#[1]Scholarpedia (en) [2]Scholarpedia Atom feed

Neutrino astronomy

   From Scholarpedia
   Francis Halzen and Markus Ahlers (2018), Scholarpedia, 13(4):42649.
   [3]doi:10.4249/scholarpedia.42649 revision #197031 [[4]link to/cite this article]
   Jump to: [5]navigation, [6]search
   Post-publication activity
   (BUTTON)

   Curator: [7]Markus Ahlers
   Contributors:


   0.50 -

   [8]Francis Halzen
   0.25 -

   [9]Atri Bhattacharya
   0.25 -

   [10]Lydia Roos
   0.25 -

   [11]Michelle L. Jones

   [12]Fabrice Piquemal

   [13]Lu Lu

   [14]Christian Spiering
     * [15]Dr. Francis Halzen, University of Wisconsin-Madison, Madison, Wisconsin,
       USA
     * [16]Mr. Markus Ahlers, NBIA, Niels Bohr Institute, Copenhagen, Denmark

   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.

Contents

     * [17]1 High-energy neutrino astronomy
     * [18]2 Detection principle of high-energy neutrinos
     * [19]3 Status of cosmic neutrino observations
     * [20]4 Multimessenger relations of astrophysical neutrinos
     * [21]5 Future avenues
     * [22]6 References
     * [23]7 Further reading
     * [24]8 External links

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
   [25]black holes and from the nuclear furnaces where [26]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 [27]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 [28]burst (GRB). Searches for
   point sources associated with these, or any other point sources, in the sky have
   come up empty so far ([29]Aartsen, 2017b; [30]Adrian-Martinez, 2015b;
   [31]Aartsen, 2017a; [32]Adrian-Martinez, 2013). This is also the case for the
   search of a Galactic component in the diffuse neutrino flux observed so far
   ([33]Adrian-Martinez, 2016a; [34]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
   ([35]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.

   [36]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; [37]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
   [38]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 [39]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 [40]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 [41]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 ([42]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
   [43]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 [44]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
   [45]5.

   In general, the arrival times of photons at the optical sensors determine the
   particle's [46]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 [47]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 ([48]Aartsen, 2016b), which cannot be accommodated by
   the atmospheric flux; see Figure [49]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 $(0.90^{+0.30}
   {-0.27})\,\times10^{-18}\,\rm GeV^{-1}\rm cm^{-2} \rm sr^{-1}$ ([50]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. ([51]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 ([52]Aartsen,
   2014a). Also shown are two illustrative [53]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 ([54]Aartsen, 2013a; [55]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
   [56]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
   ([57]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 ([58]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 ([59]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
   $\nu_e+\bar\nu_e$ ([60]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 [61]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 ([62]Aartsen, 2016c) (brown), ANITA ([63]Gorham,
   2010) (orange), and Auger ([64]Aab, 2015) (blue).

   The energy dependence of the high-energy neutrinos collected in four years of
   data ([65]Aartsen, 2014b) is compared to that of atmospheric backgrounds in
   Figure [66]7. It is, above an energy of $200$ TeV, consistent with the flux of
   muon neutrinos penetrating the Earth shown in Figure [67]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 [68]6 and Figure [69]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 ([70]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 [71]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 [72]8, with potential sources or source classes has reached the level of
   $3\sigma$ ([73]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 [74]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
   [75]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

   \begin{equation}\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}\,. \end{equation}

   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 [76]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 ([77]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

   \begin{equation}\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}\,. \end{equation}
   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 ([78]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 ([79]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 ([80]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 $\xi_z$
   ([81]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 [82]cosmic rays as pointed out by the seminal work by Waxman and Bahcall
   ([83]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 [84]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 [85]cosmic rays to neutrinos ($f_\pi\simeq1$). An
   example for this scenario are sources embedded in starburst galaxies, where
   [86]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. (([87]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 [88]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 ([89]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 [90]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 ([91]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) ([92]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.

References

     * Aab, A et al. (2015). Phys. Rev. D91: 92008.
       [93]http://arxiv.org/abs/1504.05397 [astro-ph.HE].
     * Aartsen, M G et al. (2013a). Phys. Rev. Lett. 111: 21103.
       [94]http://arxiv.org/abs/1304.5356 [astroph.HE].
     * Aartsen, M G et al. (2013b). Science 342: 1242856.
       [95]http://arxiv.org/abs/1311.5238 [astro-ph.HE].
     * Aartsen, M G et al. (2014a). Phys. Rev. D89: 102001.
       [96]http://arxiv.org/abs/1312.0104 [astroph.HE].
     * Aartsen, M G et al. (2014b). Phys. Rev. Lett. 113: 101101.
       [97]http://arxiv.org/abs/1405.5303 [astroph.HE].
     * Aartsen, M G et al. (2016a). Astrophys. J. 824: L28.
       [98]http://arxiv.org/abs/1605.00163 [astro-ph.HE].
     * Aartsen, M G et al. (2016b). Astrophys. J. 833: 3.
       [99]http://arxiv.org/abs/1607.08006 [astro-ph.HE].
     * Aartsen, M G et al. (2016c). Phys. Rev. Lett. 117: 241101.
       [100]http://arxiv.org/abs/1607.05886 [astro-ph.HE].
     * Aartsen, M G et al. (2017a). Astrophys. J. 834: 112.
       [101]http://arxiv.org/abs/1702.06868 [astro-ph.HE].
     * Aartsen, M G et al. (2017b). Astrophys. J. 849: 67.
       [102]http://arxiv.org/abs/1707.03416 [astro-ph.HE].
     * Aartsen, M G et al. (2017c). GRB Coordinates Network, Circular Service 21916:
       .
     * Adrian-Martinez, S et al. (2015b). Astrophys. J. 823: 65.
       [103]http://arxiv.org/abs/1511.02149 [hep-ex].
     * Adrian-Martinez, S et al. (2016a). Phys. Lett. B760: 143.
       [104]http://arxiv.org/abs/1602.03036 [astro-ph.HE].
     * Adrian-Martinez, S et al. (2016b). J. Phys. G43: 84001.
       [105]http://arxiv.org/abs/1601.07459 [astro-ph.IM].
     * Ageron, M et al. (2011). Nucl. Instrum. Meth. A656: 11.
       [106]http://arxiv.org/abs/1104.1607 [astro-ph.IM].
     * Ahlers(2014). Phys. Rev. D90: 043005. [107]http://arxiv.org/abs/1406.2160
       [astro-ph.HE].
     * Avrorin, A. D. et al. (2015). Proceedings of the International Workshop on
       Prospects of Particle Physics: "Neutrino Physics and Astrophysics" (PPP
       2014): Valday, Russia, January 26-February 2, 2014 Phys. Part. Nucl. 46: 211.
     * Gorham, P W et al. (2010). Phys. Rev. D82: 022004 [Erratum: Phys. Rev.
       D85,049901 (2012)]. [108]http://arxiv.org/abs/1011.5004 [astro-ph.HE].
     * Murase, K; Ahlers, M and Lacki, B C (2013). Phys. Rev. D88: 121301.
       [109]http://arxiv.org/abs/1306.3417 [astro-ph.HE].
     * Waxman(1999). Phys. Rev. D59: 23002. [110]http://arxiv.org/abs/hep-ph/9807282
       [hep-ph].

Further reading

     * Aartsen, M G et al. (2014). JINST 9: P03009.
       [111]http://arxiv.org/abs/1311.4767 [astro-ph.IM].
     * Coniglione, R et al. (2017).  : . [112]http://arxiv.org/abs/1701.05849
       [astro-ph.IM].

External links

   IceCube [113][1]

   KM3NeT [114][2]

   Baikal [115][3]
   Sponsored by: [116]Dr. Lu Lu, International Centre for Hadron Astrophysics, Chiba
   University, Chiba, Japan
   [117]Reviewed by: [118]Dr. Christian Spiering, Deutsches Elektronensynchrotron,
   DESY, Zeuthen, Germany
   [119]Reviewed by: [120]Dr. Fabrice Piquemal, CNRS, Gradignan, France
   Accepted on: [121]2018-04-13 15:03:58 GMT
   Retrieved from
   "[122]http://www.scholarpedia.org/w/index.php?title=Neutrino_astronomy&oldid=1970
   31"
   [123]Categories:
     * [124]Astrophysics
     * [125]Cosmology
     * [126]Experimental high energy physics
     * [127]Experimental neutrino physics

Personal tools

     * [128]Log in

Namespaces

     * [129]Page
     * [130]Discussion

Variants

Views

     * [131]Read
     * [132]View source
     * [133]View history

Actions

Search

   ____________________ (BUTTON) Search

Navigation

     * [134]Main page
     * [135]About
     * [136]Propose a new article
     * [137]Instructions for Authors
     * [138]Random article
     * [139]FAQs
     * [140]Help

Focal areas

     * [141]Astrophysics
     * [142]Celestial mechanics
     * [143]Computational neuroscience
     * [144]Computational intelligence
     * [145]Dynamical systems
     * [146]Physics
     * [147]Touch
     * [148]More topics

Activity

     * [149]Recently published articles
     * [150]Recently sponsored articles
     * [151]Recent changes
     * [152]All articles
     * [153]List all Curators
     * [154]List all users
     * [155]Scholarpedia Journal

Tools

     * [156]What links here
     * [157]Related changes
     * [158]Special pages
     * [159]Printable version
     * [160]Permanent link

     * [161][twitter.png?303]
     * [162][gplus-16.png]
     * [163][facebook.png?303]
     * [164][linkedin.png?303]

     * [165]Powered by MediaWiki [166]Powered by MathJax [167]Creative Commons
       License

     * This page was last modified on 12 January 2022, at 10:14.
     * This page has been accessed 54,391 times.
     * "Neutrino astronomy" by [168]Francis Halzen and Markus Ahlers is licensed
       under a [169]Creative Commons Attribution-NonCommercial-ShareAlike 3.0
       Unported License. Permissions beyond the scope of this license are described
       in the [170]Terms of Use

     * [171]Privacy policy
     * [172]About Scholarpedia
     * [173]Disclaimers

References

   Visible links:
   1. http://www.scholarpedia.org/w/opensearch_desc.php
   2. http://www.scholarpedia.org/w/index.php?title=Special:RecentChanges&feed=atom
   3. http://dx.doi.org/10.4249/scholarpedia.42649
   4. http://www.scholarpedia.org/w/index.php?title=Neutrino_astronomy&action=cite&rev=197031
   5. http://www.scholarpedia.org/article/Neutrino_astronomy#mw-head
   6. http://www.scholarpedia.org/article/Neutrino_astronomy#p-search
   7. http://www.scholarpedia.org/article/User:Markus_Ahlers
   8. http://www.scholarpedia.org/article/User:Francis_Halzen
   9. http://www.scholarpedia.org/article/User:Atri_Bhattacharya
  10. http://www.scholarpedia.org/article/User:Lydia_Roos
  11. http://www.scholarpedia.org/article/User:Michelle_L._Jones
  12. http://www.scholarpedia.org/article/User:Fabrice_Piquemal
  13. http://www.scholarpedia.org/article/User:Lu_Lu
  14. http://www.scholarpedia.org/article/User:Christian_Spiering
  15. http://www.scholarpedia.org/article/User:Francis_Halzen
  16. http://www.scholarpedia.org/article/User:Markus_Ahlers
  17. http://www.scholarpedia.org/article/Neutrino_astronomy#High-energy_neutrino_astronomy
  18. http://www.scholarpedia.org/article/Neutrino_astronomy#Detection_principle_of_high-energy_neutrinos
  19. http://www.scholarpedia.org/article/Neutrino_astronomy#Status_of_cosmic_neutrino_observations
  20. http://www.scholarpedia.org/article/Neutrino_astronomy#Multimessenger_relations_of_astrophysical_neutrinos
  21. http://www.scholarpedia.org/article/Neutrino_astronomy#Future_avenues
  22. http://www.scholarpedia.org/article/Neutrino_astronomy#References
  23. http://www.scholarpedia.org/article/Neutrino_astronomy#Further_reading
  24. http://www.scholarpedia.org/article/Neutrino_astronomy#External_links
  25. http://www.scholarpedia.org/article/Black_holes
  26. http://www.scholarpedia.org/article/High_energy_cosmic_rays
  27. http://www.scholarpedia.org/article/High_energy_cosmic_rays
  28. http://www.scholarpedia.org/article/Bursting
  29. http://www.scholarpedia.org/article/Neutrino_astronomy#Aartsen2017b
  30. http://www.scholarpedia.org/article/Neutrino_astronomy#Adrian-Martinez2015b
  31. http://www.scholarpedia.org/article/Neutrino_astronomy#Aartsen2017a
  32. http://www.scholarpedia.org/article/Neutrino_astronomy#Adrian-Martinez2013
  33. http://www.scholarpedia.org/article/Neutrino_astronomy#Adrian-Martinez2016a
  34. http://www.scholarpedia.org/article/Neutrino_astronomy#Aartsen2017b
  35. http://www.scholarpedia.org/article/Neutrino_astronomy#Aartsen2017c
  36. http://www.scholarpedia.org/article/High_energy_cosmic_rays
  37. http://www.scholarpedia.org/article/High_energy_cosmic_rays
  38. http://www.scholarpedia.org/article/Periodic_Orbit
  39. http://www.scholarpedia.org/article/Neutrino_astronomy#fig:NA_CCNC.jpg
  40. http://www.scholarpedia.org/article/Neutrino_astronomy#fig:NA_concept.png
  41. http://www.scholarpedia.org/article/Neutrino_astronomy#fig:NA_Sketch.png
  42. http://www.scholarpedia.org/article/Neutrino_astronomy#Ageron2011
  43. http://www.scholarpedia.org/article/Neutrino_astronomy#fig:NA_IC86.png
  44. http://www.scholarpedia.org/article/Neutrino_astronomy#fig:NA_Sketch.png
  45. http://www.scholarpedia.org/article/Neutrino_astronomy#fig:erniekloppo.jpg
  46. http://www.scholarpedia.org/article/Dynamical_Systems
  47. http://www.scholarpedia.org/article/Neutrino_astronomy#fig:NA_Sketch.png
  48. http://www.scholarpedia.org/article/Neutrino_astronomy#Aartsen2016b
  49. http://www.scholarpedia.org/article/Neutrino_astronomy#fig:NA_diffusenumu.jpg
  50. http://www.scholarpedia.org/article/Neutrino_astronomy#Aartsen2016b
  51. http://www.scholarpedia.org/article/Neutrino_astronomy#Aartsen2014b
  52. http://www.scholarpedia.org/article/Neutrino_astronomy#Aartsen2014a
  53. http://www.scholarpedia.org/article/Scale-Free_Networks
  54. http://www.scholarpedia.org/article/Neutrino_astronomy#Aartsen2013a
  55. http://www.scholarpedia.org/article/Neutrino_astronomy#Aartsen2013b
  56. http://www.scholarpedia.org/article/Neutrino_astronomy#fig:erniekloppo.jpg
  57. http://www.scholarpedia.org/article/Neutrino_astronomy#Aartsen2016b
  58. http://www.scholarpedia.org/article/Neutrino_astronomy#Aartsen2016b
  59. http://www.scholarpedia.org/article/Neutrino_astronomy#Aartsen2014b
  60. http://www.scholarpedia.org/article/Neutrino_astronomy#Aarsten2016b
  61. http://www.scholarpedia.org/article/Neutrino_astronomy#fig:NA_Energy_distribution4yrhese.png
  62. http://www.scholarpedia.org/article/Neutrino_astronomy#Aartsen2016c
  63. http://www.scholarpedia.org/article/Neutrino_astronomy#Gorham2010
  64. http://www.scholarpedia.org/article/Neutrino_astronomy#Aab2015
  65. http://www.scholarpedia.org/article/Neutrino_astronomy#Aartsen2014b
  66. http://www.scholarpedia.org/article/Neutrino_astronomy#fig:NA_Energy_distribution4yrhese.png
  67. http://www.scholarpedia.org/article/Neutrino_astronomy#fig:NA_diffusenumu.jpg
  68. http://www.scholarpedia.org/article/Neutrino_astronomy#fig:NA_diffusenumu.jpg
  69. http://www.scholarpedia.org/article/Neutrino_astronomy#fig:NA_Energy_distribution4yrhese.png
  70. http://www.scholarpedia.org/article/Neutrino_astronomy#Aartsen2016a
  71. http://www.scholarpedia.org/article/Neutrino_astronomy#fig:NA_Map6yr.jpg
  72. http://www.scholarpedia.org/article/Neutrino_astronomy#fig:NA_map6yr.jpg
  73. http://www.scholarpedia.org/article/Neutrino_astronomy#Aartsen2016a
  74. http://www.scholarpedia.org/article/Neutrino_astronomy#fig:NA_NuSummary.jpg
  75. http://www.scholarpedia.org/article/Resonance
  76. http://www.scholarpedia.org/article/Neutrino_astronomy#fig:NA_NewfermiPlot2.jpg
  77. http://www.scholarpedia.org/article/Neutrino_astronomy#Murase2013
  78. http://www.scholarpedia.org/article/Neutrino_astronomy#Murase2013
  79. http://www.scholarpedia.org/article/Neutrino_astronomy#Aartsen2014b
  80. http://www.scholarpedia.org/article/Neutrino_astronomy#Aartsen2016b
  81. http://www.scholarpedia.org/article/Neutrino_astronomy#Ahlers2014
  82. http://www.scholarpedia.org/article/High_energy_cosmic_rays
  83. http://www.scholarpedia.org/article/Neutrino_astronomy#Waxman1999
  84. http://www.scholarpedia.org/article/High_energy_cosmic_rays
  85. http://www.scholarpedia.org/article/High_energy_cosmic_rays
  86. http://www.scholarpedia.org/article/High_energy_cosmic_rays
  87. http://www.scholarpedia.org/article/Neutrino_astronomy#Eq-2
  88. http://www.scholarpedia.org/article/High_energy_cosmic_rays
  89. http://www.scholarpedia.org/article/Neutrino_astronomy#Adrian-Martinez2016b
  90. http://www.scholarpedia.org/article/Neutrino_astronomy#fig:NA_mdom.jpg
  91. http://www.scholarpedia.org/article/Neutrino_astronomy#Adrian-Martinez2016b
  92. http://www.scholarpedia.org/article/Neutrino_astronomy#Avrorin2015
  93. http://arxiv.org/abs/1504.05397
  94. http://arxiv.org/abs/1304.5356
  95. http://arxiv.org/abs/1311.5238
  96. http://arxiv.org/abs/1312.0104
  97. http://arxiv.org/abs/1405.5303
  98. http://arxiv.org/abs/1605.00163
  99. http://arxiv.org/abs/1607.08006
 100. http://arxiv.org/abs/1607.05886
 101. http://arxiv.org/abs/1702.06868
 102. http://arxiv.org/abs/1707.03416
 103. http://arxiv.org/abs/1511.02149
 104. http://arxiv.org/abs/1602.03036
 105. http://arxiv.org/abs/1601.07459
 106. http://arxiv.org/abs/1104.1607
 107. http://arxiv.org/abs/1406.2160
 108. http://arxiv.org/abs/1011.5004
 109. http://arxiv.org/abs/1306.3417
 110. http://arxiv.org/abs/hep-ph/9807282
 111. http://arxiv.org/abs/1311.4767
 112. http://arxiv.org/abs/1701.05849
 113. http://www.icecube.wisc.edu/
 114. http://www.km3net.org/
 115. http://baikalweb.jinr.ru/
 116. http://www.scholarpedia.org/article/User:Lu_Lu
 117. http://www.scholarpedia.org/w/index.php?title=Neutrino_astronomy&oldid=186285
 118. http://www.scholarpedia.org/article/User:Christian_Spiering
 119. http://www.scholarpedia.org/w/index.php?title=Neutrino_astronomy&oldid=186285
 120. http://www.scholarpedia.org/article/User:Fabrice_Piquemal
 121. http://www.scholarpedia.org/w/index.php?title=Neutrino_astronomy&oldid=186285
 122. http://www.scholarpedia.org/w/index.php?title=Neutrino_astronomy&oldid=197031
 123. http://www.scholarpedia.org/article/Special:Categories
 124. http://www.scholarpedia.org/article/Category:Astrophysics
 125. http://www.scholarpedia.org/article/Category:Cosmology
 126. http://www.scholarpedia.org/article/Category:Experimental_high_energy_physics
 127. http://www.scholarpedia.org/article/Category:Experimental_neutrino_physics
 128. http://www.scholarpedia.org/w/index.php?title=Special:UserLogin&returnto=Neutrino+astronomy
 129. http://www.scholarpedia.org/article/Neutrino_astronomy
 130. http://www.scholarpedia.org/w/index.php?title=Talk:Neutrino_astronomy&action=edit&redlink=1
 131. http://www.scholarpedia.org/article/Neutrino_astronomy
 132. http://www.scholarpedia.org/w/index.php?title=Neutrino_astronomy&action=edit
 133. http://www.scholarpedia.org/w/index.php?title=Neutrino_astronomy&action=history
 134. http://www.scholarpedia.org/article/Main_Page
 135. http://www.scholarpedia.org/article/Scholarpedia:About
 136. http://www.scholarpedia.org/article/Special:ProposeArticle
 137. http://www.scholarpedia.org/article/Scholarpedia:Instructions_for_Authors
 138. http://www.scholarpedia.org/article/Special:Random
 139. http://www.scholarpedia.org/article/Help:Frequently_Asked_Questions
 140. http://www.scholarpedia.org/article/Scholarpedia:Help
 141. http://www.scholarpedia.org/article/Encyclopedia:Astrophysics
 142. http://www.scholarpedia.org/article/Encyclopedia:Celestial_Mechanics
 143. http://www.scholarpedia.org/article/Encyclopedia:Computational_neuroscience
 144. http://www.scholarpedia.org/article/Encyclopedia:Computational_intelligence
 145. http://www.scholarpedia.org/article/Encyclopedia:Dynamical_systems
 146. http://www.scholarpedia.org/article/Encyclopedia:Physics
 147. http://www.scholarpedia.org/article/Encyclopedia:Touch
 148. http://www.scholarpedia.org/article/Scholarpedia:Topics
 149. http://www.scholarpedia.org/article/Special:RecentlyPublished
 150. http://www.scholarpedia.org/article/Special:RecentlySponsored
 151. http://www.scholarpedia.org/article/Special:RecentChanges
 152. http://www.scholarpedia.org/article/Special:AllPages
 153. http://www.scholarpedia.org/article/Special:ListCurators
 154. http://www.scholarpedia.org/article/Special:ListUsers
 155. http://www.scholarpedia.org/article/Special:Journal
 156. http://www.scholarpedia.org/article/Special:WhatLinksHere/Neutrino_astronomy
 157. http://www.scholarpedia.org/article/Special:RecentChangesLinked/Neutrino_astronomy
 158. http://www.scholarpedia.org/article/Special:SpecialPages
 159. http://www.scholarpedia.org/w/index.php?title=Neutrino_astronomy&printable=yes
 160. http://www.scholarpedia.org/w/index.php?title=Neutrino_astronomy&oldid=197031
 161. https://twitter.com/scholarpedia
 162. https://plus.google.com/112873162496270574424
 163. http://www.facebook.com/Scholarpedia
 164. http://www.linkedin.com/groups/Scholarpedia-4647975/about
 165. http://www.mediawiki.org/
 166. http://www.mathjax.org/
 167. http://creativecommons.org/licenses/by-nc-sa/3.0/deed.en_US
 168. http://www.scholarpedia.org/article/Neutrino_astronomy
 169. http://creativecommons.org/licenses/by-nc-sa/3.0/deed.en_US
 170. http://www.scholarpedia.org/article/Scholarpedia:Terms_of_use
 171. http://www.scholarpedia.org/article/Scholarpedia:Privacy_policy
 172. http://www.scholarpedia.org/article/Scholarpedia:About
 173. http://www.scholarpedia.org/article/Scholarpedia:General_disclaimer

   Hidden links:
 175. http://www.scholarpedia.org/article/File:NA_CCNC.jpg
 176. http://www.scholarpedia.org/article/File:NA_CCNC.jpg
 177. http://www.scholarpedia.org/article/File:NA_concept.png
 178. http://www.scholarpedia.org/article/File:NA_concept.png
 179. http://www.scholarpedia.org/article/File:NA_Sketch.png
 180. http://www.scholarpedia.org/article/File:NA_Sketch.png
 181. http://www.scholarpedia.org/article/File:NA_IC86.png
 182. http://www.scholarpedia.org/article/File:NA_IC86.png
 183. http://www.scholarpedia.org/article/File:Erniekloppo.jpg
 184. http://www.scholarpedia.org/article/File:Erniekloppo.jpg
 185. http://www.scholarpedia.org/article/File:NA_diffusenumu.jpg
 186. http://www.scholarpedia.org/article/File:NA_diffusenumu.jpg
 187. http://www.scholarpedia.org/article/File:NA_Energy_distribution4yrhese.png
 188. http://www.scholarpedia.org/article/File:NA_Energy_distribution4yrhese.png
 189. http://www.scholarpedia.org/article/File:NA_map6yr.jpg
 190. http://www.scholarpedia.org/article/File:NA_map6yr.jpg
 191. http://www.scholarpedia.org/article/File:NA_NUsummary.jpg
 192. http://www.scholarpedia.org/article/File:NA_NUsummary.jpg
 193. http://www.scholarpedia.org/article/File:NA_NewfermiPlot2.jpg
 194. http://www.scholarpedia.org/article/File:NA_NewfermiPlot2.jpg
 195. http://www.scholarpedia.org/article/File:NA_mdom.jpg
 196. http://www.scholarpedia.org/article/File:NA_mdom.jpg
 197. http://www.scholarpedia.org/article/Neutrino_astronomy
 198. http://www.scholarpedia.org/article/Neutrino_astronomy
 199. http://www.scholarpedia.org/article/Main_Page