instrument in Lake Baikal (Russia) as well as efforts to commission neutrino telescopes in the Mediterranean. These efforts in turn have led towards the ongoing construction of KM3NeT off the coast of Italy and GVD in Lake Baikal.

But the first telescope on the scale envisaged by the DUMAND collaboration was realized instead by transforming a large volume of transparent natural Antarctic ice into a particle detector, the Antarctic Muon and Neutrino Detector Array (AMANDA). In full operation since 2000, it represented a proof of concept for the kilometer-scale neutrino observatory, IceCube. A population of cosmic neutrinos covering the 30 TeV–1 PeV energy region were revealed by the first two years of IceCube data. The large extragalactic flux observed implies that the energy density of neutrinos matches the one observed in photons indicating a much larger role of proton accelerators in the high-energy universe. The future of neutrino astronomy looks bright.

The origin of the diffuse high-energy neutrino emission observed with IceCube is so far unknown. Astrophysical neutrinos are one of the by-products of cosmic ray accelerators. Accounting for the enormous luminosity and energy of the extragalactic cosmic rays observed has been challenging to the point that few compelling ideas have emerged. The speculations are very much centered on powering the accelerator by tapping the gravitational energy of supermassive black holes in active galactic nuclei (AGN) and, alternatively, of the collapse of a massive star into a black hole in a gamma ray burst (GRB). Searches for point sources associated with these, or any other point sources, in the sky have come up empty so far (Aartsen, 2017b; Adrian-Martinez, 2015b; Aartsen, 2017a; Adrian-Martinez, 2013). This is also the case for the search of a Galactic component in the diffuse neutrino flux observed so far (Adrian-Martinez, 2016a; Aartsen, 2017b). Maybe the multimessenger observations of a flaring active galaxy, actually a blazar, in spatial and time coincidence with a 290 TeV cosmic neutrino detected by IceCube on September 22, 2017, represents a breakthrough in the search for the sources of cosmic neutrinos (Aartsen, 2017c).

## Detection principle of high-energy neutrinos

Figure 1: An example of Feynman diagrams representing the charged current (left) and neutral current (right) interactions of neutrinos with up-type and down-type quarks in a nucleus. At high energies, the struck quark and the other spectator quarks in the nucleus (not shown) produces a particle shower.

Cosmic rays have been observed for more than a century. They reach energies in excess of $10^8$ TeV ($10^{11}$ GeV). Approaching these energies, the universe becomes opaque to electromagnetic radiation. We don't yet know where or how particles are accelerated to these extreme energies, and neutrino astronomy is a key to directly solving this puzzle. The rationale is simple; cosmic rays interact with gas and radiation in so-called $pp$ and $p\gamma$ interactions at various stages: during their acceleration in their sources, after their release into the surrounding environment, and while propagating over cosmic distances in radiation backgrounds. For instance, the interactions of cosmic ray protons ($p$) with background photons ($\gamma_{\rm bg}$) produce neutral and charged pion secondaries by processes like $p\gamma_{\rm bg}\to p\pi^0$ and $p\gamma_{\rm bg}\to n\pi^+$. While neutral pions decay as $\pi^0\to2\gamma$ and create a flux of high-energy gamma rays, the charged pion decays into three high-energy neutrinos ($\nu$) and anti-neutrinos ($\bar\nu$) via the decay chain $\pi^+\to\mu^+\nu_\mu$ followed by $\mu^+\to e^+\bar \nu_\mu \nu_e$ and the charged-conjugate processes. We refer to the secondaries as pionic photons and neutrinos.

Although neutrinos have mass, it is negligible relative to the TeV to EeV energies targeted by neutrino telescopes. They do however give rise to neutrino oscillations. For an initial neutrino flavor ratio of $\nu_e:\nu_\mu:\nu_\tau \simeq 1:2:0$ from the decay of pions and muons, the oscillation-averaged composition arriving at the detector is approximately an equal mix of electron, muon, and tau neutrino flavors because of the astronomical baseline, $\nu_e:\nu_\mu:\nu_\tau \simeq 1:1:1$

Figure 2: Conceptual design of a large neutrino detector. A neutrino, selected by the fact that it traveled through the Earth, interacts with a nucleus in a transparent medium like water or ice and produces a muon that is detected by the wake of Cherenkov photons it leaves inside the detector. A high-energy neutrino has a reduced mean free path ($\lambda_\nu$), and the secondary muon an increased range ($\lambda_{\mu}$), so the probability for observing a muon, $\lambda_\mu/\lambda_\nu$, increases with energy; it is about $10^{-6}$ for a 1 TeV neutrino.

Unfortunately, their weak interactions make neutrinos very difficult to detect. High-energy neutrinos interact with matter via deep inelastic scattering off nucleons. In this process, a neutrino scatters off quarks in the target nucleus via the exchange of a $Z$ or $W$ boson, referred to as neutral current (NC) and charged current (CC) interactions, respectively, as shown in Figure 1. Whereas the former interaction leaves the neutrino state intact, the latter creates a charged lepton associated with the initial neutrino flavor. The inelastic CC cross section is at the level of $10^{-33}~{\rm cm}^{2}$ at a neutrino energy of $10^3$ TeV and grows with energy as $\sigma_{\rm tot}\propto E_\nu^{0.36}$. The relative energy fraction transferred from the neutrino to the lepton is at the level of 80% at these energies. The struck nucleus does not remain intact and its high-energy fragments typically initiate hadronic showers in the target medium.

Figure 3: The principal idea of neutrino telescopes from the point of view of IceCube located at the South Pole. The background of high-energy muons (solid blue arrows) produced in the atmosphere can be reduced by placing the detector underground. The surviving fraction of muons is further reduced by looking for upgoing muon tracks that originate from muon neutrinos (dashed blue arrows) interacting close to the detector. This still leaves the contribution of muons generated by atmospheric muon neutrino interactions, which can be further reduced by energy cuts.

Immense particle detectors are required to collect cosmic neutrinos in statistically significant numbers. Already by the 1970s, it had been understood that a kilometer-scale detector was needed to observe the cosmogenic neutrinos produced in the interactions of CRs with background microwave photons. There exist a variety of methods to detect the high-energy secondary particles created in CC and NC interactions. One particularly effective method observes the radiation of optical Cherenkov light produced in CC interactions of muon neutrinos, yielding long-lived muon tracks, so-called “track” events. This requires the use of transparent detector media like water or ice. A sketch of the signal is shown in Figure 2. Photomultipliers placed in the medium transform the Cherenkov light of muons generated in neutrino interactions into electrical signals using the photoelectric effect. This information allows scientists to reconstruct the various Cherenkov light patterns produced in neutrino events and infer their arrival directions, their energies and—in most cases only on a statistical basis—their flavor. Because of the large background of muons produced by CR interactions in the atmosphere, the signal is limited to upgoing muon tracks that are produced in interactions inside or close to the detector by neutrinos that have passed through the Earth (see Figure 3). Even in a cubic kilometer detector, the production of atmospheric neutrinos is suppressed once their energy exceeds hundreds of TeV. Thus, energy alone allows separating atmospheric and high-energy cosmic neutrinos.

The hadronic particle showers that develop after the neutrino strikes a nucleus in the ice or water are also visible by optical Cherenkov emission. Due to the high multiplicity of secondary particles and the repeated scattering in the medium, the signal will develop as a mostly spherical emission pattern, called “cascade.” Also, the direct electron or tau produced in CC interactions of electron or tau neutrinos, respectively, will add to this cascade emission. The direction of the initial neutrino can only be reconstructed from the Cherenkov emission of secondary particles close to the neutrino interaction point, and the angular resolution is much worse than for track events. On the other hand, cascade events allow for a better energy resolution since the Cherenkov light is proportional to the energy transferred to the cascade, which is fully contained in the instrumented volume.

## Status of cosmic neutrino observations

Figure 4: Architecture of the IceCube observatory (left) and the schematics of a digital optical module (right).

Following the pioneering work of DUMAND, several neutrino telescope projects were initiated in the Mediterranean in the 1990s. In 2008, the construction of the ANTARES detector (Ageron, 2011) off the coast of France was completed. With an instrumented volume at about one percent of a cubic kilometer, ANTARES reaches roughly the same sensitivity as AMANDA and is currently the most sensitive observatory for high-energy neutrinos in the Northern Hemisphere. It has demonstrated the feasibility of neutrino detection in the deep sea and has provided a wealth of technical experience and design solutions for deep-sea components.

However, the recent breakthrough of neutrino astronomy by the first observation of high-energy astrophysical neutrinos was achieved by the IceCube observatory. The IceCube detector transforms deep natural Antarctic ice 1,450 m below the geographic South Pole into a Cherenkov detector. The instrument consists of 5,160 digital optical modules that instrument a cubic kilometer of ice; see Figure 4. Each digital optical module consists of a glass sphere that contains a 10-inch photomultiplier and the electronics board that digitizes the signals locally using an onboard computer. The digitized signals are given a global time stamp with an accuracy of two nanoseconds and are subsequently transmitted to the surface. Processors at the surface continuously collect the time-stamped signals from the optical modules, each of which functions independently. These signals are sorted into telltale patterns of light that reveal the direction, energy, and flavor of the incident neutrino.

Figure 5: (Left) Light pool produced in IceCube by a shower initiated by an electron or tau neutrino. The measured energy is $1.14$ PeV, which represents a lower limit on the energy of the neutrino that initiated the shower. White dots represent sensors with no signal. For the colored dots, the color indicates arrival time, from red (early) to purple (late) following the rainbow, and size reflects the number of photons detected. (Right) An upgoing muon track traverses the detector at an angle of $11^\circ$ below the horizon. The deposited energy inside the detector is 2.6 PeV.

Even at a depth of 1,450 m, IceCube detects a background of atmospheric cosmic-ray muons originating in the Southern Hemisphere at a rate of 3,000 per second (Figure 3). Two methods are used to identify neutrinos. Traditionally, neutrino searches have focused on the observation of muon neutrinos that interact primarily outside the detector to produce kilometer-long muon tracks passing through the instrumented volume. Although this allows the identification of neutrinos that interact outside the detector, it is necessary to use the Earth as a filter in order to remove the huge background of cosmic-ray muons. This limits the neutrino view to a single flavor and half the sky because of the presence of an energetic muon secondary in the debris of the neutrino interaction. An alternative method exclusively identifies high-energy neutrinos interacting inside the detector, so-called high-energy starting events (HESE). It divides the instrumented volume of ice into an outer veto shield and a $\sim420$-megaton inner fiducial volume. The advantage of focusing on neutrinos interacting inside the instrumented volume of ice is that the detector functions as a total absorption calorimeter, measuring the neutrino energy of cascades with a 10–15% resolution. Furthermore, with this method, neutrinos from all directions in the sky can be identified, including both muon tracks as well as secondary showers, produced by charged-current interactions of electron and tau neutrinos, and neutral current interactions of neutrinos of all flavors. The Cherenkov patterns initiated by an electron (or tau) neutrino of 1 PeV energy and a secondary muon depositing 2.6 PeV energy while traversing the detector are contrasted in Figure 5.

In general, the arrival times of photons at the optical sensors determine the particle’s trajectory, while the number of photons is a proxy for the deposited energy. The two methods, upgoing muon tracks and HESE, of separating neutrinos from the cosmic-ray muon background have complementary advantages. The long tracks produced by muon neutrinos can be pointed back to their sources with a $\le 0.4^\circ$ angular resolution. In contrast, the reconstruction of the direction of cascades in the HESE analysis, in principle possible to a few degrees, is still in the development stage in IceCube. They can be pointed to within $10^\circ\sim15^\circ$ of the direction of the incident neutrino. Determining the deposited energy from the observed light pool is, however, relatively straightforward, and a resolution of better than 15% is possible; the same value holds for the reconstruction of the energy deposited by a muon track inside the detector.

Figure 6: Spectrum of secondary muons initiated by muon neutrinos that have traversed the Earth, i.e., with zenith angle less than $5^\circ$ above the horizon, as a function of the energy they deposit inside the detector. For each reconstructed muon energy, the median neutrino energy is calculated assuming the best-fit spectrum. The colored bands (blue/red) show the expectation for the conventional and astrophysical contributions. The black crosses show the measured data. Additionally, the neutrino energy probability density function for the highest energy event assuming the best-fit spectrum is shown (dashed line).

For high-energy neutrino astronomy, the first challenge is to select a pure sample of neutrinos, roughly 100,000 per year above a threshold of 0.1 TeV for IceCube, in a background of ten billion atmospheric muons (Figure 3), while the second is to identify the small fraction of these neutrinos that is astrophysical in origin, roughly at the level of tens of events per year. Atmospheric neutrinos are an overwhelming background for cosmic neutrinos, at least at energies below $\sim100$ TeV. Above this energy, however, the atmospheric neutrino flux reduces to a few events per year, even in a kilometer-scale detector, and thus events in that energy range are cosmic in origin.

Using the Earth as a filter, a flux of neutrinos has been identified that is predominantly of atmospheric origin. IceCube has measured this flux over three orders of magnitude in energy with a result that is consistent with theoretical calculations. However, with seven years of data, an excess of events is observed at energies beyond 100 TeV (Aartsen, 2016b), which cannot be accommodated by the atmospheric flux; see Figure 6. Allowing for large uncertainties on the extrapolation of the atmospheric component to higher energy, the statistical significance of the excess astrophysical flux is $6\sigma$. While IceCube measures only the energy deposited by the secondary muon inside the detector, from Standard Model physics we can infer the energy spectrum of the parent neutrinos represented in the figure. For the highest energy event, already shown in on the right, the most likely energy of the parent neutrino is about 7 PeV. Independent of any calculation, the energy lost by the muon inside the instrumented detector volume is $2.6\pm0.3$ PeV. The cosmic neutrino flux is well described by a power law with a spectral index $\gamma=2.13\pm0.13$ and a normalization at 100 TeV neutrino energy of $(0.90^{+0.30} {-0.27})\,\times10^{-18}\,\rm GeV^{-1}\rm cm^{-2} \rm sr^{-1}$ (Aartsen, 2016b). The error range is estimated from a profile likelihood using Wilks’ theorem and includes both statistical and systematic uncertainties. The neutrino energy contributing to this flux covers the range of 200 TeV to 9 PeV.

Figure 7: Deposited energies, by neutrinos interacting inside IceCube, observed in four years of data. (Aartsen, 2014b). The hashed region shows uncertainties on the sum of all backgrounds. The atmospheric muon flux (red) and its uncertainty is computed from simulation to overcome statistical limitations in our background measurement and scaled to match the total measured background rate. The atmospheric neutrino flux is derived from previous measurements of both the $\pi, K$, and charm components of the atmospheric spectrum (Aartsen, 2014a). Also shown are two illustrative power-law fits to the spectrum.

However, it was the alternative HESE method, which selects isolated neutrinos interacting inside the detector, that revealed the first evidence for cosmic neutrinos (Aartsen, 2013a; Aartsen, 2013b) with only two years of collected data. A clear separation between neutrinos of atmospheric origin and those of cosmic origin was possible because the neutrinos were not accompanied by other particles from above that may have been generated in the same air shower and they had excellent energy measurement due to their containment in the instrumented volume. A sample event with a light pool of roughly one hundred thousand photoelectrons extending over more than 500 meters is shown in Figure 5. The geometry of the veto and active signal regions has been optimized to reduce the background of atmospheric muons and neutrinos to a handful of events per year while a large fraction of the cosmic signal.

With PeV energy and no trace of accompanying muons from an atmospheric shower, these events are highly unlikely to be of atmospheric origin. It is indeed important to realize that the muon produced in the same pion or kaon decay as an atmospheric neutrino, will reach the detector provided that the muon energy is sufficiently high and the zenith angle sufficiently small. PeV atmospheric neutrinos come with their own self-veto. This self-veto limits the contribution of atmospheric neutrinos in the HESE selection.

Figure 8: Mollweide projection in Galactic coordinates of the arrival direction of neutrino events. We show the results of the six-year upgoing track analysis (Aartsen, 2016b) muon energy proxy $E_\mu>200$~TeV ($\odot$). The red numbers show the most probable neutrino energy (in TeV) assuming the best-fit astrophysical flux of the analysis (Aartsen, 2016b). The events of the four-year high-energy starting event (HESE) analysis with deposited energy (green numbers) larger than 100 TeV (tracks $\otimes$ and cascades $\oplus$) are also shown (Aartsen, 2014b). Cascade events ($\oplus$) are indicated together with their median angular uncertainty (thin circles). One event (*) appears in both event samples. The grey-shaded region indicates the zenith angle range where Earth absorption of 100 TeV neutrinos is larger than 90%. The star symbol ($\bigstar$) indicates the Galactic Center and the thin curved solid black line indicates the horizon.
Figure 9: Summary of neutrino observations and upper limits (per flavor). The black and grey data shows IceCube’s measurement of the atmospheric $\nu_e+\bar\nu_e$ (Aarsten, 2016b) and $\nu_\mu +\bar\nu_\mu$ spectra. The green data show the inferred bin-wise spectrum of the four-year high-energy starting event (HESE) analysis. The green line and green-shaded area indicate the best-fit and $1\sigma$ uncertainty range of a power-law fit to the HESE data. Note that the HESE analysis vetoes atmospheric neutrinos, and the true background level is much lower as indicated in the plot (cf. Figure 7). In red we show the corresponding fit to the six-year $\nu_\mu+\bar\nu_\mu$ analysis. The dashed lines show 90% C.L. upper limits of an $E^{-2}$ neutrino emission flux (dashed) at higher energies from IceCube (Aartsen, 2016c) (brown), ANITA (Gorham, 2010) (orange), and Auger (Aab, 2015) (blue).

The energy dependence of the high-energy neutrinos collected in four years of data (Aartsen, 2014b) is compared to that of atmospheric backgrounds in Figure 7. It is, above an energy of $200$ TeV, consistent with the flux of muon neutrinos penetrating the Earth shown in Figure 6. A purely atmospheric explanation of the observation is excluded at $7\sigma$.

In summary, IceCube has observed cosmic neutrinos using both methods for rejecting background; each analysis has reached a statistical significance of more than $6\sigma$. Based on different methods for reconstruction and energy measurement, their results agree, pointing at extragalactic sources whose flux has equilibrated in the three flavors after propagation over cosmic distances with $\nu_e:\nu_\mu:\nu_\tau \sim 1:1:1$.

The four-year data set, under the HESE analysis, contains a total of 54 neutrino events with deposited energies ranging from 30 to 2000 TeV. The data in both Figure 6 and Figure 7 is consistent with an astrophysical component with a spectrum close to $E^{-2}$ above an energy of $\sim 200$ TeV. An extrapolation of this high-energy flux to lower energy suggests an excess of events in the $30-100$ TeV energy range over and above a single power-law fit. This conclusion is supported by a subsequent analysis that has lowered the threshold of the starting-event analysis (Aartsen, 2016a). The astrophysical flux measured by IceCube is not featureless; either the spectrum of cosmic accelerators cannot be described by a single power law or a second component of cosmic neutrino sources emerges in the spectrum. Due to the self-veto of atmospheric neutrinos, it is very difficult to accommodate this component as a feature in the atmospheric background.

In Figure 8 we show the arrival directions of the most energetic events of the six-year upgoing $\nu_\mu+\bar\nu_\mu$ analysis ($\odot$) and the four-year HESE analysis, separated into tracks ($\otimes$) and cascades ($\oplus$). The median angular resolution of the cascade events is indicated by thin circles around the bestfit position. The most energetic muons with energy $E_\mu>200$ TeV in the upgoing $\nu_\mu+\bar\nu_\mu$ analysis accumulate just below the horizon in the Northern Hemisphere due to the absorption of neutrinos via interactions in the Earth before reaching the vicinity of the detector. This effect causes the apparent anisotropy of the events in the Northern Hemisphere. Although HESE events with deposited energy of $E_{\rm dep}>100$ TeV also suffer from Earth absorption, they are detected when originating in the Southern Hemisphere. Various analyses of the IceCube event distribution could not reveal a strong anisotropy from extended emission regions, which could indicate, e.g., a contribution from Galactic sources along the Galactic plane. In fact, no correlation of the arrival directions of the highest energy events, shown in Figure 8, with potential sources or source classes has reached the level of $3\sigma$ (Aartsen, 2016a).

Various scenarios have been invoked to explain the observed diffuse emission, see, e.g., the review. The absence of strong anisotropies in the arrival direction of the data disfavors scenarios with strong Galactic emission. However, the limited event number and the low angular resolution of cascade-dominated samples can hide this type of emission. On the other hand, an isotropic arrival direction of neutrinos is expected for extragalactic source populations.

An overview of the current information on the flux of cosmic neutrinos is shown in Figure 9. A challenge of most of these Galactic and extragalactic scenarios is the high intensity of the neutrino data at $10-100$ TeV, which implies an equally high intensity of gamma rays produced via neutral pion production and decay. For extragalactic scenarios, this emission is not directly visible due to the strong absorption in the extragalactic radiation background. However, this emission induces electromagnetic cascades that contribute strongly to, and far exceed, the extragalactic gamma-ray background observed by the Fermi satellite in the GeV-TeV range. We will discuss this in more detail next.

## Multimessenger relations of astrophysical neutrinos

Having established, with the observation of neutrinos, a prominent role for hadronic accelerators in the nonthermal universe, we investigate how the accelerated CRs may produce photons and neutrinos after the relatively brief acceleration process. The absolute flux of gamma rays and neutrinos depends on the pion production efficiency $f_\pi$ in CR interactions with gas or dust ($pp$ scenarios) and with radiation ($p\gamma$ scenarios). This quantity can be evaluated from the target density, the inelasticity of the interaction, and the total time the CR spent in the interaction region. The maximum efficiency $f_\pi=1$ corresponds to a calorimetric environment, where the full bolometric energy of CRs is transferred to that of secondary pions via repeated CR interactions.

The relative flux of gamma rays and neutrinos depends on the average charged-to-neutral pion ratio $K_\pi$. Pion production of CRs via scattering off photons can proceed resonantly via $p + \gamma \rightarrow \Delta^+ \rightarrow \pi^0 + p$ or $p + \gamma \rightarrow \Delta^+ \rightarrow \pi^+ + n$. These channels produce charged and neutral pions with probabilities of 2/3 and 1/3, respectively. However, the contribution of non-resonant pion production at the resonance changes this ratio to approximately 1/2 and 1/2, i.e., $K_\pi\simeq 1$ in $p\gamma$ scenarios. In contrast, CRs interacting with hydrogen, e.g., in the Galactic disk, produce equal numbers of pions of all three charges in hadronic collisions: $p+p \rightarrow N_\pi\,[\,\pi^{0}+\pi^{+} +\pi^{-}]+X$, where $N_\pi$ is the pion multiplicity. The charged-to-neutral pion ratio is therefore $K_\pi\simeq 2$ in $pp$ scenarios.

In both cases, the average inelasticity per pion can be approximated as $\kappa_\pi \simeq 0.2$. Here we make the approximation that, on average, the four leptons in the decay of $\pi^\pm$ equally share the charged pion's energy. The energy of the leptons relative to the CR nucleon ($N$) is then $\langle E_{\nu} /E_{\pi^\pm}\rangle \simeq 1/4$ and therefore $\langle E_{\nu} /E_{N}\rangle \simeq 1/20$. For gamma rays, we have simply $\langle E_{\gamma} /E_{\pi^0} \rangle = 1/2$ and therefore $\langle E_{\gamma} /E_{N} \rangle \simeq 1/10$.

From this line of argument, one can derive two important multimessenger relations between neutrinos, gamma rays, and CRs. Let us first discuss the relative contributions of neutrinos and gamma rays from the decay of charged and neutral pions, respectively. The emission rate density $Q_\nu$ (averaged over flavors $\alpha$) can be related to that of gamma-rays $Q_\gamma$ as

$$\tag{1} \frac{1}{3}\sum_{\alpha}E^2_\nu Q_{\nu_\alpha}(E_\nu) \simeq \frac{K_\pi}{4}\left[E^2_\gamma Q_\gamma(E_\gamma)\right]_{E_\gamma = 2E_\nu}\,.$$

Here, the prefactor $1/4$ accounts for the energy ratio $E_\nu/E_\gamma\simeq 1/2$ and the two gamma rays produced in the neutral pion decay. The relation simply reflects the fact that a $\pi^0$ produces two $\gamma$ rays for every charged pion producing a $\nu_\mu + \bar\nu_\mu$ pair, which cannot be separated by current experiments.

It seems surprising that no gamma ray has ever been observed matching the 100 to 10,000 TeV energy range of IceCube neutrinos. However, this is just a consequence of the universe’s opacity to high-energy photons. Unlike neutrinos, gamma rays interact with photons of the cosmic microwave background before reaching Earth. The resulting electromagnetic shower subdivides the initial photon energy, resulting in multiple photons in the GeV-TeV energy range by the time the shower reaches Earth. Calculating the cascaded gamma-ray flux accompanying IceCube neutrinos is straightforward. It is intriguing that the resulting flux shown in Figure 10 matches the extragalactic high-energy gamma-ray flux observed by the Fermi satellite.

The matching energy densities of the extragalactic gamma-ray flux detected by Fermi and the high-energy neutrino flux measured by IceCube suggest that, rather than detecting some exotic sources, it is more likely that IceCube to a large extent observes the same phenomena astronomers do. The finding implies that a large fraction, possibly most, of the energy in the nonthermal universe originates in hadronic processes, indicating a larger role than previously thought. In the context of this discussion, the energy associated with the photons that accompany the neutrino excess below 100TeV is not seen in the Fermi data (Murase, 2013). This might indicate that these neutrinos originate in hidden sources or in sources with a very strong cosmological evolution resulting in a shift of the photons to sub-GeV energies.

Is it possible that the sources of the extragalactic CRs are themselves neutrino sources? By integrating the spectrum of ultra-high-energy (UHE) CRs, i.e., CRs above an energy of 1 EeV, one can derive that the emission rate density of nucleons is at the level of $\xi_z E^2_NQ_N(E_p) \simeq {(1-2)\times10^{44}\,{\rm erg}\,{\rm Mpc}^{-3}\,{\rm yr}^{-1}}$. Now, the measured energy density of UHE CRs limits the production of secondary neutrinos and provides another important multimessenger relation. Assuming $pp$ or $p\gamma$ interactions of these Crs with efficiency $f_\pi$ leads to the relation

$$\tag{2} \frac{1}{3}\sum_{\alpha}E_\nu^2\phi_{\nu_\alpha}(E_\nu) \simeq {f_\pi}{\frac{\xi_zK_\pi}{1+K_\pi}}(2-4)\times10^{-8}\,{\rm GeV}\,{\rm cm}^{-2}\,{\rm s}^{-1}\,{\rm sr}\,.$$

Figure 10: Two models of the astrophysical neutrino flux (black lines) observed by IceCube and the corresponding cascaded gamma-ray flux (blue lines) observed by Fermi. The models assume that the decay products of neutral and charged pions from $pp$ interactions are responsible for the nonthermal emission in the universe (Murase, 2013). The thin dashed lines represent an attempt to minimize the contribution of the pionic gamma-ray flux to the Fermi observations. It assumes an injected flux of $E^{-2}$ with exponential cutoff at low and high energy. The green data show the binned neutrino spectrum inferred from the four-year “high-energy starting event” (HESE) analysis (Aartsen, 2014b). The green solid line and shaded band indicate the corresponding power-law fit with uncertainty range. Also shown as a red solid line and shaded band is the best fit to the flux of high-energy muon neutrinos penetrating the Earth (Aartsen, 2016b).

The previous equation involves an integration over redshift which depends on the evolution of the sources. This integration is parametrized by the factor $\xi_z$ (Ahlers, 2014). For instance, $\xi_z \simeq2.4$ for evolution corresponding to star formation and $\xi_z \simeq0.6$ in the absence of red-shift evolution.

The requirement $f_\pi\leq1$ limits the neutrino production by the actual sources of the cosmic rays as pointed out by the seminal work by Waxman and Bahcall (Waxman, 1999). For optically thin sources, $f_\pi\ll1$, neutrino production is only a small by-product of the acceleration process. The energy loss associated with pion production must not limit the sources' ability to accelerate the cosmic rays. On the other hand, optically thick sources, $f_\pi\simeq 1$, may be efficient neutrino emitters. Realistic sources of this type need different zones, one zone for the acceleration process ($f_\pi\ll1$) and a second zone for the efficient conversion of cosmic rays to neutrinos ($f_\pi\simeq1$). An example for this scenario are sources embedded in starburst galaxies, where cosmic rays can be stored over sufficiently long timescales to yield significant neutrino production.

Interestingly, the upper limit on neutrino production of UHE CR sources, corresponding to $f_\pi=1$ in of Eq. ((2)), is at the level of the neutrino flux observed by IceCube, assuming $\xi_z \simeq2.4$ and $K_\pi\simeq 1-2$. Therefore, it is possible that the observed extragalactic CRs and neutrinos have the same origin. A plausible scenario is a calorimeter in which only CRs with energy below a few $10$ PeV interact efficiently. An energy dependence of the calorimetric environment can be introduced by energy–dependent diffusion. Plausible astrophysical environments are galaxy clusters or starburst galaxies.

The Universe itself also corresponds to a calorimetric environment for distant sources of UHE cosmic rays. Soon after the discovery of the cosmic microwave background (CMB), Greisen, Zatsepin and Kuzmin realized that extragalactic CRs are attenuated by interactions with background photons. Interactions with the CMB led to a significant attenuation of proton fluxes after propagation over distances on the order of 200 Mpc at an energy above $E_{\rm GZK}\simeq 50$ EeV, which is known as the GZK suppression. Also, heavier nuclei are attenuated at a similar energy by photodisintegration of the nucleus by CMB photons via the giant dipole resonance.

The pions produced in GZK interactions decay, resulting in a detectable flux of cosmogenic neutrinos first estimated by Berezinsky and Zatsepin in 1969. This guaranteed flux of neutrinos became one of the benchmarks for high-energy neutrino astronomy, leading early on to the concept of kilometer-scale detectors. The maximal cosmogenic neutrino flux level is again determined by the power density of UHE CRs above the GZK threshold and saturates at EeV neutrino energies. A particularly strong emission is expected for scenarios where the UHE CRs are dominated by protons. However, UHE CR models with a strong contribution of heavy nuclei typically have a much lower energy density above the GZK threshold, and the model uncertainties of the flux level cover more than two orders of magnitude.

## Future avenues

Accelerators of CRs produce neutrino fluxes limited in energy to roughly 5% of the maximal energy of the protons or nuclei. For Galactic neutrino sources, we expect neutrino spectra with a cutoff in the range of a few hundred TeV. Detection of these neutrinos requires optimized sensitivities in the TeV range. At these energies, the atmospheric muon background limits the field of view of neutrino telescopes to the downward hemisphere. With IceCube focusing on high energies, a second kilometer-scale neutrino telescope in the Northern Hemisphere would ideally be optimized to observe the Galactic center and the largest part of the Galactic plane.

This can be realized by the construction of a multi-cubic-kilometer neutrino telescope in the Mediterranean Sea, KM3NeT (Adrian-Martinez, 2016b). Major progress has been made in establishing the reliability and the cost-effectiveness of the design. This includes the development of a digital optical module that incorporates 31 3-inch photomultipliers instead of one large photomultiplier tube, as shown in Figure 11. The advantages are a tripling of the photocathode area per optical module, a segmentation of the photocathode allowing for a clean identification of coincident Cherenkov photons, some directional sensitivity, and a reduction of the overall number of penetrators and connectors, which are expensive and failure-prone. For all photomultiplier signals exceeding the noise level, time-over-threshold information is digitized and time-stamped by electronic modules housed inside the optical modules. This information is sent via optical fibers to shore, where the data stream will be filtered online for event candidates.

Figure 11: The KM3NeT optical module (Adrian-Martinez, 2016b). The optical module consists of a glass sphere with a diameter of 42 cm, housing 31 photosensors (yellowish disks). The glass sphere can withstand the pressure of the water and is transparent to the faint light that must be detected to see neutrinos.

KM3NeT in its second phase will consist of 115 strings (detection units) carrying more than 2,000 optical modules. The detection units are anchored to the seabed with deadweights and kept vertical by submerged buoys. The vertical distances between optical modules will be 36 meters, with horizontal distances between detection units at about 90 meters. Construction is now ongoing near Capo Passero (east of Sicily).

A parallel effort is underway in Lake Baikal with the deep underwater neutrino telescope Baikal-GVD (Gigaton Volume Detector) (Avrorin, 2015). The first GVD cluster, named DUBNA, was upgraded in spring 2016 to its final size (288 optical modules, 120 meters in diameter, 525 meters high, and instrumented volume of 6 Mton). Each of the eight strings consists of three sections with 12 optical modules. Deployment of a second cluster was completed in spring 2017.

IceCube has discovered a flux of extragalactic cosmic neutrinos with an energy density that matches that of extragalactic high-energy photons and UHE CRs. This may suggest that neutrinos and high-energy CRs share a common origin. They may originate in calorimetric environments like starburst galaxies or galaxy clusters hosting the cosmic-ray accelerators. Identification of the sources by observation of multiple neutrino events from these sources with IceCube will be challenging. However, the possibility exists for revealing the sources by the comprehensive IceCube multimessenger program.

Further progress requires larger instruments. We therefore propose as a next step capitalizing on the opportunity of instrumenting $10\rm\,km^3$ of glacial ice at the South Pole and thereby improving on IceCube’s sensitive volume by an order of magnitude. This large gain is made possible by the unique optical properties of the Antarctic glacier revealed by the construction of IceCube. As a consequence of the extremely long photon absorption lengths in the deep Antarctic ice, the spacing between strings of light sensors can be increased from 125 to over 250 meters without loss of performance of the instrument. The instrumented volume can therefore grow by one order of magnitude while keeping the construction budget of a next-generation instrument at the level of the cost of the current IceCube detector. The new facility will increase the event rates of cosmic events from hundreds to thousands over several years.