The strength of neutrino astronomy is also its challenge. Since neutrinos interact only weakly with matter, large detector mass is required in order to detect them. The detection of solar neutrinos became possible with the construction of detectors with kilotons of detecting medium. The probability that a neutrino passing through kilotons of matter would be ”captured,” i.e. would interact within the detector, is still very small. However, the large flux of neutrinos from the Sun, some 100 billion neutrinos per square centimeter per second, allows hundreds of them to be detected every year.

The detection of solar neutrinos enabled direct observations of nuclear reactions in the core of the Sun, confirming the hypothesis that the energy source of the Sun is nuclear fusion and demonstrating the validity of solar structure models. It has also taught us that the standard model of particle physics is incomplete. Neutrinos come in three types, or ”flavors:” electron-type, muon-type and tau-type. Solar neutrino detection demonstrated that neutrinos can change their flavor as they propagate in matter or in vacuum, a phenomenon not accounted for by the standard model. This flavor change also indicates that neutrinos are not mass-less, as assumed in the standard model, but rather have finite, albeit small, masses.

The characteristic energy of neutrinos produced in the Sun is Mega (million) electron-Volt, MeV. eV is the energy typically required to detach an electron from an atom, while MeV is the characteristic energy released in the fusion or fission of atomic nuclei. Solar neutrino detectors, ”telescopes,” are capable of detecting MeV neutrinos from supernova explosions in our ”local” Galactic neighborhood, at distances smaller than 100,000 light years. Since the rate of such explosions is one per few decades, only one supernova, the famous SN 1987A, has so far been detected. Much like the detection of solar neutrinos, the detection of neutrinos from SN 1987A provided a direct observation of the physical process powering the explosions, the collapse of the core of a massive star to a neutron star, as well as constraints on fundamental neutrino properties.

The detection of MeV neutrinos from sources well outside our local neighborhood, lying at distances ranging from several million light years, the typical distance between galaxies, to several billion light years, the size of the observable universe, is impossible using present techniques. In order to extend the distance accessible to neutrino astronomy to the edge of the observable universe, several high-energy neutrino telescopes are currently being constructed. These telescopes are designed for the detection of neutrinos with energies exceeding Terra-electron-Volt (TeV, equal to million-MeV).

The detection of astrophysical high-energy neutrinos will allow to answer some of the most important open questions of high energy astrophysics. These include, e.g., the identity and physics of the most powerful accelerators in the universe and the mechanisms for energy extraction from black holes. It will also allow to study fundamental neutrino physics issues, e.g. neutrino coupling to gravity and the existence of weakly interacting massive particles (WIMPs). These issues are discussed at some length below. It should be kept in mind, however, that as the construction of high energy neutrino telescopes opens a new, unexplored window of observations on the universe, one should be ready for surprises. It may well be that the most important things that we will learn would be related to such surprises, rather than to the open questions discussed below.

Reaching out to the edge of the universe: High energy neutrinos

The neutrino flux from cosmologically distant sources is too low to be detectable by kiloton detectors of MeV neutrinos. The construction of orders of magnitude larger detectors, that would be required for the detection of extra-Galactic sources at this energy, is currently unfeasible. This situation changes at higher neutrino energy, due to two reasons. First, the interaction cross section increases with energy, that is, higher energy neutrinos are more likely to interact with matter than lower energy ones. This implies that smaller fluxes of higher energy neutrinos may be detectable with a given detector mass. Second, at TeV neutrino energy the construction of Giga-ton, rather than kiloton, telescopes becomes feasible.

Interactions of high energy, > 1 TeV, muon-type neutrinos with atomic nuclei on Earth produce muons (charged particles about hundred times heavier than the electron), which propagate at a straight line and at nearly the speed of light over more than a kilometer through rock, water or ice. While propagating at nearly the speed of light, the muon emits visible light, ”Cerenkov radiation.” Thus, if the muon propagates through transparent water or ice, its ”track” may be identified by detecting the light it emits. Since the muon track is co-linear to within one degree with the initial neutrino trajectory, the direction to the neutrino source may be determined.

The feasibility of detection of high energy muons in deep sea or lake water has been demonstrated by the DUMAND experiment off the coast of Hawaii and by the Lake Baikal experiment. The AMANDA collaboration has demonstrated that the deep ice of the South Pole is also a suitable medium, and that construction of a cubic kilometer ice detector, with a Giga-ton of ice as detecting medium, is feasible. A schematic description of the AMANDA detector is presented in Fig. 1.

FIG. 1: The AMANDA experiment. > 1 TeV muons, produced by high-energy neutrinos interacting with atomic nuclei near or within the detector, are identified by an array of photo-multipliers (PMTs) deployed 2 km deep under the South-Pole surface. Detection by the PMTs of the muon emission of visible, Cerenkov, light allows to reconstruct the > 1 kilometer long muon track. A neutrino event recorded in AMANDA is presented in fig. 2.

The reason for constructing neutrino telescopes in deep water or ice is twofold. First, the ice and water properties improve with depth. The scattering of light is weaker at large depth, thus allowing to place the photo-multipliers, the detectors of the muon Cerenkov light, at larger spacing. This implies that at larger depth a smaller number of photo-multipliers is required to instrument a given detector volume, and allows the instrumentation of a cubic-km of ice or water at an acceptable cost. Second, the atmospheric muon background to the neutrino signal is reduced at larger depth. High-energy muons are produced in the atmosphere of the Earth by interaction of cosmic rays with air. The cosmic rays, which hit the atmosphere are mostly high energy nuclei, believed to be produced in Galactic supernovas. The muons produced by their interactions in the atmosphere constitute a background to the signal of neutrino-induced muons, that is, to the signal of muons produced by neutrino interactions. Since the muons penetrate a distance of order a km in ice or water, putting the detector several kilometers deep under water or ice strongly suppresses the atmospheric muon background. The large depth does not affect the neutrino induced muon signal, since neutrinos can easily penetrate the Earth and interact near or within the detector.

FIG. 2: A high-energy muon track reconstructed by the AMANDA detector [E. Andres et al., Nature 410, 441 (2001)]. Each dot represents an optical module, shown in detail on the right. The colored circles show pulses from the PMTs: The size of the circle indicates the pulse amplitude, and its color corresponds to photon’s arrival time, earlier times are red and later times are blue. The arrow indicates the upward moving muon track.

Fig. 2 shows a neutrino event detected by the AMANDA telescope. The fact that the muon track is ”upgoing,” crossing the detector from bottom to top, allows to confidently identify it as a neutrino-induced muon: Only neutrinos can cross the Earth to approach the detector from below and produce upgoing muons. This neutrino is, most likely, an ”atmospheric neutrino.” The interaction of cosmic rays in the atmosphere produces both muons and neutrinos. While the atmospheric muon flux is suppressed by going to large depth, the atmospheric neutrino flux is not. Atmospheric neutrinos constitute therefore an unavoidable background, which sets a lower limit to the flux of astronomical sources, which are detectable (for a given detector size).

The AMANDA detector, which is roughly 0.1 Giga-ton in mass, is currently expanded in the IceCube project to a cubic-km, 1 Giga-ton, detector. In addition, several efforts are currently underway in the Mediterranean to construct Giga-ton scale under-water detectors (the ANATRES, NESTOR and NEMO projects).

The most powerful cosmic accelerators

Nuclear fusion in stars generally does not lead to production of neutrinos at energy much higher than MeV. Should we expect, therefore, any sources of TeV neutrinos to be out there? If so, what is the mechanism by which they produce neutrinos, and what is the detector size that is required to detect them? The answers to these questions rely largely on observations of high-energy cosmic rays.

The cosmic-ray spectrum extends to energies of 10²⁰ eV, 100 million TeV. We have strong indications that ultra-high energy cosmic rays (UHECRs), cosmic rays of energy exceeding 10 million TeV, are produced by extra-galactic sources, and that they are light nuclei, most likely protons. The identity of the sources is yet unknown: The high energies, 100 million times larger than the highest energy achieved by man made accelerators, challenge all models proposed for particle acceleration. Moreover, the cosmic-ray arrival directions do not necessarily point back to their sources, since protons (being charged particles, unlike photons and neutrinos) are deflected by Galactic and extra-galactic magnetic fields, and do not propagate along straight lines.

The essence of the challenge of accelerating to 10²⁰ eV, or 100 million TeV, can be understood from figure 3. Most models involve the acceleration of charged particles, like protons, which are confined to the accelerator by magnetic fields. Magnetic confinement requires the product of accelerator magnetic field strength and accelerator size to exceed a value, which increases with particle energy. Only two types of astrophysical sources are known to be large enough and to contain magnetic fields strong enough to possibly allow proton acceleration to 10²⁰ eV: Gamma-Ray Bursts (GRBs) and Active Galactic Nuclei (AGN). GRBs are the brightest transient sources known in the universe. Lying at cosmological distances, they produce short (typically 1 to 100 s long) flashes with luminosity exceeding that of the Sun by 19 orders of magnitude. AGN are the brightest known steady sources, with luminosity exceeding that of the Sun by 12 orders of magnitude. While GRBs and AGN are plausible candidates for UHECR production, we have no direct evidence for proton acceleration in these sources despite many years of photon observations. Furthermore, our theoretical models describing these sources are incomplete, a point to which we return below.

FIG. 3: Size and magnetic field strength of possible sites of particle acceleration. The magnetic field is measured in Gauss units, where the Earth’s magnetic field is ~ 1 Gauss. Proton acceleration to 1 TeV or 1020 eV is possible only for sources lying above the appropriately marked lines. This is a necessary, but not sufficient requirement: Proton acceleration to 1020 eV is impossible in galaxy clusters, since the acceleration time in these objects is larger than the age of the universe, and unlikely in highly magnetized neutron stars, due to severe energy losses.

Irrespective of the nature of the UHECR sources, some fraction of their energy output is bound to be carried by high-energy neutrinos. Protons, p’s, of sufficiently high energy may interact with photons, g’s, to produce charged pions, p⁺’s, particles that decay to muons and neutrinos. This interaction is represented symbolically as

where n stands for a neutron. The subsequent decay of the pion produces neutrinos:

The neutrinos produced by the decay of the pions carry a significant fraction of the energy of the parent proton. Neutrinos produced, for example, by the decay of pions produced by interaction with photons, eq. (1), typically carry 5% of the proton energy. UHECR sources are expected therefore to be sources also of high-energy neutrinos. The detection of high-energy neutrinos emitted by extra-Galactic sources will provide the first direct evidence for acceleration of protons in such sources, and may resolve the mystery of the UHECR source identity.

The need for Giga-ton neutrino telescopes

UHECR observations provide guidance to estimating the expected high-energy neutrino signal and the detector size required to detect it. Assuming that UHECRs are protons produced by extra-Galactic sources, the observed flux of UHECRs determines the average rate, per unit time and volume, at which such high energy protons are produced in the universe. The UHECR production rate sets, in turn, an upper bound to the neutrino flux produced by extra-Galactic sources. This upper bound, which came to be known as the ”Waxman-Bahcall” (WB) bound, may be presented as:

The upper bound is compared in fig. 4 with current experimental limits, and with the expected sensitivity of planned neutrino telescopes. The figure indicates that Giga-ton neutrino telescopes are needed to detect the expected extra-Galactic flux in the energy range of ~ 1 TeV to ~ 1000 TeV, and that much larger effective mass is required to detect the flux at higher energy. Few tens of ~ 100 TeV events per year are expected in a Giga-ton telescope if GRBs are the sources of ultra-high energy protons. These events will be correlated in time and direction with GRB photons, allowing for an essentially background free experiment. A lower rate is expected if AGN are the UHECR proton sources.

FIG. 4: The upper bound imposed by UHECR observations on the extra-Galactic high energy muon neutrino intensity, compared with the atmospheric neutrino background and with the experimental upper bounds (solid lines) of optical Cerenkov experiments, BAIKAL and AMANDA, and of coherent Cerenkov radio experiments (RICE, GLUE). The curve labeled ”GZK” shows the intensity due to interaction with micro-wave background photons. Dashed curves show the expected sensitivity of 0.1 Gton (AMANDA, ANTARES, NESTOR) and 1 Gton (IceCube, NEMO) optical Cerenkov detectors, of the coherent radio Cerenkov (balloon) experiment ANITA and of the Auger air-shower detector (sensitivity to nt). Space air-shower detectors (EUSO) may also achieve the sensitivity required to detect fluxes lower than the WB bound at energies > 1018 eV.

”GZK” neutrinos: A guaranteed source or ”new physics”?

Protons of sufficiently high energy, exceeding ~ 5 x 10¹⁹ eV, may interact with photons of the cosmic microwave background, the big bang ”relic” of 2.7⁰ K radiation permeating the universe, to produce pions as described by eq. (1). Protons of sufficiently high energy, > 10²⁰ eV, lose most of their energy over less than 300 million years, a time much shorter than the age of the universe, which is ~ 10 billion years. All the energy injected into the universe in the form of such protons is thus converted to pions, which decay to neutrinos, producing a background neutrino intensity similar to the WB-bound. The expected neutrino intensity is schematically shown in fig. 4. It is denoted ”GZK neutrinos,” where ”GZK” stands for Greisen, Zatsepin & Kuszmin, who were the first to point out the rapid energy loss of high-energy protons due to interaction with the microwave background. The GZK neutrino flux peaks at ~ 5 x 10¹⁸ eV, since neutrinos produced by pg interactions typically carry 5% of the ~ 10²⁰ eV proton energy.

The detection of GZK neutrinos will be a milestone in neutrino astronomy. Most important, neutrino detectors with sensitivity better than the WB-bound at energies > 10¹⁸ eV will test the hypothesis that the UHECR are protons (possibly somewhat heavier nuclei) of extra-Galactic origin. The large effective detector mass, much larger than Giga-ton, required to achieve this sensitivity may be obtained by detectors searching for radio, rather than optical, Cerenkov emission. ”Air shower” detectors, which detect the ”shower” of high energy particles produced in the atmosphere following the interaction of a high energy neutrino in the atmosphere, may also achieve sufficiently large effective mass at ultra-high energy.

The challenge posed by the existence of UHECRs to models of particle acceleration, and the lack of direct evidence for proton acceleration in any extra-Galactic source, have led many to speculate that modifications of the basic laws of physics are required in order to account for the existence of UHECRs. Such ”new physics” models commonly postulate the existence of very massive particles, the decay of which produces the observed UHECRs, and generally predict large fluxes of ~ 10¹⁸ eV neutrinos, well above the WB bound. Measurements of the neutrino flux above ~ 10¹⁹ eV would therefore allow to discriminate between ”new physics” models for UHECR production and models where UHECRs are produced by ”standard physics” acceleration in astrophysical objects, like GRBs and AGN.

Looking inside black hole engines

GRBs and AGN are believed to be powered by the accretion of mass onto black holes. GRBs are most likely powered by the accretion of a fraction of a Solar mass on second time scale onto a newly born Solar mass black hole. Recent observations strongly suggest that the formation of the black hole is associated with the collapse of the core of a very massive star. AGN are believed to be powered by accretion of mass onto massive, million to billion Solar mass, black holes residing at the centers of distant galaxies.

As illustrated in figure 5, the gravitational energy released by the accretion of mass onto the black hole is assumed in both cases to drive a relativistic jet, which travels at nearly the speed of light and produces the observed radiation at a large distance away from the central black hole.

FIG. 5: GRBs and AGN are believed to be powered by black holes. The accretion of mass onto the black hole, through an accretion disk, releases large amounts of gravitational energy. If the black hole is rotating rapidly, another energy source becomes available: The rotational energy may be released by slowing the black hole down through interaction with the accretion disk. The energy released drives a jet-like relativistic outflow. The observed radiation is produced as part of the energy carried by the jets is converted, at large distance from the central black hole, to electromagnetic radiation.

The models describing the physics responsible for powering these objects, though successful in explaining most observations, are largely phenomenological. In particular, the answer to the question of whether or not the out flowing jet carries protons, which has major implications to our understanding of the mechanism by which gravitational energy is harnessed to power the jet, is not known despite many years of photon observations. This situation is common also to our understanding of Galactic micro-Quasars, which may be considered as a scaled down versions of AGN, with ~ 1 Solar mass black hole (or neutron star) ”engines.” Neutrino observations of GRBs, AGN and micro-Quasars will provide new information that can not be obtained using photon observations, and that may allow to answer the underlying open questions.

Neutrino physics with cosmic accelerators

Since neutrinos are expected to be produced in astrophysical sources via the decay of charged pions, production of high-energy muon and electron neutrinos with a 2:1 ratio, as described in eq. (2), is expected. Because of neutrino flavor changes during propagation, usually termed ”neutrino oscillations,” neutrinos that get to Earth are expected to be almost equally distributed between flavors. This implies that one should detect equal numbers of muon-type and tau-type neutrinos. Upgoing taus, rather than muons, would be a distinctive signature of such oscillations.

Although the Cerenkov emission along the track of a high energy tau is similar to that produced by a muon, it may be possible to distinguish between taus and muons in a cubic-km ice or water detector, since at 1000 TeV the tau decays after propagating ~ 1 km. This will allow a ”tau appearance experiment.” At present, the oscillation of muon-type neutrinos to tau-type neutrinos is inferred from the ”disappearance” of muon-type neutrinos produced by cosmic-ray interactions in the atmosphere, without detecting the tau-type neutrinos that should be produced by such oscillation. The detection of taus in a neutrino telescope will provide direct confirmation of the oscillation hypothesis.

Detection of neutrinos from GRBs could be used to test the simultaneity of neutrino and photon arrival to an accuracy of ~ 1 s (~ 1 ms for short bursts), checking the assumption of special relativity that photons and neutrinos have the same limiting speed. These observations would also test the weak equivalence principle, the basic assumption of general relativity, according to which photons and neutrinos should suffer the same time delay as they pass through a gravitational potential. With 1 s accuracy, a fractional difference in limiting speed of 1 part in 10¹⁷ and a fractional difference in gravitational time delay of order 1 in 10⁶ , may be revealed. Previous applications of these ideas to supernova 1987A, where simultaneity could be checked only to an accuracy of order several hours, yielded much weaker upper limits: of order 10^-8 and 10^-2 for fractional differences in the limiting speed and time delay, respectively.

Weakly interacting massive particles: The missing dark matter?

Most of the mass in the universe is currently believed to be in the form of ”dark matter,” composed of particles which were not detected in laboratories on Earth, and which interact with the normal matter that we know essentially only through gravitational forces. Weakly Interacting Massive Particles (WIMPs) are the leading dark matter particle candidates. If WIMPs populate the halo of our galaxy, the Sun or Earth would capture them, where they would annihilate occasionally into high-energy neutrinos. The annihilation rate depends on the details of the model. Gigaton neutrino telescopes currently under construction complement detectors constructed for direct WIMP detection (i.e. detection through WIMP interaction in the detector) by reaching good sensitivity at high WIMP masses, typically in excess of a few hundred GeV.