Neutrino astronomy

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Curator: Markus Ahlers



[THE FOLLOWING IS PLACEHOLDER/DRAFT – guidelines state: “Start your article with defining the topic. … This paragraph should contain a few sentences and should be understandable to non-experts”]

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

The advent of 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, 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 inner neighborhood of black holes and from the nuclear furnaces where cosmic rays 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 (Roberts:1992re).

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 (Markov:1960vja). 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 (Babson:1989yy). 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 (Balkanov:2000cf) as well as efforts to commission neutrino telescopes in the Mediterranean (Aggouras:2005bg,Aguilar:2006rm,Migneco:2008zz). These efforts in turn have led towards the ongoing construction of KM3NeT (Adrian-Martinez:2016fdl) off the coast of Italy and GVD (Avrorin:2015wba) 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 operation beginning in 2000, it represented a proof of concept for the kilometer-scale neutrino observatory, IceCube (ICPDD2001,Ahrens:2003ix). 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 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.


Detection principle of high-energy neutrinos

Figure 1: 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 (Halzen:2006mq).

The observation of high-energy neutrinos as cosmic messengers is directly motivated by the presence of high-energy cosmic rays. These energetic particles have been observed for more than a century and are known to reach energies in excess of $10^8$ TeV. We don’t know what cosmic sources are capable of accelerating particles to these extreme energies (Sommers:2008ji,Hillas:2006ms,Berezinsky:2008qh,Kotera:2011cp) and neutrino astronomy might be the key to solve this puzzle (Ahlers:2015lln). The rationale is simple: cosmic rays interact with gas and radiation (so-called $pp$ and $p\gamma$ interactions, respectively) at various stages of their acceleration in their sources, the gradual emission into the source periphery, and their propagation over cosmic distances. 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 $p\gamma_{\rm bg}\to n\pi^+$. Neutral pions decay as $\pi^0\to2\gamma$ and create a flux of high-energy $\gamma$-rays. On the other hand, 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 $\mu^+\to e^+\nu_\mu \bar\nu_e$ and the charged-conjugate processes.

Neutrinos carry a very small mass and can be treated as relativistic radiation in the context of neutrino astronomy. Neutrinos produced via the decay of pions are the so-called flavor eigenstates, which are related to the neutrino mass eigenstates via mixing matrices. The combination of small neutrino mass differences and flavor mixing leads to the phenomenon of neutrino flavor oscillations over long propagation distances. For cosmic sources, the length scale of flavor oscillations is much shorter than the distance to the source, and the only observable flavor composition is the oscillation average. For instance, the initial mix of two muon neutrinos and one electron neutrino in the decay of charged pions will be observable as an almost equal mix between electron, muon and tau neutrino flavors, $\nu_e:\nu_\mu:\nu_\tau \simeq 1:1:1$.

However, their weak interactions also make neutrinos very difficult to detect. High-energy neutrinos interact with matter via deep inelastic scattering off nucleons. In this process, a neutrino flavor state scatters off quarks via the exchange of a $Z$ boson (neutral current (NC)) or $W$ boson (charged current (CC)). Whereas the former interaction leaves the neutrino flavor state intact, the latter creates a charged lepton corresponding to the initial neutrino flavor. The inelastic CC cross section is only at the level of $10^{-33}~{\rm cm}^{2}$ at a neutrino energy of about $10^3$ TeV and has a soft energy scaling of $\sigma_{\rm tot}\propto E_\nu^{0.36}$ towards higher energies, see e.g., Ref. (Gandhi:1998ri). The relative energy fraction transferred from the neutrino to the nucleus is at the level of $20$% at these energies. The struck nucleus does not remain intact after the scattering and its high-energy fragments typically initiate hadronic cascades in the target medium.

Immense particle detectors are required to collect cosmic neutrinos in statistically significant numbers (Gaisser1995,Learned:2000sw,Halzen:2002pg,Becker:2008ra,Katz:2011ke). Already by the 1970s, it had been understood (Roberts1992) that a kilometer-scale detector was needed to observe the cosmogenic neutrinos produced in the interactions of cosmic rays with background microwave photons (Beresinsky:1969qj). There are various possible ways to detect the high-energy secondary particles created in charged and neutral current interactions. One way that is particularly useful for neutrino astronomy is the observation of long-lived muons produced in charged current interactions of muon neutrinos via optical Cherenkov light emission. This requires the use of transparent media like water or ice. A sketch of the signal is shown in Figure 1. Photomultipliers placed in the medium transform the Cherenkov light from neutrino interactions into electrical signals using the photoelectric effect. This information allows scientists to reconstruct neutrino events and infer their arrival directions and energies. Due to the large background of muons produced by CR interactions in the atmosphere, the classical signal for neutrino interactions are upgoing tracks that can only be produced by interactions close to the detector from neutrinos that have passed through the Earth. Then, the soft spectrum of atmospheric neutrinos (also produced by CR showers) can be used to identify hard emission from cosmic sources.


IceCube Neutrino Observatory

Figure 2: Architecture of the IceCube observatory (left) and the schematics of a digital optical module (right).

The IceCube detector (Aartsen:2016nxy) 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 2. 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 residuals accurate to 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 3: (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. 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. An alternative method exclusively identifies neutrinos interacting inside the detector (Schonert:2008is). It divides the instrumented volume of ice into an outer veto shield and a $500$-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 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 muon neutrino depositing 2.6 PeV energy while traversing the detector are contrasted in Figure 3.

In general, the arrival times of photons at the optical sensors determine the particle’s trajectory (Ahrens:2003fg), while the number of photons is a proxy for the deposited energy. The two methods for 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 secondary showers, in principle possible to a few degrees, is still in the development stage in IceCube (Aartsen:2013vja). 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.


Status of cosmic neutrino observations

Figure 4: 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 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 cosmic-ray muons, while the second is to identify the small fraction of these neutrinos that is astrophysical in origin, observed 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 is too low to produce events, even in a kilometer-scale detector, and 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 (Waxman:1998yy,Bahcall:1999yr). However, in seven years of data, an excess of events is observed at energies beyond 100 TeV (Aartsen:2015rwa,Aartsen:2016xlq), which cannot be accommodated by the atmospheric flux; see Figure 4. Allowing for large uncertainties on the extrapolation of the atmospheric component, 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 , the most likely energy of the parent neutrino approaches 10 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:2016xlq}. 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 5: Deposited energies of muons observed in four years of data. 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. Also shown are two illustrative power-law fits to the spectrum.

However, it was the alternative method, which selects isolated neutrinos interacting inside the detector, that revealed the first evidence for cosmic neutrinos (Aartsen:2013bka,Aartsen:2013jdh). Their isolation and well-measured energy allows for a clear separation between neutrinos of atmospheric origin and those of cosmic origin; a sample event with a light pool of roughly one hundred thousand photoelectrons extending over more than 500 meters is shown in Figure 3. 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 keeping 98% 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 neutrino energy is sufficiently high and the zenith angle sufficiently small (Schonert:2008is,Gaisser:2014bja). PeV atmospheric neutrinos come with their own self-veto. This self-veto is applied to IceCube cosmic neutrino candidates that exclusively consist of isolated neutrino events.

Figure 6: Mollweide projection in Galactic coordinates of the arrival direction of neutrino events. We show the results of the six-year upgoing track analysis with energy proxy ${\rm MuEx} >50$ ($\odot$}). The red numbers show the most probable neutrino energy (in TeV) assuming the best-fit astrophysical flux of the analysis. The events of the four-year high-energy starting event (HESE) analysis with deposited energy (green numbers) larger than 60 TeV (tracks $\otimes$ and cascades $\oplus$) are also shown. 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 7: Summary of neutrino observations and upper limits (per flavor). The black and grey data shows IceCube’s measurement of the atmospheric $\nu_e+\bar\nu_e$ 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 5). 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 (brown), ANITA (orange), and Auger (blue).

The energy dependence of the high-energy neutrinos collected in four years of data (Aartsen:2014gkd) is compared to that of atmospheric backgrounds in . It is, above an energy of $200$ TeV, consistent with the flux of muon neutrinos penetrating the Earth shown in Figure 4. 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 (Aartsen:2015ivb) with $\nu_e:\nu_\mu:\nu_\tau \sim 1:1:1$.

The four-year data set contains a total of 54 neutrino events with deposited energies ranging from 30 to 2000 TeV. The data in both Figure 4 and Figure 5 support 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:2016tpb). 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. The events are isolated neutrinos, and it is therefore very difficult to accommodate them as a feature in the atmospheric background, of charm origin or not (Halzen:2016thi).

In Figure 6 we show the arrival directions of the most energetic events of the 6-year upgoing $\nu_\mu+\bar\nu_\mu$ analysis ($\odot$) and the 4-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 apparent anisotropy of the arrival directions is dominated by the effective area of the analysis. 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 Earth absorption. The HESE events with deposited energy of $E_{\rm dep}>100$ TeV also suffer from Earth absorption, but can also be visible 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 (Ahlers:2015moa,Aartsen:2015zva). In fact, no correlation of the arrival directions of the highest energy events, shown in Figure 6, with potential sources or source classes has reached the level of $3\sigma$ (Aartsen:2016tpb).

Various scenarios have been invoked to explain the observed diffuse emission, see, e.g., the review (Ahlers:2015lln). 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 7. 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 the Fermi gamma-ray background in the GeV-TeV range. We will discuss these multimessenger relations in the next section.


Multimessenger relations of astrophysical neutrinos

Having established a prominent role for hadronic accelerators in the nonthermal universe, we investigate how the accelerated cosmic rays may produce photons and neutrinos after the relatively brief acceleration process. The principal mechanism at work is the production of pions in interactions of high-energy cosmic rays with photons or nuclei. Targets include strong radiation fields that may be associated with the accelerator as well as any concentrations of matter or molecular clouds in their vicinity. Finally, attenuation of the cosmic rays when propagating through the interstellar or intergalactic backgrounds can lead to further production of pions. A high-energy flux of neutrinos is then produced in the subsequent decay of charged pions via $\pi^+\to\mu^++\nu_\mu$ followed by $\mu^+ \to e^++\nu_e+\bar\nu_\mu$ and the charge-conjugate processes. High-energy gamma rays are produced in the decay of neutral pions, $\pi^0\to2\gamma$.

Pion production of cosmic rays 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 nonresonant pion production at the resonance changes this ratio to about 1/2 and 1/2. In contrast, cosmic rays 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.

To evaluate the flux of neutrinos from the cosmic-ray interaction region, we start from the pion production rate $Q_{\pi^\pm}$, providing the number of charged pions per unit energy and time (units of ${\rm GeV}^{-1} {\rm s}^{-1}$). This quantity is proportional to the corresponding cosmic-ray nucleon density $Q_N$ by a bolometric proportionality factor $f_\pi\leq 1$ that parametrizes the efficiency of the conversion of cosmic-ray energy into pion energy:

\begin{equation}\tag{1} E_\pi^2Q_{\pi^\pm}(E_\pi) \simeq f_\pi\, \frac{K_\pi}{1+K_\pi}\,\left[E^2_NQ_N(E_N)\right]_{E_N = E_\pi/\kappa_\pi}\,. \end{equation}

The factor introducing $K_\pi$ accounts for the different ratio between charged and neutral pions in interactions with gas or dust ($pp$) and with radiation ($p\gamma$), with $K_\pi\simeq2$ and $1$, respectively. The total energy loss of the hadronic interaction ($pp$ or $p\gamma$) is in the form of pions with average energy $E_\pi$, average multiplicity $N_\pi$, and total inelasticity $\kappa$. For $p\gamma$ interactions, the total inelasticity is about $\kappa\simeq 0.2$, whereas it is about $\kappa\simeq0.5$ for $pp$ interactions. In both cases the average inelasticity per pion can be approximated as $\kappa_\pi = \kappa/N_\pi \simeq 0.2$ (Kelner:2006tc). The average energy per pion is then $E_\pi = \kappa_\pi E_N$. For a target with nucleon density $n$ and diameter $\ell$, the efficiency factor for producing pions can be expressed as $f_\pi = 1-\exp(-\kappa\ell\sigma n)$ with cross section $\sigma$ and inelasticity $\kappa$ for either $p\gamma$ or $pp$ interactions.

Subsequently, the pions decay into gamma rays and neutrinos that carry, on average, 1/2 and 1/4 of the energy of the parent pion. We here 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 pionic leptons relative to the proton is:

$x_{\nu} = E_{\nu}/E_p = 1/4$, $\kappa_\pi\simeq {1}/{20}$ and $x_\gamma = E_{\gamma}/E_p = \kappa_\pi/2 \simeq1/10$. With this approximation, the neutrino production rate $Q_{\nu_\alpha}$ can be related to the one for charged pions:

\begin{equation}\tag{2} \frac{1}{3}\sum_{\alpha}E_\nu Q_{\nu_\alpha}(E_\nu) \simeq \left[E_\pi Q_{\pi^\pm}(E_\pi)\right]_{E_\pi \simeq 4E_\nu}\,. \end{equation}

Using Eqs. (1) and (2), we arrive at the final relation for neutrino production:

\begin{equation}\tag{3} \frac{1}{3}\sum_{\alpha}E^2_\nu Q_{\nu_\alpha}(E_\nu) \simeq \frac{1}{4}f_\pi \frac{K_\pi}{1+K_\pi}\left[E^2_NQ_N(E_N)\right]_{E_N = 4E_\nu/\kappa_\pi}\,. \end{equation}

The production rate of gamma rays from the decay of neutral pions can be obtained in exactly the same way.

From the two equations for the productions of neutrinos and gamma rays, one can eliminate $Q_N$ to obtain a model-independent relation that is independent of the details of the cosmic-ray beam, except for the relative contribution of charged-to-neutral pions,

\begin{equation}\tag{4} \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 8 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 universe 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:2013rfa). This might indicate that these neutrinos originate in hidden sources (Murase:2015xka) or in sources with a very strong cosmological evolution resulting in a shift of the photons to sub-GeV energies (Wang:2016vbf).

Is it possible that the sources of the extragalactic cosmic rays are themselves neutrino sources? From the measured cosmic-ray spectrum, one can derive that the emission rate density of nucleons is at the level of (Ahlers:2012rz,Katz:2013ooa) $\mathcal{L}_N = \rho_0E^2_NQ_N(E_p) \simeq {(1-2)\times10^{44}\,{\rm erg}\,{\rm Mpc}^{-3}\,{\rm yr}^{-1}}$.

Combining this with Eq.(3) we can derive the diffuse neutrino flux

\begin{equation}\tag{5} \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 8: 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. 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. 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.

Here $\xi_z$ is the evolution factor previously introduced. 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:1998yy). 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.

For $\xi_z \simeq2.4$ and $K_\pi\simeq 1-2$, the upper bound resulting from Eq. (5) and $f_\pi=1$ is at the level of the neutrino flux observed by IceCube. Therefore, it is possible that the observed extragalactic cosmic rays and neutrinos have the same origin. A plausible scenario is a calorimeter in which only cosmic rays 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 (Berezinsky:1996wx,Murase:2008yt,Murase:2013rfa,Zandanel:2014pva) or starburst galaxies (Loeb:2006tw,Murase:2013rfa).


Cosmogenic neutrinos

The production of neutrinos in the sources that accelerate the high-energy cosmic rays depends on the source environment. In order to efficiently accelerate cosmic rays, any loss mechanism, including pion production in $p\gamma$ and $pp$ interactions, must be suppressed as it reduces the acceleration time. Efficient accelerators are likely to be inefficient beam dumps for producing neutrinos. High-efficiency neutrino production can be achieved by separating the sites of acceleration and neutrino production. For instance, after acceleration, extragalactic cosmic rays propagate over cosmological distances of more than 10 Mpc and can efficiently produce neutrinos on the dilute extragalactic medium.

In this section, we will discuss the production of neutrinos in the interactions of extragalactic cosmic rays with cosmic radiation backgrounds. Soon after the discovery of the cosmic microwave background (CMB), Greisen, Zatsepin and Kuzmin (Greisen:1966jv,Zatsepin:1966jv) (GZK) realized that extragalactic cosmic rays are attenuated by interactions with background photons. Actually, protons interact resonantly via $p\gamma\to\Delta^+\to\pi^+ n$ with background photons with mean energy $\epsilon \simeq 0.33$ meV at energies $E_p \simeq (m^2_\Delta-m_p^2)/4/\epsilon \simeq 500$ EeV. The width of the Planck spectrum leads 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 (Beresinsky:1969qj) 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 flux of cosmogenic neutrinos peaks at EeV neutrino energy depending on the chemical composition and the evolution with redshift of the unknown sources. The largest neutrino flux results from proton-dominated models. A particularly strong emission can be expected in such models if the proton spectrum extends below the ankle. Referred to as dip models, the ankle results from the absorption of protons by Bethe–Heitler pair production on CMB photons. A fit to the observed cosmic-ray spectrum requires relative strong source evolution with redshift that enhances pion production. However, the corresponding electromagnetic emission via neutral pions as well as $e^\pm$ pairs is constrained by the isotropic gamma-ray background (IGRB) observed by Fermi LAT (Abdo:2010nz,Ackermann:2014usa) and limits the neutrino intensity of these proton-dominated scenarios, for a review see (Ahlers:2015lln). Recent upper limits on cosmogenic neutrinos resulting from the failure by IceCube to observe EeV neutrinos constrains proton-dominated models (Aartsen:2016ngq) (see also Refs. (Heinze:2015hhp,Supanitsky:2016gke)).

In contrast, the IceCube constraint can be accommodated by introducing a heavy nuclear composition. Resonant neutrino production still proceeds via the interaction of individual nucleons with background photons, but the threshold of the production is increased to $E_{\rm CR} \gtrsim AE_{\rm GZK}$ for nuclei with mass number $A$. Therefore, efficient cosmogenic neutrino production would require an injected cosmic-ray flux that extends well above $E_{\rm GZK}$. Especially for heavier nuclear composition of the primary flux, the production of neutrinos on photons of the extragalactic background light (EBL) becomes relatively important. The interaction with optical photons produces neutrino fluxes in the PeV energy range. However, the overall level is much lower because of the low intensity of the EBL photons. It is unlikely that the PeV neutrino flux observed with IceCube could be related to the neutrino production in the EBL (Roulet:2012rv). The observed PeV neutrino flux level is too high to be consistent with associated electromagnetic contributions to the IGRB or upper limits on the EeV neutrino flux.


Future avenues

IceCube has discovered a flux of extragalactic cosmic neutrinos with an energy density that matches that of extragalactic high-energy photons and ultra-high-energy cosmic rays. This may suggest that neutrinos and high-energy cosmic rays 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 the extraordinary 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 (Aartsen:2015dkp). 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

Further reading

[THE FOLLOWING IS PLACEHOLDER – guidelines state: “a good place to cite introductory books, tutorials, and reviews”]

  • SURNAME1, FORENAME1 (YEAR). Further Reading 1 PUBLISHER, ADDRESS. . This is a good starting point.
  • SURNAME1, FORENAME1 (YEAR). Further Reading 2 PUBLISHER, ADDRESS. . This book offers an introduction to similar topics in astronomy and astrophysics.


External links

IceCube [1]

See also

[THE FOLLOWING IS PLACEHOLDER – guidelines state: “a good place to cite introductory books, tutorials, and reviews”]

Neutrino, Astrophysics

Sponsored by: Dr. Lu Lu, International Centre for Hadron Astrophysics, Chiba University, Chiba, Japan
Reviewed by: Dr. Christian Spiering, Deutsches Elektronensynchrotron, DESY, Zeuthen, Germany
Reviewed by: Dr. Fabrice Piquemal, CNRS, Gradignan, France
Accepted on: 2018-04-13 15:03:58 GMT
Retrieved from "http://www.scholarpedia.org/w/index.php?title=Neutrino_astronomy&oldid=176475"
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