Chapter 1. High-Energy Astrophysical Neutrinos

Transcription

1 July 9, :42 ws-rv9x6 Book Title trisep halzen page 1 Chapter 1 High-Energy Astrophysical Neutrinos Francis Halzen Wisconsin IceCube Particle Physics Center UW Madison, Madison, WI USA halzen@icecube.wisc.edu Chargeless, weakly-interacting neutrinos are ideal astronomical messengers because y travel through space without scattering, absorption, or deflection. They provide only unobstructed view of cosmic accelerators. But this weak interaction also makes m notoriously difficult to detect, leading to neutrino observatories requiring large-scale detectors. The IceCube experiment discovered PeV-energy neutrinos originating beyond Sun, with energies bracketed by those of TeV-energy gamma rays and EeV-energy extragalactic cosmic rays. In this chapter, we discuss IceCube neutrino telescope, status of observation of cosmic neutrinos, and what neutrinos can tell us about nonrmal Universe. Besides search for sources of Galactic and extragalactic cosmic rays, scientific missions of IceCube and similar instruments under construction in Mediterranean Sea and Lake Baikal include observation of Galactic supernova explosions, search for dark matter, and study of neutrinos mselves. 1

2 July 9, :42 ws-rv9x6 Book Title trisep halzen page 2 2 Francis Halzen Contents 1. Neutrino Astronomy: a Brief History IceCube Detecting Very High-Energy Neutrinos Detector Performance Atmospheric Neutrinos Rationale for Construction of Kilometer-Scale Neutrino Detectors Cosmic-Ray Accelerators Neutrinos and Gamma Rays Associated with Cosmic Rays Neutrinos Associated with Cosmic Ray Accelerators Neutrino-Producing Cosmic Beam Dumps Cosmic Neutrinos and Ultra-High-Energy Cosmic Rays Generic Fireballs Galactic Neutrino-Producing Beam Dumps Cosmogenic Neutrinos Status Of Observations of Cosmic Neutrinos Multimessenger Interfaces IceCube Neutrinos and Fermi Photons IceCube Neutrinos and Ultra-High-Energy Cosmic Rays Pinpointing Astrophysical Sources of Cosmic Neutrinos Are Blazars Sources of Cosmic Neutrinos (and Extragalactic Cosmic rays)? Beyond Astronomy Searching for Dark Matter Neutrino Oscillations New Neutrino Physics Supernovae and Solar Flares IceCube, Facility From Discovery to Astronomy, and more Acknowledgements References

3 July 9, :42 ws-rv9x6 Book Title trisep halzen page 3 High-Energy Astrophysical Neutrinos 3 1. Neutrino Astronomy: a Brief History Soon after 1956 observation of neutrino, 1 idea emerged that it represented ideal astronomical messenger. Neutrinos travel from edge of Universe without absorption and with no deflection by magnetic fields. Having essentially no mass and no electric charge, neutrino is similar to photon, except for one important attribute: its interactions with matter are extremely feeble. So, high-energy neutrinos may reach us unscad from cosmic distances: from inner neighborhood of black holes and from nuclear furnaces where cosmic rays are born. But, ir weak interactions also make cosmic neutrinos very difficult to detect. Immense particle detectors are required to collect cosmic neutrinos in statistically significant numbers. 2 By 1970s, it was clear that a cubic-kilometer detector was needed to observe cosmic neutrinos produced in interactions of cosmic rays with background microwave photons. 3 Subsequent estimates for observing potential cosmic accelerators such as Galactic supernova remnants and gamma-ray bursts unfortunately pointed to same exigent requirement. 4 6 Building a neutrino telescope has been a daunting technical challenge. Given detector s required size, early efforts concentrated on transforming large volumes of natural water into Cherenkov detectors that collect light produced when neutrinos interact with nuclei in or near detector. 7 After a two-decade-long effort, building Deep Underwater Muon and Neutrino Detector (DUMAND) in sea off main island of Hawaii unfortunately failed. 8 However, DUMAND paved way for later efforts by pioneering many of detector technologies in use today, and by inspiring deployment of a smaller instrument in Lake Baikal 9 as well as efforts to commission neutrino telescopes in Mediterranean These efforts in turn have led towards construction of KM3NeT. But first telescope on scale envisaged by DUMAND collaboration was realized instead by transforming a large volume of transparent natural Antarctic ice into a particle detector, Antarctic Muon and Neutrino Detector Array (AMANDA). In operation beginning in 2000, it represented a proof of concept for kilometer-scale neutrino observatory, IceCube. 13,14 Neutrino astronomy has achieved spectacular successes in past: neutrino detectors have seen Sun and detected a supernova in Large Magellanic Cloud in Both observations were of tremendous importance; former showed that neutrinos have mass, opening first crack

4 July 9, :42 ws-rv9x6 Book Title trisep halzen page 4 4 Francis Halzen in Standard Model of particle physics, and latter confirmed basic nuclear physics of death of stars. Fig. 1 illustrates neutrino energy spectrum covering an enormous range, from microwave energies (10 12 ev) to ev. 15 The figure is a mixture of observations and oretical predictions. At low energy, neutrino sky is dominated by neutrinos produced in Big Bang. At MeV energy, neutrinos are produced by supernova explosions; flux from 1987 event is shown. At yet higher energies, figure displays measured atmospheric-neutrino flux, up to energies of 100 TeV by AMANDA experiment. 16 Atmospheric neutrinos are a main player in our story, because y are dominant background for extraterrestrial searches. The flux of atmospheric neutrinos falls dramatically with increasing energy; events above 100 TeV are rare, leaving a clear field of view for extraterrestrial sources. Fig. 1. The cosmic-neutrino spectrum. Sources are Big Bang (CνB), Sun, supernovae (SN), atmospheric neutrinos, active galactic nuclei (AGN) galaxies, and GZK neutrinos. The data points are from detectors at Frejus underground laboratory 17 (red) and from AMANDA 16 (blue).

5 July 9, :42 ws-rv9x6 Book Title trisep halzen page 5 High-Energy Astrophysical Neutrinos 5 The highest energy neutrinos in Fig. 1 are decay products of pions produced by interactions of cosmic rays with microwave photons. 18 Above a threshold of ev, cosmic rays interact with microwave background introducing an absorption feature in cosmic-ray flux, Greisen-Zatsepin-Kuzmin (GZK) cutoff. As a consequence, mean free path of extragalactic cosmic rays propagating in microwave background is limited to roughly 75 megaparsecs, and, refore, secondary neutrinos are only probe of still enigmatic sources at longer distances. What y will reveal is a matter of speculation. The calculation of neutrino flux associated with observed flux of extragalactic cosmic rays is straightforward and yields one event per year in a kilometer-scale detector. The flux, labeled GZK in Fig. 1, shares high-energy neutrino sky with neutrinos anticipated from gamma-ray bursts and active galactic nuclei (AGN). 4 6 A population of cosmic neutrinos covering 30 TeV 1 PeV energy region were revealed by first two years of IceCube data. Association of cosmic neutrinos with se, or any or source candidates, is still a work in progress. The goal of this chapter is to discuss se topics in some detail. Subsequently, it will briefly cover or uses of neutrino telescopes. 2. IceCube 2.1. Detecting Very High-Energy Neutrinos Cosmic rays have been studied for more than a century. They reach energies in excess of 10 8 TeV, populating an extreme universe that is opaque to photons because y interact with background radiation fields. mostly microwave photons, before reaching Earth. We don t yet know where or how cosmic rays are accelerated to se extreme energies, and with recent observation of a blazar in coincidence with direction and time of a very high energy muon neutrino, neutrino astronomy might have taken a first step in solving this puzzle. 19,20 The rationale is however simple: near neutron stars and black holes, gravitational energy released in accretion of matter or binary mergers can power acceleration of protons (p) or heavier nuclei that subsequently interact with gas ( pp ) or ambient radiation ( pγ ). Neutrinos are produced by cosmic-ray interactions at various epochs: in ir sources during ir acceleration, in source environment after ir release, and while propagating through universal radiation backgrounds from source to Earth. In interactions of

6 July 9, :42 ws-rv9x6 Book Title trisep halzen page 6 6 Francis Halzen cosmic-ray protons with background photons (γ bg ), neutral and charged pion secondaries are produced in processes p + γ bg p + π 0 and p+γ bg n+π +. While neutral pions decay as π 0 γ+γ and create a flux of high-energy gamma rays, charged pions decay into three high-energy neutrinos (ν) and anti-neutrinos ( ν) via decay chain π + µ + + ν µ followed by µ + e + + ν µ + ν e, and charged-conjugate process. We refer to se photons as pionic photons to distinguish m from photons radiated by electrons that may be accelerated along with protons and nuclei. Because of ir weak interactions, neutrinos will reach our detectors, unless produced within extremely dense environments. y essentially act like photons; ir small mass is negligible relative to TeV to EeV energies targeted by neutrino telescopes. They do however oscillate over cosmic distances. For instance, for an initial neutrino flavor ratio of ν e : ν µ : ν τ 1 : 2 : 0 from decay of pions and muons, oscillationaveraged composition arriving at detector is approximately an equal mix of electron, muon, and tau neutrino flavors, ν e : ν µ : ν τ 1 : 1 : High-energy neutrinos interact predominantly with matter via deep inelastic scattering off nucleons: neutrino scatters off quarks in target nucleus by exchange of a Z or W weak boson, referred to as neutral current (NC) and charged current (CC) interactions, respectively. Whereas NC interaction leaves neutrino state intact, in a CC interaction a charged lepton is produced that shares initial neutrino flavor. The average relative energy fraction transferred from neutrino to lepton is at level of 80% at se energies. The inelastic CC cross section on protons is at level of cm 2 at a neutrino energy of 10 3 TeV and grows with neutrino energy as σ tot Eν ,23 The struck nucleus does not remain intact and its high-energy fragments typically initiate hadronic showers in target medium. Immense particle detectors are required to collect cosmic neutrinos in statistically significant numbers. Already by 1970s, it had been understood 3 that a kilometer-scale detector was needed to observe cosmogenic neutrinos produced in interactions of CRs with background microwave photons. 24 A variety of methods are used to detect high-energy secondary particles created in CC and NC neutrino interactions. One particularly effective method observes radiation of optical Cherenkov light given off by secondary charged particles produced in CC and NC interactions that travel faster than speed of light in medium. The detection concept is that of a Cherenkov detector, a transparent medium instrumented with photomultipliers that transform Cherenkov light into

7 July 9, :42 ws-rv9x6 Book Title trisep halzen page 7 High-Energy Astrophysical Neutrinos 7 cosmic ray Atmosphere cosmic neutrino IceCube atmospheric muon π-θ ~12,700 km muon up-going down-going cosmic ray atmospheric neutrino Cherenkov light detection in optical modules Fig. 2. The principal idea of neutrino telescopes from point of view of IceCube located at South Pole. Neutrinos dominantly interact with a nucleus in a transparent medium like water or ice and produce a muon that is detected by wake of Cherenkov photons it leaves inside detector. The background of high-energy muons (solid blue arrows) produced in atmosphere can be reduced by placing detector underground. The surviving fraction of muons is furr reduced by looking for upgoing muon tracks that originate from muon neutrinos (dashed blue arrows) interacting close to detector. This still leaves contribution of muons generated by atmospheric muon neutrino interactions. This contribution can be separated from diffuse cosmic neutrino emission by an analysis of combined neutrino spectrum. electrical signals using photoelectric effect; see Figs. 2 and 3. IceCube consists of 80 strings, each instrumented with inch photomultipliers spaced by 17 m over a total length of 1 kilometer. The deepest module is located at a depth of km so that instrument is shielded from large background of cosmic rays at surface by approximately 1.5 km of ice. Strings are arranged at apexes of equilateral triangles that are 125 m on a side. The instrumented detector volume is a cubic kilometer of dark, highly transparent and sterile Antarctic ice. Radioactive background is dominated by instrumentation deployed into this natural ice. Each optical sensor consists of a glass sphere containing photomultiplier and electronics board that digitizes signals locally using an on-board computer. The digitized signals are given a global time stamp with residuals accurate to less than 3 ns and are subsequently transmitted to surface. Processors at surface continuously collect se time-stamped signals from optical modules, each of which functions

8 July 9, :42 ws-rv9x6 Book Title 8 Fig. 3. trisep halzen Francis Halzen Sketch of IceCube observatory (left) and digital optical module (right). independently. The digital messages are sent to a string processor and a global event trigger. They are subsequently sorted into Cherenkov patterns emitted by secondary muon tracks, or electron and tau showers, that reveal flavor, energy and direction of incident neutrino.25 There are two principle classes of Cherenkov events that can be easily identified this way, tracks and cascades as illustrated in Fig. 4. There are two basic topologies: tracks from νµ and cascades from νe, ντ, and neutral current interactions from all flavors. On scale of IceCube, PeV cascades have a length of less than 10 m and are refore point sources of Cherenkov light in a detector of kilometer size. The term tracks refers to Cherenkov emission of long-lived muons passing through detector. These muons can be produced in CC interactions of muon neutrinos inside or in vicinity of detector. Energetic electrons and taus produced in CC interactions of electron and tau neutrino interactions, respectively, will in general not produce elongated tracks due to rapid scattering of electrons and short lifetime of tau. Because of large background of muons produced by CR interactions in atmosphere, observation of muon neutrinos is limited to upgoing muon tracks that are produced in interactions inside or close to detector by neutrinos that have passed through Eartha as illustrated in Fig. 2. The remaining background consists of atmospheric neutrinos, which are indistinguishable from cosmic neutrinos on an event-by-event basis. However, steeply falling spectrum a Note, that while at high-energy neutrino cross section grows, resulting in a reduced mean free path (λν ), range of secondary muon (λµ ) increases as does probability for observing a muon, λµ /λν ; it is about 10 6 for a 1 TeV neutrino. page 8

9 July 9, :42 ws-rv9x6 Book Title trisep halzen page 9 High-Energy Astrophysical Neutrinos 9 Fig. 4. Contrasting Cherenkov light patterns produced by muons (left) and by showers initiated by electron and tau neutrinos (right) and by neutral current interactions. The patterns are routinely referred to as tracks and cascades (or showers). Cascades are produced by radiation of particle showers, whose dimensions are in tens of meters, i.e., an approximate point source of light with respect to dimensions of detector. ( E 3.7 ) of atmospheric neutrinos allows identifying diffuse astrophysical neutrino emission above a few hundred TeV by a spectral analysis, as we will highlight in following sections. The atmospheric background is also reduced for muon neutrino observation from point-like sources, in particular transient neutrino sources. The hadronic particle shower generated by target struck by a neutrino in ice also radiates Cherenkov photons. Because of large multiplicity of secondary particles and repeated scattering of Cherenkov photons in medium, light pattern is mostly spherical; it is referred to as a cascade. The light patterns produced by particle showers initiated by electron or tau produced in CC interactions of electron or tau neutrinos, respectively, will be superimposed on cascade. The direction of initial neutrino can only be reconstructed from Cherenkov emission of secondary particles produced close to neutrino interaction point, and angular resolution is worse than for track events. On or hand, energy of initial neutrino can be constructed with a better resolution than for tracks. For both tracks and cascades, observable energy of secondary charged leptons can be estimated from total number of Cherenkov photons and is related to neutrino energy of charged particles after accounting for kinematic effects and detection efficiencies. The Cherenkov light observed in cascades is proportional to

10 July 9, :42 ws-rv9x6 Book Title trisep halzen page Francis Halzen energy transferred to cascade and can be fully contained in instrumented volume. In contrast, muons produced by CC muon neutrino interactions lose energy gradually by ionization, bremsstrahlung, pair production, and photo-nuclear interactions while y range our passing through detector. This allows estimating muon energy as it enters detector and setting a lower limit on neutrino energy. Using Standard Model physics, one can subsequently derive a probability distribution for energy of initial neutrino that determines its most probable value. The neutrino energy may only be determined within a factor of 2 or reabout, depending on energy, but uncertainties drop out when measuring a neutrino spectrum involving multiple events. Muons range out, over kilometers at TeV energy to tens of kilometers at EeV energy, generating showers along ir track by bremsstrahlung, pair production, and photonuclear interactions. The charged particles produced are sources of additional Cherenkov radiation. Because energy of muon degrades along its track, energy of secondary showers decreases, which reduces distance from track over which associated Cherenkov light can trigger a PMT. The geometry of light pool surrounding muon track is refore a kilometer-long cone with a gradually decreasing radius. In its first kilometer, a high-energy muon typically loses energy in a couple of showers having one-tenth of muon s initial energy. So initial radius of cone is radius of a shower with 10% of muon energy. At lower energies of hundreds of GeV and less, muon becomes minimum-ionizing. Because of stochastic nature of muon s energy loss, relationship between observed energy loss inside detector and muon energy varies from muon to muon. Additionally, only muon energy lost in detector can be determined; we do not know its energy loss before entering instrumented volume nor how much energy it carries out upon exiting. An unfolding process is required to determine neutrino energy based on observed muon energy; fortunately, it is based on well-understood Standard Model physics. In contrast, for ν e and ν τ, detector is a total energy calorimeter, and determination of ir energy is superior. The different topologies each have advantages and disadvantages. For ν µ interactions, long lever arm of muon tracks, up to tens of kilometers at very high energies, allows muon direction (and neutrino direction) to be determined accurately with an angular resolution measured online that is better than 0.4. Superior angular resolution can be reached for selected events. Sensitivity to point sources is refore better as well.

11 July 9, :42 ws-rv9x6 Book Title trisep halzen page 11 High-Energy Astrophysical Neutrinos 11 The disadvantages are a large background, of atmospheric neutrinos below 100 TeV and cosmic-ray muons at all energies, and indirect determination of neutrino energy that must be inferred from sampling energy loss of muon when it transits detector. Observation of ν e and ν τ flavors represents significant advantages. They are detected from both Norrn and Sourn Hemispheres. (This is also true for ν µ with energy in excess of several hundred TeV, where background from steeply falling atmospheric spectrum becomes negligible.) At TeV energies and above, background of atmospheric ν e is lower by over an order of magnitude, and re are essentially no atmospheric ν τ produced. High energy atmospheric ν τ are of cosmic origin (one such clear event has been observed and a complete analysis is in progress). At higher energies, long-lived pions, source of atmospheric ν e, no longer decay, and relatively rare K-decays become dominant source of background ν e. Furrmore, because neutrino events are totally, or at least partially, contained inside instrumented detector volume, neutrino energy is determined by total-absorption calorimetry. One can establish cosmic origin of a single event by demonstrating that energy cannot be reached by muons and neutrinos of atmospheric origin. Finally, ν τ are not absorbed by Earth: 26 ν τ interacting in Earth produce secondary ν τ of lower energy, eir directly in a neutral current interaction or via decay of a secondary tau lepton produced in a chargedcurrent interaction. High-energy ν τ will thus cascade down to energies of hundred of TeV where Earth becomes transparent. In or words, y are detected with a reduced energy but not absorbed. Although cascades are nearly pointlike and, in practice, spatially isotropic, pattern of arrival times of photons at individual optical modules reveals direction of secondary leptons with 3. While a fraction of cascade events can be reconstructed accurately to within a degree, 27 precision is inferior to that reached for ν µ events and typically not better than 10 using present techniques. At energies above about 100 PeV, electromagnetic showers begin to elongate because of Landau-Pomeranchuk-Migdal effect. 28 An extended length scale is associated with abundant radiation of soft photons that results in interactions of shower particles on two target atoms. Negative interference in this process results in reduced energy loss.

12 July 9, :42 ws-rv9x6 Book Title trisep halzen page Francis Halzen 2.2. Detector Performance Cosmic neutrinos must be separated from large backgrounds of atmospheric neutrinos and atmospheric cosmic-ray muons. This is possible for two classes of events: neutrinos that interact inside instrumented volume ( starting events ) and events where a muon enters detector from below, created by a neutrino traversing Earth (throughgoing events), thus pointing back to its origin. In this latter case, Earth is used as a filter for cosmic-ray muons. For starting events, pathlength l(θ) traversed within detector volume by a neutrino with zenith angle θ is determined by detector s geometry. Neutrinos are detected if y interact within detector volume, i.e., within instrumented volume of one cubic kilometer. That probability is P (E ν ) = 1 exp[ l/λ ν (E ν )] l/λ ν (E ν ), (1) where λ ν (E ν ) = [ρ ice N A σ νn (E ν )] 1 is mean free path in ice for a neutrino of energy E ν. Here, ρ ice = 0.9 g cm 3 is density of ice, N A = is Avogadro s number, and σ νn (E ν ) is neutrinonucleon cross section. A neutrino flux dn/de ν (neutrinos per GeV per cm 2 per second) crossing a detector with energy threshold and cross sectional area A(E ν ) facing incident beam will produce N ev = T E th ν A(E ν ) P (E ν ) dn de ν de ν (2) events after a time T. The effective detector area A(E ν ) is also a function of zenith angle θ. It isn t strictly equal to geometric cross section of instrumented volume facing incoming neutrino, because even neutrinos interacting outside instrumented volume may produce enough light inside detector to be detected. In practice, A(E ν ) is determined as a function of incident neutrino direction and zenith angle by a fulldetector simulation, including trigger. This formalism applies to contained events. For muon neutrinos, any neutrino producing a secondary muon that reaches detector (and has sufficient energy to trigger it) will be detected. Because muon travels kilometers at TeV energy and tens of kilometers at PeV energy, neutrinos can be detected outside instrumented volume; probability is obtained by substitution in Eq. 1, l λ µ, (3)

13 July 9, :42 ws-rv9x6 Book Title trisep halzen page 13 High-Energy Astrophysical Neutrinos 13 reby giving, P = λ µ /λ ν. (4) Here, λ µ is range of muon determined by its energy losses. Values for neutrino nucleon cross section and range of muon can be found in Ref. 29 The complete expression for flux of ν µ -induced muons at detector is given by a convolution of neutrino spectrum φ (= dn/de ν ) with probability P to produce a muon reaching detector: 4 6 φ µ (Eµ min, θ) = P (E ν, Eµ min ) exp[ σ tot (E ν ) N A X(θ)] φ(e ν, θ)de ν. E min µ (5) The additional exponential factor accounts for absorption of neutrinos along a chord of Earth of length X(θ) at zenith angle θ. Absorption becomes important for σ ν (E ν ) cm 2 or E ν 100 TeV. For back-of-envelope calculations, P -function can be approximated by P E 2.2 for E = TeV, (6) E 0.8 for E = TeV. (7) At EeV energy, increase is reduced to only E 0.4. Clearly, high-energy neutrinos are more likely to be detected because of increase with energy of both cross section and muon range. Tau neutrinos interacting outside detector can be observed provided tau lepton y produce reaches instrumented volume within its lifetime. In Eq. 1, l is replaced by l γcτ = E/mcτ, (8) where m, τ, and E are mass, lifetime, and energy of tau, respectively. The tau s decay length λ τ = γcτ 50 m (E τ /10 6 ) GeV grows linearly with energy and actually exceeds range of muon near 1 EeV. At yet higher energies, tau eventually ranges out by catastrophic interactions, just like muon, despite reduction of energy-loss cross sections by a factor of (m µ /m τ ) 2. Tracks and showers produced by tau neutrinos are difficult to distinguish from those initiated by muon and electron neutrinos, respectively. To be clearly identified, both initial neutrino interaction and subsequent tau decay must be contained within detector; for a cubic- kilometer detector, this happens for neutrinos with energies from a few PeV to a few tens of PeV. 30 For an in-depth discussion of neutrino detection, energy measurement, and flavor separation, and for detailed references, see IceCube Preliminary Design Document 13 and Ref. 2

14 July 9, :42 ws-rv9x6 Book Title trisep halzen page Francis Halzen 2.3. Atmospheric Neutrinos Muons and neutrinos from decay of mesons produced by cosmic-ray interactions in atmosphere are background in search for neutrinos of extraterrestrial origin. The 3 khz trigger rate of IceCube is dominated by atmospheric muons from decay of pions and kaons produced in atmosphere above detector. The distribution peaks near zenith and decreases with increasing angle as muon energy required to reach deep detector increases. Most atmospheric muons are easily identified as entering tracks from above and rejected. Because of large ratio of muons to neutrinos, however, misreconstructed atmospheric muons remain an important source of background for all searches. Measurement of spectrum of atmospheric neutrinos is an important benchmark for a neutrino telescope. IceCube detects an atmospheric neutrino every six minutes. The spectrum of atmospheric ν µ has been measured by unfolding measured rate and energy deposition of neutrinoinduced muons entering detector from below horizon, 31 as shown in Fig. 9. More challenging is measurement of flux of atmospheric electron neutrinos. This has been done by making use of DeepCore, more densely instrumented subarray in deep center of IceCube, to identify contained shower events. The known spectrum of ν µ is used to calculate contribution of neutral current interactions to observed rate of showers. Subtracting neutral current contribution leads to measurement of spectrum of atmospheric electron neutrinos from 100 GeV to 10 TeV, 32 as shown in Fig. 9. In general, atmospheric neutrinos are indistinguishable from astrophysical neutrinos. An important exception occurs in case of muon neutrinos from above when neutrino energy is sufficiently high and zenith angle sufficiently small that muon produced in same decay as neutrino is guaranteed to reach detector. 33 This is used to reject atmospheric neutrinos in analyses where y are a background. Monte Carlo simulation can be used to evaluate atmospheric neutrino passing rate more generally by also including or high-energy muons produced in same cosmic-ray shower as neutrino. In this way, method can be extended to electron neutrinos. In practice, passing rate is significantly reduced for zenith angles θ < 70 and E ν > 100 TeV. The spectrum of atmospheric neutrinos becomes one power steeper than spectrum of primary nucleons at high energy as competition between interaction and decay of pions and kaons increasingly suppresses ir decay.

15 July 9, :42 ws-rv9x6 Book Title trisep halzen page 15 High-Energy Astrophysical Neutrinos 15 For dominant kaon channel, characteristic energy for steepening is E ν 1 TeV/ cos θ. A furr steepening occurs above 100 TeV as a consequence of knee in primary spectrum. Astrophysical neutrinos should reflect cosmic-ray spectrum in source and are refore expected to have a significantly harder spectrum than atmospheric neutrinos. Establishing an astrophysical signal above steep atmospheric background requires an understanding of atmospheric neutrino spectrum around 100 TeV and above. Although re is some uncertainty associated with composition through knee region, 34 major uncertainty in spectrum of atmospheric neutrinos at high energy is level of charm production. The short lived charmed hadrons preferentially decay up to a characteristic energy of 10 7 GeV, producing prompt muons and neutrinos with same spectrum as ir parent cosmic rays. This prompt flux of leptons has not yet been measured. Existing limits 35,36 allow a factor of two or three around level predicted by a standard calculation 37 (after correction for steepening at knee). For reasonable assumptions, charm contribution is expected to dominate conventional spectrum above 10 TeV for ν e, above 100 TeV for ν µ, and above 1 PeV for muons. 38 The expected hardening in spectrum of atmospheric neutrinos due to prompt neutrinos is partially degenerate with a hard astrophysical component. However, spectrum of astrophysical neutrinos should reflect spectrum of cosmic rays at ir sources, which is expected to be harder than spectrum of cosmic rays at Earth. It should eventually be possible with IceCube to measure charm contribution by requiring a consistent interpretation of neutrino flavors and cosmic-ray muons for which re is no astrophysical component. An additional signature of atmospheric charm is absence of seasonal variations for this component Rationale for Construction of Kilometer-Scale Neutrino Detectors The construction of kilometer-scale neutrino detectors was primarily motivated by prospect of detecting neutrinos associated with sources of high-energy cosmic rays. Cosmic accelerators produce particles with energies in excess of 100 EeV; we still do not know where or how; 40 see Fig. 5 b. b We will use energy units TeV, PeV and EeV, increasing by factors of 1000 from GeV energy.

16 July 9, :42 ws-rv9x6 Book Title trisep halzen page Francis Halzen The bulk of cosmic rays are Galactic in origin. Any association with our Galaxy presumably disappears at EeV energy when gyroradius of a proton in Galactic magnetic field exceeds its size. The cosmic-ray spectrum exhibits a rich structure above an energy of 0.1 EeV, but where exactly transition to extragalactic cosmic rays occurs is a matter of debate Knee sr -1 ] 1.6 m -2 s -1 F(E) [GeV 2.6 E Grigorov JACEE MGU Tien-Shan Tibet07 Akeno CASA-MIA HEGRA Fly s Eye Kascade Kascade Grande IceTop-73 HiRes 1 HiRes 2 Telescope Array Auger 2nd Knee Ankle E [ev] Fig. 5. At energies of interest here, cosmic-ray spectrum follows a sequence of three power laws. The first two are separated by knee, second and third by ankle. Cosmic rays beyond ankle are a new population of particles produced in extragalactic sources. Note that spectrum F (E)(= dn/de) has been multiplied by a power E 2.7 in order to visually enhance structure in spectrum (data compiled by Particle Data Group 29 ) Cosmic-Ray Accelerators The detailed blueprint for a cosmic-ray accelerator must meet two challenges: highest-energy particles in beam must reach energies beyond 10 3 TeV (10 8 TeV) for Galactic (extragalactic) sources and ir luminosities must accommodate observed flux. Both requirements represent severe constraints that have guided oretical speculations. Acceleration of protons (or nuclei) to TeV energy and above requires massive bulk flows of relativistic charged particles. The blueprint of accelerator can be copied from solar flares where particles are accelerated to GeV energy by

17 July 9, :42 ws-rv9x6 Book Title trisep halzen page 17 High-Energy Astrophysical Neutrinos 17 shocks and, possibly, reconnection; see Fig. 6. Requiring that gyroradius of accelerated particle be contained within accelerating B-field region, E/ZecB R, leads to an upper limit on energy of particle, E Ze c B R. (9) Reaching energies much above 10 GeV in solar flares is dimensionally impossible. In a solar flare, extent R of accelerating region and magnitude of magnetic fields B are not large enough to accelerate particles of charge Ze to energies beyond GeV; ir velocity is taken to be speed of light, c. The central idea for accommodating higher energies of Galactic and extragalactic cosmic rays observed is that a fraction of gravitational energy released in a stellar collapse is converted into particle acceleration, presumably by shocks. Baade and Zwicky 41 suggested as early as 1934 that supernova remnants could be sources of Galactic cosmic rays. It is assumed that, after collapse, erg of energy is transformed into particle acceleration by diffusive shocks associated with young ( 1000 year old) supernova remnants expanding into interstellar medium. Like a snowplow, shock sweeps up 1 proton/cm 3 density of hydrogen in Galactic plane. The accumulation of dense filaments of particles in outer reaches of shock, clearly visible as sources of intense X-ray emission, are sites of high magnetic fields; see Fig. 7. It is orized that particles crossing se structures multiple times can be accelerated to high energies following an approximate power-law spectrum dn/de E 2. The mechanism copies solar flares where filaments of high magnetic fields, visible in Fig. 6, are sites for accelerating nuclear particles to tens of GeV. The higher energies reached in supernova remnants are consequence of particle flows of much larger intensity powered by gravitational energy released in stellar collapse. This idea has been widely accepted despite fact that to date no source has been conclusively identified, neir by cosmic rays nor by accompanying gamma rays and neutrinos produced when cosmic rays interact with Galactic hydrogen. Galactic cosmic rays reach energies of at least several PeV, knee in spectrum; refore, ir interactions should generate gamma rays and neutrinos from decay of secondary pions reaching hundreds of TeV. Such sources, referred to as PeVatrons, have not been found; see, however, Ref. 42 Neverless, Zwicky s suggestion has become stuff of textbooks, and reason is energetics: three Galactic

18 July 9, :42 ws-rv9x6 Book Title trisep halzen page Francis Halzen Fig. 6. Opportunities exist near intense charged particle flows, seen as filaments in this X-ray picture of a solar flare, for solar particles to accelerate to GeV energy. supernova explosions per century converting a reasonable fraction of a solar mass into particle acceleration can accommodate steady flux of cosmic rays in Galaxy. It is interesting to note that Zwicky originally assumed that sources were extragalactic since most recent supernova in Milky Way was in After diffusion in interstellar medium was understood, supernova explosions in Milky Way became source of choice for origin of Galactic cosmic rays, 43 although after more than 50 years issue is still debated. 44 Energetics also guides speculations on origin of extragalactic cosmic rays. By integrating cosmic-ray spectrum above ankle at 4 EeV, it is possible to estimate 45 energy density in extragalactic cosmic rays as erg cm 3. This value is rar uncertain because of our ignorance of energy where transition from Galactic to extragalactic

19 July 9, :42 ws-rv9x6 Book Title trisep halzen page 19 High-Energy Astrophysical Neutrinos 19 Fig. 7. This X-ray picture of supernova remnant CasA reveals strong particle flows near its periphery. We believe y are site for accelerating Galactic cosmic rays to energies reaching knee in spectrum. sources occurs. The power required for a population of sources to generate this energy density over Hubble time of years is erg s 1 per Mpc 3. Long-duration gamma-ray bursts have been associated with collapse of massive stars to black holes, and not to neutron stars, as is case in a collapse powering a supernova remnant. A gamma-ray-burst fireball converts a fraction of a solar mass into acceleration of electrons, seen as synchrotron photons. The observed energy in extragalactic cosmic rays can be accommodated with reasonable assumption that shocks in expanding gamma-ray burst (GRB) fireball convert roughly equal energy into acceleration of electrons and cosmic rays. 46 It so happens that erg per GRB will yield observed energy density in cosmic rays after years, given that ir rate is on order of 300 per Gpc 3 per year. Hundreds of bursts per year over a Hubble time produce observed cosmic-ray density, just as three supernovae per century accommodate steady flux in Galaxy. Problem solved? Not really: it turns out that same result can be achieved assuming that active galactic nuclei convert, on average, erg s 1 each into particle acceleration. 15 This is an amount that matches ir output in electromagnetic radiation. An active galactic nucleus (AGN) is center of a galaxy that hosts a supermassive black hole.

20 July 9, :42 ws-rv9x6 Book Title trisep halzen page Francis Halzen Fig. 8. Colliding shocks in simulation of a gamma-ray burst (GRB) fireball may accelerate cosmic rays to highest energies observed. The filaments in particle flow are directed along rotation axis of black hole. Animated view at We will return to this point furr on Neutrinos and Gamma Rays Associated with Cosmic Rays Neutrinos will be produced at some level in association with cosmic-ray beam. Cosmic rays accelerated in regions of high magnetic fields near black holes or neutron stars inevitably interact with radiation surrounding m. Thus, cosmic-ray accelerators are also beam dumps producing neutrino beams. The method is what is used for production of neutrino beams at accelerator laboratories: beam is dumped in a dense target where it produces pions and kaons that decay into neutrinos. All particles are absorbed in extended target except for neutrinos. Cosmic rays accelerated in supernova shocks interact with gas in Galactic disk, producing equal numbers of pions of all three charges that decay into pionic photons and neutrinos. A larger source of secondaries is likely to be gas near sources, for example cosmic rays interacting with high-density molecular clouds that

21 July 9, :42 ws-rv9x6 Book Title trisep halzen page 21 High-Energy Astrophysical Neutrinos 21 [GeV cm 2 s 1 sr 1 ] 2 ν Φ ν E conventional ν e This Work ν e conventional ν µ Super K ν µ Frejus ν µ Frejus ν e AMANDA ν µ unfolding forward folding IceCube ν µ unfolding forward folding prompt ν µ, ν e Galactic Supernovae GRB GZK log (E [GeV]) 10 ν 8 9 Fig. 9. Anticipated astrophysical neutrino fluxes compared with measured and calculated fluxes of atmospheric neutrinos. Measurements of ν µ from Super-K, 47 Frejus, 48 AMANDA, 49,50 and IceCube 31,51 are shown along with electron-neutrino spectrum at high energy from Ref. 32 (green open triangles). Calculations of conventional ν e (red line) and ν µ (blue line) from Honda et al., 52 ν e (red dotted line) from Bartol, 53 and charm-induced neutrinos (magenta band) 37 are also shown. are ubiquitous in star-forming regions where supernovae are more likely to explode. For extragalactic sources, neutrino-producing target may be electromagnetic, for instance photons radiated by accretion disk of an AGN, or synchrotron photons that coexist with protons in expanding fireball producing a GRB. In Fig. 9, estimates of astrophysical neutrino fluxes are compared with measurements of atmospheric neutrinos. The shaded band indicates level of model-dependent expectations for highenergy neutrinos of astrophysical origin. The estimates that we will discuss in more detail furr on optimistically predicted a neutrino flux at a level of E 2 ν dn ν /de ν 10 8 GeV cm 2 s 1 sr 1 (10)

22 July 9, :42 ws-rv9x6 Book Title trisep halzen page Francis Halzen per flavor and formed rationale for building a kilometer-scale detector; this is indeed magnitude of cosmic component of neutrino spectrum above 100 TeV revealed by IceCube s data. How many neutrinos and, inevitably, gamma rays are produced in association with cosmic-ray beam? Generically, a cosmic-ray source should also be a beam dump. Cosmic rays accelerated in regions of high magnetic fields near black holes may interact with radiation surrounding m, e.g., UV photons in some active galaxies or MeV photons in GRB fireballs. In se interactions, neutral and charged pion secondaries are produced by processes p + γ + π 0 + p and p + γ + π + + n. (11) While secondary protons may remain trapped and lose energy in high magnetic fields, neutrons and decay products of neutral and charged pions escape with high energy. The energy escaping source is refore distributed among cosmic rays, gamma rays and neutrinos, particles produced by decay of neutrons, neutral pions and charged pions, respectively. Galactic supernova shocks are in contrast an example of a hadronic beam dump. Cosmic rays mostly interact with hydrogen in Galactic disk, producing equal numbers of pions of all three charges in hadronic collisions p + p n π [ π 0 + π + + π ] + X; n π is pion multiplicity. In a generic cosmic beam dump, accelerated cosmic rays, assumed to be protons for illustration, interact with a photon target. These may be photons radiated by accretion disk in AGNs and synchrotron photons that co-exist with protons in exploding fireball producing a GRB. Their interactions produce charged and neutral pions according to Eq. 11, with probabilities of 2/3 and 1/3, respectively. Subsequently, pions decay into gamma rays and neutrinos that carry, on average, 1/2 and 1/4 of energy of parent pion. We furr assume that, on average, four leptons in decay π + ν µ + µ + ν µ + (e + + ν e + ν µ ) equally share charged pion s energy. The energy of pionic leptons relative to proton is: and x ν = E ν E p = 1 4 x p π 1 20 (12) x γ = E γ E p = 1 2 x p π (13)

23 July 9, :42 ws-rv9x6 Book Title trisep halzen page 23 High-Energy Astrophysical Neutrinos 23 Here, x p π = E π E p 0.2 (14) is average energy transferred from proton to pion. While both gamma-ray and neutrino fluxes can be calculated knowing density of accelerated protons and density of target material, ir relative flux is independent of details of production mechanism. The spectral production rates dn/dedt of neutrinos and gamma rays are related by 1 dn ν E ν 3 de ν ν dt (E ν) K π 2 E dn γ γ de γ dt (E γ). (15) α Here, N and E denote number and energy of neutrinos and gamma rays and ν stands for neutrino flavor. Note that this relation is solid and depends only on charged-to-neutral secondary pion ratio, with K π = 1(2) for γ(pp) neutrino-producing interactions. In deriving relative number of neutrinos and gamma rays, one must be aware of fact that neutrino flux represents sum of neutrinos and antineutrinos, which cannot be separated by current experiments: in short, a π 0 produces two γ rays for every charged pion producing a ν µ + ν µ pair. A more formal derivation of this relation will be given in Section 7. The production rate of gamma rays described by Eq. 15 is not necessarily emission rate observed. For instance, in cosmic accelerators that efficiently produce neutrinos via pγ interactions, target photon field can also efficiently reduce pionic gamma rays via pair production. This is a calorimetric process that will, however, conserve total energy of hadronic gamma rays. The production of photons in association with cosmic neutrinos is inevitable. The relation is however calorimetric; unlike neutrinos, photons reach Earth after propagation in universal microwave and infrared photon backgrounds to reach our telescopes with TeV energy, or below. Also, one must be aware of fact that inverse- Compton scattering and synchrotron emission by accelerated electrons in magnetic fields in source have potential to produce gamma rays; not every high-energy gamma ray is pionic. The estimates in Fig. 9 of neutrino flux associated with cosmic rays accelerated in supernova remnants and GRBs are relatively straightforward as both beam, identified with observed cosmic-ray flux, and targets, observed by astronomers, are known. In case of supernova remnants, main uncertainty is availability of nearby target material.

24 July 9, :42 ws-rv9x6 Book Title trisep halzen page Francis Halzen In case of GRBs, main uncertainty is fraction of extragalactic cosmic ray population that comes from this source. The ongoing search by IceCube for neutrinos in coincidence with and in direction of GRB alerts issued by astronomical telescopes has limited GRB neutrino flux to less that 1% of diffuse cosmic neutrino flux actually observed by experiment. 54,55 However, this may not conclusively rule out GRBs as a source of cosmic rays; events that produce spectacular photon displays catalogued by astronomers as GRBs may not be stellar collapses that are sources of high-energy neutrinos. We will return to this point furr on when we discuss acceleration of cosmic rays in GRB fireballs. Neverless, failure of IceCube to observe neutrinos from GRBs has lately promoted AGNs as best-bet source of cosmic neutrinos observed. Active galaxies are complex systems with many possible sites for accelerating cosmic rays and for targets to produce neutrinos. First, if acceleration occurs mainly at spectacular termination shocks of jets in intergalactic space, 56 re would be little target material available and few neutrinos produced. In contrast, production of neutrinos near black hole, 57 or in collisions with interstellar matter of accelerated particles diffusing in magnetic field of galaxy hosting black hole, 58 could yield fluxes at level observed. We will work through se examples furr on. One generic picture in which neutrino luminosity is directly related to contribution of sources to extragalactic cosmic rays arises if acceleration occurs in jets of AGNs (or GRBs). 59,60 High-energy protons interact in intense radiation fields inside jets. In pγ pπ 0 channel, protons remain in accelerator. In pγ nπ + channel, however, neutrons escape and eventually decay to produce cosmic-ray protons, while pions decay to neutrinos. The luminosity of neutrinos from photo-pion production is n directly related by kinematics to cosmic-ray protons that come from decay of escaping neutrons. TeV gamma rays are measured from many AGN blazars. 62 Although observed gamma rays are likely to be from accelerated electrons, which radiate more efficiently than protons, gamma-ray luminosity may give an indication of overall cosmic-ray luminosity and hence of possible level of neutrino production. 63,64 In this context, we introduce Fig showing IceCube upper limits 61 on neutrino flux from nearby AGNs as a function of ir distance. The sources at red shifts between 0.03 and 0.2 are Norrn Hemisphere blazars for which distances and intensities are listed

25 July 9, :42 ws-rv9x6 Book Title trisep halzen page 25 High-Energy Astrophysical Neutrinos 25 1e+46 1e+45 TeVCat IC40+IC59 limits Luminosity estimate (erg/s) 1e+44 1e+43 1e+42 1e+41 Cen A 1ES M87 1e Red shift z Fig. 10. Limits on neutrino flux from selected active galaxies derived from IceCube data taken during construction, when instrument was operating with 40 and 59 strings of total 86 instrumented strings of DOMs. 61 These are compared with TeV photon flux for nearby AGNs. Note that energy units are in ergs, not TeV. in TeVCat 62 and for which IceCube also has upper limits. In several cases, muon-neutrino limits have reached level of TeV photon flux. One can sum sources shown in figure into a diffuse flux. The result, after accounting for distances and luminosities, is GeV cm 2 s 1 sr 1, or approximately 10 8 GeV cm 2 s 1 sr 1 for all neutrino flavors. This is at level of generic astrophysical neutrino flux of Eq. 10. At this intensity, neutrinos from orized cosmic-ray accelerators will cross steeply falling atmospheric neutrino flux above an energy of 300 TeV; see Fig. 9. The level of events observed in a cubic-kilometer neutrino detector is ν µ -induced events per year. Such estimates reinforce logic for building a cubic kilometer neutrino detector. 66

26 July 9, :42 ws-rv9x6 Book Title trisep halzen page Francis Halzen 4. Neutrinos Associated with Cosmic Ray Accelerators In this section we will introduce generic framework used to calculate neutrino flux associated with a astronomical source that accelerate a proton beam to energies exceeding threshold for producing pions that decay into neutrinos. Next, we will apply formalism to three examples: production of neutrinos in active galaxies when protons accelerated near black hole interact with nearby gas or radiation fields, production of neutrinos in interactions of Galactic cosmic rays with nearby gas or molecular clouds, and, finally, production of neutrinos when protons interact with photons in relativistically expanding fireball following stellar collapse, such as in a gamma ray burst Neutrino-Producing Cosmic Beam Dumps Neutrinos are produced when pions, and, at higher energies, kaons and charm particles decay. We start by calculating number of pions produced when an accelerated proton beam interacts with a target of density n in its vicinity. We introducing source function q π (E π ) defined such that q π (E π ) de π represents rate at which pions are produced within energy range E π and E π + de π per time: q π = dn π de π dt = de p τ 0 dτ dn p e τ dn π (E π ). (16) de p de π Here a proton beam, with a flux dn/de p, in units GeV 1 cm 2 s 1, is absorbed in a target with optical depth τ producing secondary pions with an energy distribution dn π /de π, normalized to unity. In case that all pions are produced with same energy dn π (E p ) de π = n π ± δ (E π E π ), (17) where we assume that a multiplicity of n π secondary pions are produced with average energy < E π >. The optical depth of target is τ = exp( l 0 dr α (r )), (18) where l is path length of beam in a target and α is attenuation coefficient ( inverse of mean-free path λ) which is determined by cross section and density n α = nσ, (19)

27 July 9, :42 ws-rv9x6 Book Title trisep halzen page 27 High-Energy Astrophysical Neutrinos 27 and, assuming isotropy, τ = nlσ = Nσ, (20) where N is optical depth. Typically, one also makes approximation that proton cross section is independent of energy, σ cm 2 and refore integrals over τ and E p separate: q π ± = (1 exp( τ)) de p dn p de p n π δ (E π E π ), (21) In most astrophysical situations, where optical depth is small, pion production efficiency (1 exp( τ)) τ, with τ = l n σ. The integral can be performed by rewriting delta function as a function of E p. Each time a proton interacts, it deposits K p E p energy into n π pions of average energy E π ; here, K p is total proton inelasticity. Energy conservation implies that K p E p = E tot π = n π ± E π. (22) It is common to introduce at is point energy fraction f π of pions relative to proton beam We obtain result that q π ± = τ n π or f π = E π E p = K p n π. (23) de p dn p de p δ (E π f π E p ), (24) ( ) 1 dn p Eπ q π ± = N σ n π. (25) f π de p f π The result is transparent: pion source function is proportional to intensity of intensity of proton beam, optical depth of target and cross section, and multiplicity of pions produced. We are now able to compute rate at which sources are produced, with total rate at source given by sum of emissivities of first muon neutrino, directly from pion, and those of second muon neutrino and electron neutrino from muon decay: q ν,tot = q (1) ν µ + q (2) ν µ + q νe. (26) As previously discussed, we will make approximation that total energy of pions is distributed equally among four decay leptons (see e.g., Ref. 67 ), q νi (E νi ) = q π (4E νı )de π /de νi = 4q π (4E νi ) (27)

28 July 9, :42 ws-rv9x6 Book Title trisep halzen page Francis Halzen for each neutrino, ν i = ν e or ν e, ν µ, ν µ. As IceCube does not distinguish between neutrinos and antineutrinos, we will not separate m. In this approximation number of neutrinos produced per flavor in energy bin de ν originate from original pion in energy bin de π = 4dE ν ; refore, q ν (E ν ) de ν = q π (4 E ν )de π. The point source flux observed at Earth is q ν (E ν )/4πr 2, where r is distance to source. So far IceCube has not pinpointed such a flux, instead it discovered a diffuse flux from a, yet unidentified, source population with uniform density ρ(r) in Universe. We introduce diffuse flux Φ = 1 4π d 3 r ρ (r) q ν (E ν ) 4πr 2, (28) where first factor 1/4π is introduced in order to define diffuse flux with conventional units GeV 1 cm 2 s 1 sr 1. We obtain result Φ = 1 dr 4πr 2 ρ (r) q ν (E ν ) 4π 4πr 2, (29) or Φ = 1 4π drρ (r) q ν (E ν ). (30) This is Euclidian result which can at best be an approximation for nearby sources. Integrating over cosmology of Universe is done by changing integration from dr cdt cdz(dt/dz), with dz/dt = H(z), Hubble scaling factor. We thus can rewrite integral in covariant form Φ = c 4π dz H (z) ρ (z) q ν ((1 + z) E ν ). (31) For standard ΛCDM cosmological model, Hubble parameter scales as H 2 (z) = H0 2 [(1 + z) 3 Ω m + Ω Λ ], with Ω m 0.3, Ω Λ 0.7, and c/h Gpc. 68 A more formal derivation on how to introduce cosmological evolution of sources can be found in section 6.2. In following, we will assume that neutrino emission rate q να follows a power law E γ. The flavor-averaged neutrino flux can n be written as 1 3 α Eνφ 2 να (E ν ) = c ξ z 1 ρ 0 4π H 0 3 where we introduce redshift factor ξ z = 0 Eνq 2 να (E ν ), (32) α (1 + z) γ ρ(z) dz ΩΛ + (1 + z) 3 Ω m ρ(0). (33)

29 July 9, :42 ws-rv9x6 Book Title trisep halzen page 29 High-Energy Astrophysical Neutrinos 29 A spectral index of γ 2.0 and no source evolution, ρ(z) = ρ 0, yields ξ z 0.6, whereas same spectral index and source evolution following star formation rate yields ρ 2.4. The identical procedure can be followed for production of neutral pions that subsequently decay into two gamma rays. This will lead to Eq. 15, previously introduced Cosmic Neutrinos and Ultra-High-Energy Cosmic Rays The charged pion production rate q π ± is proportional to density of protons in cosmic accelerator beam that produces pions, q p, by bolometric proportionality factor f π 1 introduced above. For, both, pp and pγ interactions f π = K p /n π 0.2. The average energy per pion is n E π = fπe p, and average energy of pionic leptons relative to nucleon is E ν E π /4 = (f π /4)E N 0.05E p. In summary f π denotes average inelasticity per pion and refore normalizes conversion of proton energy into pion energy on target. Therefore: E 2 πq π ±(E π ) f π K π 1 + K π [ E 2 p q p (E p ) ] E p=e π/f π, (34) with, as before, K π 2 for pp and K π 1 for pγ interactions. In many application accelerated proton beam is associated with observed flux of cosmic rays. The association is often introduced to investigate a possible common origin of extragalactic cosmic rays and IceCube cosmic neutrinos. Do y have common sources? In general, proton emission rate, q p, has to be generalized to composition of cosmic rays; using superposition one can relate spectra of nuclei with mass number A as q N (E N ) = A A2 q A (AE N ). One can derive an upper limit on diffuse cosmic neutrino flux by assuming that flux of extragalactic neutrinos is dominated by protons and that sources are transparent, i.e. f π << 1. 69,70 The local emission rate density of cosmic rays is given by Q p = ρ 0 q p, where ρ is local density of sources. It is insensitive to luminosity evolution of sources at high redshift and can be estimated from measured spectra to be at level of [ Ep 2 Q p (E p ) ] ( ) ev 1044 erg/mpc 3 /yr Note, that measurements indicate that mass composition above ankle also requires a contribution of heavier nuclei. However, estimated local UHE CR power density based on proton models is a good proxy for that of UHE CR models including heavy nuclei, as long as spectral index is close to γ 2. For instance, a recent analysis of Auger 74 provides a

30 July 9, :42 ws-rv9x6 Book Title trisep halzen page Francis Halzen solution with spectral index γ 2.04 and a combined nucleon density of [E 2 N Q N(E N )] ev erg/mpc 3 /yr Example I: Neutrino Production in Active Galaxies An active galaxy presents multiple opportunities for acceleration of particles in inflows and outflows associated with a supermassive black hole. The high-energy particles may subsequently produce neutrinos in interactions with a variety of possible targets such as dense matter near black hole, hydrogen in galactic disk of galaxy associated with black hole and photons produced in jet or radiated from accretion disk on black hole. It is refore useful to start by considering a generic beam dump where a beam of protons with an initial flux dn p /de p interacts with a target of density n over a distance l using formalism introduced above. For analytic calculations one can use a parameterization that allows for increase of pion multiplicity with proton energy starting from a pair of pions produced at threshold E th in reaction pp pp + π + π : 75 and n π ± = 2 ( ) 1/4 Ep E th, (35) GeV E π = 1 6 (E p m p c 2 ) 3/4 GeV. (36) The approximations reproduce results of simulations. Given number of protons produced by accelerator per energy and time interval ( dn p Ep m p c 2 ) γ = A p, (37) de p GeV we obtain a pion rate at source using Eq. 21: ( ) 4 6Eπ 3 (γ 1 2 ) q π ±(E π ) 26 n l A p σ. (38) GeV The final result for total neutrino emission rate at source is given by ( ) 4 q ν,tot Eν 3 γ+ 2 3 n l A p σ, (39) GeV which provides us with an estimate of total neutrino flux at source in terms of three key quantities: A p and γ, normalization and spectral

31 July 9, :42 ws-rv9x6 Book Title trisep halzen page 31 High-Energy Astrophysical Neutrinos 31 slope of flux of accelerator, and column density of target N ln. The spectral index is routinely taken to be γ = 2, a value suggested by diffusive shock acceleration and, in any case, typical for spectra of gamma rays observed for nonrmal sources. The column density N = ln is taken from astronomical information, with l being distance that cosmic rays travel through a photon target of density n. For instance l could be diffusion length of cosmic rays in magnetic field of galaxy. This allows protons to interact with typical density of hydrogen of n 1 cm 3 over an extended pathlength determined by diffusion time. The diffusion distance before escaping galaxy is given by d diff = 2 D(E p ) t esc, (40) where D is diffusion coefficient and t esc is escape time. In this case, size of target is identified with l = ct esc. For instance l = 10 kpc for our own Galaxy. The normalization of proton flux A p can be obtained from requirement that aggregate diffuse proton flux from all AGN reproduces cosmic ray flux observed at Earth. 58 He finds that this calculation also accommodates diffuse high energy photon flux observed by Fermi. Alternatively, in Ref. 57 A p is obtained from radio luminosity of AGNs, L, resulting from synchrotron radiation of accelerated electrons with L e = χl with χ 1. A p is obtained from assumptions that protons and electrons are connected by a constant fraction f e : L e = f e L p, which is on order of 0.1: 57 dnp Lp = de p χl, (41) de p f e and A p = A p (L, z) = χl [ln (E max /E min )] 1 GeV 2 (42) f e for γ = 2; generalization for γ 2 is straightforward. Having related proton flux to radio luminosity, we obtain neutrino for a single AGN from Eq. 39. The diffuse flux that can be confronted with IceCube data is obtained using formalism for summing over sources previously introduced: Φ ν = L z q ν,tot dn AGN 4 π d L (z) 2 dv dl dv dz dz dl. (43) Here, d L is luminosity distance, dn AGN /(dv dl) is radio luminosity function of AGN, and dv/dz is comoving volume at a

32 July 9, :42 ws-rv9x6 Book Title trisep halzen page Francis Halzen fixed redshift z. The radio luminosity function is usually separated into product of a luminosity-dependent and a redshift-dependent function, dn AGN /(dv dl) = g(l)f(z). The result matches IceCube observations; more details can be found in Ref. 57 for column densities typical for relatively dense matter near black hole. The two calculations illustrate how two different mechanisms manage to accommodate IceCube result. Hooper normalizes proton flux to cosmic ray flux and generates neutrino flux by diffusing protons through Galaxy, while Tjus et al. relate proton flux to radio emission of galaxies and produce neutrinos in dense matter near supermassive black hole. AGNs are episodic sources producing gamma rays in bursts, with episodes where flux increases by over one order of magnitude for periods of seconds to days, sometimes even years. A correlation of arrival of IceCube neutrinos in coincidence with such bursts can provide a smoking gun for ir origin; for a recent discussion, see Ref Example II: Neutrino Production in Jets of Active Galaxies Blazars are brightest sources of high energy gamma rays in Universe making up most, if not all, of diffuse extragalactic gamma ray flux. We will show later that diffuse cosmic neutrino flux observed by IceCube is likely to generate a significant fraction, possibly all, of se photons. Their engines must not only be powerful, but also extremely compact because ir luminosities are observed to flare by over an order of magnitude over time periods that are occasionally as short as minutes. Blazars are AGN with jet directly pointing at our telescopes thus furr boosting energy of gamma rays and contracting duration of episodes of emission. The drawing of a blazar, shown in Fig. 11, displays its most prominent features: an accretion disk of stars and gas falling onto spinning supermassive black hole as well as a pair of jets aligned with rotation axis. Large magnetic fields originating from inflow of particles on black hole are wound up along rotation axis and launch a pair of jets that are site of acceleration of electron and proton beams. The energy spectrum E 2 dn/de of gamma rays radiated by a blazar jet shows classic double-hump structure with lower energy gamma rays resulting from synchrotron radiation by a beam of accelerated electrons and a higher energy component resulting from inverse Compton scattering of

33 July 9, :42 ws-rv9x6 Book Title trisep halzen page 33 High-Energy Astrophysical Neutrinos 33 Jet γ ~ 10 γ-ray ~10 2 pc wind black hole accretion disk Fig. 11. Blueprint for production of high energy photons and neutrinos near super-massive black hole powering an AGN. Particles, electrons and protons, accelerated in sheets or blobs moving along jet, interact with photons radiated by accretion disk or produced by interaction of accelerated particles with magnetic fields. The jet is pointing at Earth in subclass of AGN dubbed blazars. same photons. Because of ir reduced synchrotron radiation, protons, unlike electrons, efficiently transfer energy in presence of magnetic field in jet. They provide a mechanism for energy transfer from central engine over distances as large as 1 parsec as well as for observed heating of dusty disk over distances of several hundred parsecs. If protons are accelerated along with electrons multiple opportunities exist

34 July 9, :42 ws-rv9x6 Book Title trisep halzen page Francis Halzen for production of neutrinos by pion photoproduction, e.g. in interactions with synchrotron photons, or photons radiated off accretion disk and dusty torus in AGN. The protons may also interact with broadline emission clouds. While relative merits of electron and proton blazar are hotly debated, issue has been settled by first multiwavelength detection of a flaring blazar TXS in coincidence with an IceCube cosmic neutrino IC The opportunities for studying first identified cosmic ray accelerator are wonderfully obvious. Confronted with challenge of explainig a E 2 high-energy photon emission spectrum reaching TeV energies, which is occassionally radiated in bursts of a duration of less than one day, models have converged on blazar blueprint shown in Fig. 11. Particles are accelerated by shocks in blobs of matter traveling along jet with a bulk Doppler (Lorenz) factor of Γ 10 and higher. This factor combines effects of special relativity and geometry of moving source. The jet consists of relatively small structures with short lifetime often referred to as blobs. In following, primes will refer to a reference frame attached to blob, which is moving with a Doppler factor Γ relative to observer. In general, transformation between blob and observer frame is R = ΓR and E = 1 Γ E for distances and energies, respectively. Blazar bursts appear more spectacular to observer than y actually are because, in frame of blob, distances are larger and times longer. High energy emission is associated with periodic formation of se blobs. The blobs are clearly identified in X-ray images of AGN jets, e.g. in M87. In order to accommodate bursts lasting a day, or less, in observer s frame, size of blob must be of order Γc t 10 2 parsecs or less. The blobs are actually more like sheets, thinner than jet s size of roughly 1 parsec. The observed radiation at all wavelengths is produced by interaction of accelerated electrons and protons in blob with multiple radiation fields in complex AGN structure, for instance synchrotron photons produced by electrons or ambient radiation in AGN which has a significant prominent component concentrated in so-called UV-bump of 10 ev photons. In order for a proton accelerated in jet to produce pions on target photons of energy E γ, a process dominated by photoproduction of resonance, it must exceed threshold energy: E p > m2 m2 p 4 1 E γ, (44)

35 July 9, :42 ws-rv9x6 Book Title trisep halzen page 35 High-Energy Astrophysical Neutrinos 35 or, E p > Γ 2 m2 m2 p 4E γ. (45) Furrmore, blob must be transparent to gamma rays that are actually detected at Earth from burst. Therefore center-of-mass energy s must be below threshold for γ + γ interactions in blob, or or, s < (2m e ) 2, (46) E γ E γ,obs < Γ 2 m 2 e. (47) The kinematic constraints imply that Γ must exceed a few ( 40) for target photon energies 10 ev (1 KeV) typical for UV (synchrotron) photons. These values of Γ render jet transparent to 50 GeV (500 GeV) photons, for example. From observed luminosity L γ we deduce energy density of photons in shocked region of size R : u γ = L γ t 4 = L γ t 3 πr 3 Γ 1 4 = 3 3 π(γc t)3 4πc 3 L γ Γ 4 t 2, (48) where t is duration of flare. The fraction of energy f π lost by protons to pion production when traveling a distance R through a photon field of density n γ = u γ/e γ is given by number of interactions lengths of proton fitting inside photon target of size R : f π = R λ pγ = R n γσ pγ x p π (49) where λ pγ is proton interaction length, with σ pγ nπ cm 2 and x p π 0.2 energy transferred from proton to pion. The final result is given by f π R L γ 1 3σ x p π λ pγ E ph Γ 2 t 4πc 2. (50) If f π approaches unity, pions will be absorbed before decaying into neutrinos, requiring substitution of f π by 1 e fπ. For a total injection rate in high-energy protons E 2 N Q N, total energy in neutrinos is 1/2f π t H E 2 N Q N, where t H Gyr is Hubble time. The secondary ν µ have energy E ν = x ν E p, with x ν 0.05, fraction of energy transferred, on average, from proton to neutrino via

36 July 9, :42 ws-rv9x6 Book Title trisep halzen page Francis Halzen -resonance. The factor 1/2 accounts for fact that 1/2 of energy in charged pions is transferred to ν µ + ν µ, see above. The neutrino flux is dn Φ ν = E ν = c 1 [ 1 de ν 4π E ν 2 f π t H ENQ 2 N ], (51) There is anor more direct way to approach problem that, additionally, allows for fact that se sources are variable on all scales, e.g. neutrino flare observed from TXS by IceCube covered a period t 110 days. When discussing IceCube observations later on we will show that such flaring blazars are capable of reproducing observed cosmic neutrinos flux provided that ir efficiency for producing pions, f π, is close to unity. The desired result can be achieved when protons in neutrino-producing blazar jets interact with 10 ev photons in galaxy ( blue bump) via -resonance; pγ πn. The pion efficiency of jet depends on Lorentz factor of jet (Γ), target photon energy (E γ ), luminosity of target photons (L γ ), and duration of flare ( t), for instance, f π L γ 1 3σ x p π E γ Γ 2 t 4πc 2, (52) and ( )( )( )( ) L γ 10 ev d f π = (4 6) erg/s E γ Γ 2 t ( ) 3σ x p π 4πc 2 (53) This suggests that sources with small Lorentz factor of jet and a UV luminosity exceeding O(10 46 ) is required for production of high-energy cosmic neutrinos. This level of UV luminosity has been reported in reference. 77 We will revisit blazars when we discuss discovery of first blazar TXS in both neutrinos and gamma rays Generic Fireballs Whereas we have confidence that electromagnetic radiation in some Galactic sources is produced by decay of neutral pions, re is no straightforward gamma-ray path to neutrino flux expected from extragalactic cosmic-ray accelerators. We presented model calculations to show that AGNs can plausibly accommodate cosmic neutrino flux observed,

37 July 9, :42 ws-rv9x6 Book Title trisep halzen page 37 High-Energy Astrophysical Neutrinos 37 assuming that y accelerate protons at level of sources of extragalactic cosmic rays. In fact, we showed how very different blueprints for beam dump can fit diffuse neutrino flux observed. As already discussed, re is an yet anor possibility. Massive stars collapsing to black holes and observed by astronomers as GRBs have potential to accelerate protons to 100 EeV energy. Neutrinos of 100 TeV PeV energy should be produced by pion photoproduction when protons and photons coexist in GRB fireball. 78 As previously discussed, model is promising because observed cosmic-ray flux can be accommodated with assumption that roughly equal energy is shared by electrons, observed as synchrotron photons, and protons. Indeed, IceCube observations indicate equal extragalactic energy densities of photons and neutrinos, as we will see furr on. The phenomenology that successfully accommodates astronomical observations is creation of a hot fireball of electrons, photons, and protons that is initially opaque to radiation. The hot plasma refore expands by radiation pressure, and particles are accelerated to a Lorentz factor Γ that grows until plasma becomes optically thin and produces GRB display. From this point on, fireball coasts with a Lorentz factor that is constant and depends on its baryonic load. The baryonic component carries bulk of fireball s kinetic energy. The energetics and rapid time structure of burst can be successfully associated with successive shocks (shells), of width R, that develop in expanding fireball. The rapid temporal variation of gamma-ray burst, t v, is on order of milliseconds and can be interpreted as collision of internal shocks with a varying baryonic load leading to differences in bulk Lorentz factor. Electrons, accelerated by first-order Fermi acceleration, radiate synchrotron gamma rays in strong internal magnetic field and thus produce spikes observed in burst spectra. The usual approach followed in interpretation of routine IceCube GRB searches 79 has proton content of fireball derived from observed electromagnetic emission. The basic assumption is that a comparable amount of energy is dissipated in fireball protons and electrons, where latter are observed as synchrotron radiation, E 2 dn ( ) [ ] ν de = ɛp 1 ɛ e 2 x ν Eγ 2 dn γ (E γ ), (54) de γ syn where ɛ p and ɛ e are energy fractions in fireball in protons and electrons, 79 respectively. One can n use data to determine baryon

38 July 9, :42 ws-rv9x6 Book Title trisep halzen page Francis Halzen loading in GRB fireball, ɛ p / ɛ e. Within this framework one can estimate baryon loading or relative abundance of protons and electrons in fireball from neutrino observations; no prediction is made. The abundance of protons in fireball is determined, or, at present, limited by observations. 54 Although simulations of GRB fireballs have reached a level of sophistication, 80 a simple energy estimate is sufficient to predict neutrino flux associated with GRB fireballs assuming that y are sources of cosmic rays. c Fig. 12. Kinematics of a relativistically expanding fireball on left, and resulting shell(s) expanding under radiation pressure on right. Simple relativistic kinematics (see Fig. 12) relates radius and width

39 July 9, :42 ws-rv9x6 Book Title trisep halzen page 39 High-Energy Astrophysical Neutrinos 39 R and R to observed duration of photon burst c t: R = γ 2 (c t) (55) R = γc t (56) From observed GRB luminosity L γ, we compute photon energy density in shell: U γ = (L γ t) /γ 4πR 2 R = L γ 4π t 2 c 3 γ 6 (57) The pion production by shocked protons in this photon field is, as before, calculated from interaction length: 1 = N γ σ x p π = U ( γ σ x p π E γ = 1 ) λ pγ γ E γ. (58) E γ Also as before, σ is cross section for pγ nπ + and x p π 0.2. The fraction of energy going into π-production is f π = R λ pγ (59) f π 1 L γ 1 4πc 2 E γ γ 4 t σ x p π (60) [ ] [ ] [ ] 4 [ ] L γ 1 MeV msec f π ergs 1 [ E γ σ ] [ xp π cm γ t ]. (61) The relevant photon energy in problem is 1 MeV, energy where typical GRB spectrum exhibits a break. The contribution of higher energy photons is suppressed by falling spectrum, and lower energy photons are less efficient at producing pions. Given large uncertainties associated with astrophysics, it is an adequate approximation to neglect explicit integration over GRB photon spectrum. The proton energy for production of pions via -resonance is Therefore, E p = m2 m2 p 4E γ. (62) ( γ ) ( ) 2 1 MeV E p = ev 300 E γ (63) E ν = 1 4 x p π E p ev. (64)

40 July 9, :42 ws-rv9x6 Book Title trisep halzen page Francis Halzen We are now ready to calculate neutrino flux: dn ν de ν = c U ν 4π E ν = c U ν = c 4π E ν 4π 1 E ν [ ] 1 2 f πt H Ė, (65) where factor 1/2 accounts for fact that only 1/2 of energy in charged pions is transferred to ν µ + ν µ. As before, Ė is injection rate in cosmic rays beyond ankle ( erg Mpc 3 yr 1 ) and t H is Hubble time of Gyr. Numerically, dn ν de ν [ 7 10 = cm 2 s 1 sr 1 14 ev E ν [ ] [ ] [ fπ 0.14 t H 10 Gyr ] Ė erg Mpc 3 yr 1 ] (66) The only subtlety here is γ 2 dependence of shell radius R ; for a simple derivation, see Ref. 6 The result is insensitive to beaming. Beaming yields more energy per burst, but fewer bursts are actually observed. The predicted rate is also insensitive to neutrino energy E ν because higher average energy yields fewer νs, but more are detected. Both effects are approximately linear. Neutrino telescopes are essentially background free for such high-energy events and should be able to identify neutrinos at all zenith angles. For typical choices of parameters, γ 300 and t v 10 2 s, about 100 events per year are predicted in IceCube, a flux that was already challenged 81 by limit on a diffuse flux of cosmic neutrinos obtained with one-half of IceCube in one year. 82 As before, energy density of extragalactic cosmic rays of TeV Mpc 3 yr 1 depends on unknown transition energy between Galactic and extragalactic components of spectrum. In end, predictions can be stretched, but having failed by now to observe high-energy neutrinos in spatial and temporal coincidence with over 1000 GRB observations, IceCube has set a limit that is less than 1% of PeV cosmic neutrino flux that is actually observed. We have neverless discussed fireballs in some detail to illustrate ir generic potential as cosmic accelerators and to point out that y may produce cosmic neutrinos without being sources of cosmic rays. For instance, y may produce neutrinos of lower energy in events where boost factor is limited, γ 10. Candidate events have been observed and are referred to as low luminosity GRBs. 83 There is also possibility that high-energy gamma rays and neutrinos are produced when shock expands furr into interstellar medium. This mechanism has been

41 July 9, :42 ws-rv9x6 Book Title trisep halzen page 41 High-Energy Astrophysical Neutrinos 41 invoked as origin of delayed high-energy gamma rays. Adapting previous calculation to external shock is straightforward. 84 The timescale is seconds rar than milliseconds, and break in spectrum shifts from 1 to 0.1 MeV. Although f π is reduced by two orders of magnitude, in external shocks higher energies can be reached, and this increases neutrino detection efficiency. In end, observed rates are an order of magnitude smaller than in internal shocks, but inherent ambiguities of estimates are such that it is difficult to establish with confidence ir relative neutrino yields Galactic Neutrino-Producing Beam Dumps The rationale for kilometer-scale neutrino detectors is that ir sensitivity is sufficient to reveal generic cosmic-ray sources with an energy density in neutrinos comparable to ir energy density in cosmic rays 59 and pionic TeV gamma rays. 63 Interestingly, this condition may be satisfied by sources of Galactic cosmic rays. The energy density of cosmic rays in our Galaxy is ρ E erg cm 3. Galactic cosmic rays do not exist forever; y diffuse within microgauss fields and remain trapped for an average containment time of years. The power needed to maintain a steady energy density requires accelerators delivering erg/s. This happens to be 10% of power produced by supernovae releasing erg every 30 years (10 51 erg correspond to 1% of binding energy of a neutron star after 99% is initially lost to neutrinos). This coincidence is basis for idea that shocks produced by supernovae exploding into interstellar medium are accelerators of Galactic cosmic rays. A generic supernova remnant releasing an energy of W erg into acceleration of cosmic rays will inevitably generate TeV gamma rays by interacting with hydrogen in Galactic disk. The emissivity in pionic gamma rays is calculated using formalism previously introduced for calculation of neutrino flux with q π 0 = 1 2 q π ±; latter is given by Eq. 21. Before proceeding, a short discussion of production of pionic photons follows. For this calculation, we define production rate Q π 0, per unit volume and time, by converting dl to cdt in τ integration in Eq. 21. Additionally one assumes that a single pion is produced carrying a fraction

42 July 9, :42 ws-rv9x6 Book Title trisep halzen page Francis Halzen f π 0.2 of proton momentum. This yields Q π 0 = c n σ pp de p n p (E p ) δ (E π 0 f π E p ), (67) which in turn yields final result Q π 0 (E π 0) = c σ pp n 1 ( ) Eπ 0 n p. (68) f π f π The emissivity Q π 0 is simply proportional to number density of hydrogen targets and number of cosmic rays n p (E p /T ev ) 1.7 cm 3 obtained from spectrum: n p = 4π de dn p c de. (69) The emissivity of photons is obtained from fact that every pion produces two photons with half its energy, refore Q γ (E γ ) = 2 2 Q π 0 (2E γ ) Q π 0, (70) where latter equality holds for an E 2 spectrum. Our final result is Q γ (E γ ) c 1 σ pp n n cr (E p > E γ ), (71) f π f π or, assuming an E 2 spectrum, ( Q γ (> 1 TeV) n ) cm 3 cm 3 s 1. (72) Notice transparency of this result. The proportionality factor in Eq. 71 is determined by particle physics, where λ pp = (nσ pp ) 1 is proton interaction length (σ pp 40 mb) in a density n of hydrogen atoms. The corresponding luminosity is W L γ (>1 TeV) Q γ (73) ρ E where W/ρ E is volume occupied by supernova remnant; given ambient density ρ E erg cm 3 of Galactic cosmic rays, 4 a supernova with energy W erg in cosmic rays occupies volume W/ρ E. We here made approximation that density of particles in remnant is not very different from ambient energy density. We thus predict 85,86 a rate of TeV photons from a supernova remnant at a nominal distance d on order of 1 kpc of dn γ de γ = L γ(> 1TeV) de γ 4πd 2 E>1TeV ( TeV cm 2 s ) ( W erg ) ( n ) ( ) 2 d 1 cm 3. (74) 1 kpc

43 July 9, :42 ws-rv9x6 Book Title trisep halzen page 43 High-Energy Astrophysical Neutrinos 43 As discussed in introduction, position of knee in cosmic ray spectrum indicates that some sources accelerate cosmic rays to energies of several PeV. These PeVatrons refore produce pionic gamma rays whose spectrum can extend to several hundred TeV without cutting off. For such sources gamma-ray flux in TeV energy range can be parametrized in terms of a spectral slope α γ, an energy E cut,γ where accelerator cuts off, and a normalization k γ : dn γ (E γ ) de γ = k γ ( ) ( αγ Eγ exp TeV E γ E cut,γ ). (75) The estimate in Eq. 74 indicates that fluxes as large as dn γ /de γ (TeV 1 cm 2 s 1 ) can be expected at energies of O (10 TeV). We will refore concentrate on search for PeVatrons, supernova remnants with required energetics to produce cosmic rays, at least up to knee in spectrum. These sources are well within sensitivity of existing high-energy gamma ray detectors such air Cherenkov telescopes and large acceptance ground-based detectors like Milagro. They may have been revealed by highest energy all-sky survey in 20 TeV gamma rays using Milagro detector. 87 A subset of sources, located within nearby star-forming regions in Cygnus and in vicinity of Galactic latitude l = 40 degrees, are identified; some cannot be readily associated with known supernova remnants or with nonrmal sources observed at or wavelengths. Subsequently, directional air Cherenkov telescopes were pointed at three of sources, revealing m as PeVatron candidates with an approximate E 2 energy spectrum that extends to tens of TeV without evidence for a cutoff, 88 in contrast with best studied supernova remnants RX J and RX J (Vela Junior). Some Milagro sources may actually be molecular clouds illuminated by cosmic-ray beam accelerated in young remnants located within 100 pc. Indeed, one expects that multi-pev cosmic rays are accelerated only over a short time period when shock velocity is high, i.e., towards end of free expansion of remnant. The high-energy particles can produce photons and neutrinos over much longer periods when y diffuse through interstellar medium to interact with nearby molecular clouds. 89 An association of molecular clouds and supernova remnants is expected, of course, in star-forming regions. In this case, any confusion with synchrotron photons is unlikely.

44 July 9, :42 ws-rv9x6 Book Title trisep halzen page Francis Halzen Ground-based and satellite-borne instruments with improved sensitivity are able to conclusively pinpoint supernova remnants as sources of cosmic-ray acceleration by identifying accompanying gamma rays of pion origin. The Fermi Large Area Telescope has detected pion-decay feature in gamma-ray spectra of two supernova remnants, IC 443 and W In contrast, GeV gamma-ray data from Fermi LAT have challenged hadronic interpretation of GeV-TeV radiation from one of beststudied candidates, RX J The most promising PeVatron candidate to date is, instead, center of Galaxy, as reported by HESS Collaboration, see Ref. 42 Detecting accompanying neutrinos from supernova remnants or Galactic Center would provide incontrovertible evidence for cosmic-ray acceleration. Particle physics dictates relation between pionic gamma rays and neutrinos and basically predicts production of a ν µ + ν µ pair for every two gamma rays seen by Milagro. This calculation can be performed using formalism discussed with approximately same outcome. Operating complete IceCube detector for several years should yield confirmation that some of Milagro sources produce pionic gamma rays; see Fig. 13. Fig. 13. Simulated sky map of IceCube in Galactic coordinates after five years of operation of completed detector. Two Milagro sources are visible with four events for MGRO J and three events for MGRO J with energy in excess of 40 TeV. These, as well as background events, have been randomly distributed according to resolution of detector and size of sources.

45 July 9, :42 ws-rv9x6 Book Title trisep halzen page 45 High-Energy Astrophysical Neutrinos 45 The quantitative statistics can be summarized in following. For average values of parameters describing flux, we find that IceCube detector could confirm sources in Milagro sky map as sites of cosmic-ray acceleration at 3σ level in less than one year and at 5σ level in three years. 85 We here assume that source extends to 300 TeV, or 10% of energy of cosmic rays near knee in spectrum. These results agree with previous estimates. 92,93 There are intrinsic ambiguities in this estimate of an astrophysical nature that may reduce or extend time required for a 5σ observation. 85 In particular, poorly known extended nature of some of Milagro sources and value of cutoff represent a challenge for IceCube analyses that are optimized for point sources. The absence of any observation of an accumulation of high-energy neutrinos in direction of se sources will seriously challenge concept that gamma-ray telescopes are seeing actual sources of cosmic rays. These predictions have been stable over years and have recently been updated in context of new gamma-ray information, in particular from HAWC experiment; see reference. 88 The predicted fluxes for Galactic sources in Norrn hemisphere are close to IceCube s current upper limits on a point source flux of TeVcm 2 s 1 ; 94 see also Ref Cosmogenic Neutrinos The production of neutrinos in sources that accelerate high-energy cosmic rays depends on source environment. In order to efficiently accelerate cosmic rays, any loss mechanism, including pion production in pγ and pp interactions, must be suppressed as it reduces acceleration time. Efficient accelerators are likely to be inefficient beam dumps for producing neutrinos. High-efficiency neutrino production can be achieved by separating 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 dilute extragalactic medium. In this section, we will discuss production of neutrinos in interactions of extragalactic cosmic rays with cosmic radiation backgrounds. Soon after discovery of cosmic microwave background (CMB), Greisen, Zatsepin and Kuzmin 96,97 (GZK) realized that extragalactic cosmic rays are attenuated by interactions with background photons. Actually, protons interact resonantly via pγ + π + n with background photons with mean energy ɛ 0.33 mev at energies E p (m 2 m2 p)/4/ɛ 500 EeV.

46 July 9, :42 ws-rv9x6 Book Title trisep halzen page Francis Halzen The width of Planck spectrum leads to a significant attenuation of proton fluxes after propagation over distances on order of 200 Mpc at an energy above E GZK 50 EeV, which is known as GZK suppression. Also heavier nuclei are attenuated at a similar energy by photodisintegration of nucleus by CMB photons via giant dipole resonance. The pions produced in GZK interactions decay, resulting in a detectable flux of cosmogenic neutrinos first estimated by Berezinsky and Zatsepin 24 in This guaranteed flux of neutrinos became one of benchmarks for high energy neutrino astronomy leading early on to concept of kilometer-scale detectors. The flux of cosmogenic neutrinos peaks at EeV neutrino energy depending on chemical composition and evolution with redshift of unknown sources. The largest neutrino flux results from proton dominated models. 18,98,99 A particularly strong emission can be expected in such models if proton spectrum extends below ankle. Referred to as dip models, ankle results from absorption of protons by Be Heitler pair production on CMB photons. A fit to observed cosmic-ray spectrum requires relative strong source evolution with redshift that enhances pion production. However, corresponding electromagnetic emission via neutral pions as well as e ± pairs is constrained by isotropic gamma-ray background (IGRB) observed by Fermi LAT satellite 104,105 and limits neutrino intensity of se proton dominated scenarios Recent upper limits on cosmogenic neutrinos resulting from failure by IceCube to observe EeV neutrinos constrains proton dominated models. 112 In contrast, IceCube constraint can be accommodated by introducing a heavy nuclear composition. Resonant neutrino production still proceeds via interaction of individual nucleons with background photons, but threshold of production is increased to E CR AE GZK for nuclei with mass number A. Therefore, efficient cosmogenic neutrino production would require an injected cosmic-ray flux that extends well above E GZK. Especially for heavier nuclear composition of primary flux, production of neutrinos on photons of extragalactic background light (EBL) becomes relatively important. 71,109, The interaction with optical photons produces neutrino fluxes in PeV energy range. However, overall level is much lower because of low intensity of EBL photons. It is unlikely that PeV neutrino flux observed with IceCube could be related to neutrino production in EBL 121 (see also Ref. 122 ). The observed PeV neutrino flux level is too high to be consistent with associated electromagnetic contributions to IGRB or upper limits on EeV

47 July 9, :42 ws-rv9x6 Book Title trisep halzen page 47 High-Energy Astrophysical Neutrinos 47 neutrino flux. 5. Status Of Observations of Cosmic Neutrinos For neutrino astronomy, 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 (see Fig. 9), while second is to identify small fraction of se neutrinos that is astrophysical in origin, roughly at level of tens of events per year. Atmospheric neutrinos are a background for cosmic neutrinos, at least at neutrino energies below 300 TeV. Above this energy, atmospheric neutrino flux reduces to less than one event per year, even in a kilometer-scale detector, and thus events in that energy range are cosmic in origin. There are two primary methods used to identify neutrinos of cosmic origin. As previously discussed, neutrino searches have historically focused on observation of muon neutrinos that interact primarily outside detector, producing kilometer-long muon tracks that pass through detection volume. Although this allows observation of neutrinos that interact outside detector, it is n necessary to use Earth as a filter in order to remove huge background of cosmic-ray muons. Even at a depth of 1,450 meters, IceCube detects atmospheric cosmic-ray muons originating in Sourn Hemisphere at a rate of 3,000 per second. This method limits neutrino view to a single flavor and half sky. An alternative method exclusively identifies neutrinos interacting inside detector. It divides instrumented volume of ice into an outer veto shield and a roughly 500 megaton inner fiducial volume. The advantage of focusing on neutrinos interacting inside instrumented volume of ice is that detector n functions as a total absorption calorimeter, measuring energy with a % resolution. Also, neutrinos from all directions in sky can be identified, including both muon tracks, produced in muon-neutrino charged-current interactions, and secondary showers, produced by electron and tau neutrinos as well as in neutral-current interactions of neutrinos of all flavors. The Cherenkov patterns initiated by an electron (or tau) neutrino of 1 PeV, or petaelectronvolt (10 15 ev), energy and by a muon neutrino depositing 2.6 PeV energy while traversing detector are contrasted in Fig. 14. In general, particle s trajectory is determined from arrival times of photons at optical sensors, 123 while number of photons is a proxy for amount of energy deposited. The two methods for separating neutri-

48 July 9, :42 ws-rv9x6 Book Title 48 trisep halzen Francis Halzen Fig. 14. Light pools produced in IceCube by neutrino interactions. White dots represent sensors with no signal. For colored dots, color indicates arrival time, from red (early) to purple (late) following rainbow, and size reflects number of photons detected. Left: A shower initiated by an electron or a tau neutrino or by neutral current interaction of a neutrino of any of three flavors. The measured energy of shower is 1.14 PeV, which represents a lower limit on energy of neutrino that initiated shower. Right: An upgoing muon track traverses detector at an angle of 11 below horizon. The deposited energy inside detector is 2.6 PeV. nos from cosmic-ray muon background have complementary advantages. The long tracks produced by muon neutrinos can point back to ir sources with a 0.4 angular resolution. In contrast, reconstruction of direction of secondary showers, still in development stage in IceCube,124 can be determined to within of direction of incident neutrino. Determining deposited energy from observed light pool is, however, relatively straightforward, and a resolution of better than 15% is possible. By now, IceCube has observed cosmic neutrinos using both methods for rejecting background, and each analysis has reached a statistical significance of more than 5σ.125,126 Based on different methods for reconstruction and energy measurement, results agree, pointing at extragalactic sources whose flux has equilibrated in three flavors after propagation over cosmic distances. Its total energy matches that of extragalactic photons and cosmic rays. Using 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 oretical calculations. However, with eight years of data, an excess of events is observed at energies beyond 100 TeV, which cannot be page 48

49 July 9, :42 ws-rv9x6 Book Title trisep halzen page 49 High-Energy Astrophysical Neutrinos 49 accommodated by atmospheric flux; see Fig. 16. Allowing for large uncertainties on extrapolation of atmospheric component to higher energy, statistical significance of excess astrophysical flux is 6.7σ. While IceCube measures only energy of secondary muon inside detector, from Standard Model physics we can infer energy spectrum of parent neutrinos. The best-fit neutrino spectrum n allows deriving probability distribution of neutrino energy for individual events. For instance, for highest energy event, shown in Fig. 14 on right, median energy of parent neutrino is about 7 PeV as indicated in Fig. 15. Note that this calculation 128 takes into account additional tracks from charged current interactions of ν τ + ν τ as well as resonant interactions of ν e with electrons (Glashow resonance) assuming a democratic composition of neutrino and antineutrino flavors. Independent of any calculation, energy lost by muon inside instrumented detector volume is 2.6 ± 0.3 PeV. The cosmic neutrino flux is well described by a power law with a spectral index Γ = 2.19 ± 0.10 and a normalization at 100 TeV neutrino energy of ( ) GeV 1 cm 2 sr The error range is estimated from a profile likelihood using Wilks orem and includes both statistical and systematic uncertainties. The neutrino energies contributing to this power-law fit cover range from 119 TeV to 4.8 PeV. However, using only two years of data, it was alternative HESE method, which selects neutrinos interacting inside detector, that revealed first evidence for cosmic neutrinos. 132,133 The segmentation of detector into a surrounding veto and active signal region has been optimized to reduce background of atmospheric muons and neutrinos to a handful of events per year, while keeping most of cosmic signal. Neutrinos of atmospheric and cosmic origin can be separated not only by using ir well-measured energy but also on basis that background atmospheric neutrinos reaching us from Sourn Hemisphere can be removed because y are accompanied by particles generated in same air shower where y originate. A sample event with a light pool of roughly one hundred thousand photoelectrons extending over more than 500 meters is shown in left panel of Fig. 14. With PeV energy, and no trace of accompanying muons from an atmospheric shower, se events are highly unlikely to be of atmospheric origin. It is indeed important to realize that muon produced in same pion or kaon decay as an atmospheric neutrino will reach detector provided that neutrino energy is sufficiently high and zenith angle sufficiently small. 33,134 As a consequence, PeV atmospheric neutrinos originating from above detector have a built-in

50 July 9, :42 ws-rv9x6 Book Title trisep halzen page Francis Halzen Fig. 15. Distribution of tracks initiated by muon neutrinos that have traversed Earth, i.e., with zenith angle less than 5 above horizon, as a function of neutrino energy. Due to event-by-event variation of energy transferred to and lost by muon before it reaches detector, initial neutrino energy is shown by its median. The black crosses represent data. The blue colored band shows expectation for atmospheric neutrino flux, while red line represents a power-law fit to cosmic component with spectral index Γ = Additionally, probability density function for neutrino energy of highest energy event is shown assuming best-fit spectrum (dashed line). self-veto in HESE analysis by ir accompanying atmospheric muons. The deposited energy and zenith dependence of high-energy starting events collected in six years of data 129 is compared to atmospheric background in Fig. 17. The expected number of events for best-fit astrophysical neutrino spectrum following a two-component power-law fit is shown as dashed lines in two panels. The corresponding neutrino spectrum is also shown in Fig. 18. It is, above an energy of 200 TeV, consistent with a power-law flux of muon neutrinos penetrating Earth inferred by data shown in Fig. 15. A purely atmospheric explanation of observation is excluded at 8σ. In summary, IceCube has observed cosmic neutrinos using both methods for rejecting background. Based on different methods for reconstruction and energy measurement, ir results agree, pointing at extragalactic sources whose flux has equilibrated in three flavors after propagation over cosmic distances 135 with ν e : ν µ : ν τ 1 : 1 : 1. The six-year data set contains a total of 82 neutrino events with de-

51 July 9, :42 ws-rv9x6 Book Title trisep halzen page 51 High-Energy Astrophysical Neutrinos 51 E 2 φν+ ν [GeV cm 2 s 1 sr 1 ] atmo. νe + νe (before HESE veto) atmo. νµ + νµ (before HESE veto) neutrino fluxes HESE (6yr) (per flavor) νµ + νµ (8yr) E [GeV] Fig. 16. Summary of diffuse neutrino observations (per flavor) by IceCube. The black and grey data show IceCube s measurement of atmospheric ν e + ν 32,130 e and ν µ + ν 31 µ spectra. The magenta line and magenta-shaded area indicate best-fit and 1σ uncertainty range of a power-law fit to six-year HESE data. Note that HESE analysis vetoes atmospheric neutrinos and can probe astrophysical neutrinos below atmospheric neutrino flux, as indicated in plot (cf. Fig. 17). The corresponding fit to eight-year ν µ + ν µ analysis is shown in red. posited energies ranging from 60 TeV to 10 PeV. The data in both and Fig. 17 are consistent with an astrophysical component with a spectrum close to E 2 above an energy of 200 TeV. An extrapolation of this highenergy flux to lower energy suggests an excess of events in TeV energy range over and above a single power-law fit; see Fig. 18. This conclusion is supported by a subsequent analysis that has lowered threshold of starting-event analysis 136 and by a variety of or analyses. The astrophysical flux measured by IceCube is not featureless; eir spectrum of cosmic accelerators cannot be described by a single power law or a second component of cosmic neutrino sources emerges in spectrum. Because of self-veto of atmospheric neutrinos in HESE analysis, i.e., veto triggered by accompanying atmospheric muons, it is very difficult to accommodate component below 100 TeV as a feature in atmospheric background. In Figure 19 we show arrival directions of most energetic events in eight-year upgoing ν µ + ν µ analysis ( ) and six-year HESE data sets. The HESE data are separated into tracks ( ) and cascades ( ). The median angular resolution of cascade events is indicated by thin circles around best-fit position. The most energetic muons with energy

52 July 9, :42 ws-rv9x6 Book Title trisep halzen page 52 of Neutrinos in Years of Data 52Observation Halzen Observation of Astrophysical Neutrinos infrancis Six Years of IceCube Observation of Astrophysical Neutrinos in Six Years of IceCube Data Observation of Astrophysical Astrophysical Neutrinos in Six Six Years of IceCube IceCube DataData (b) directions (a)arrival deposited energies (b) arrival directions (b) arrival directions PoS(ICRC2017)981 PoS(ICRC2017)981 (a) energies (a) deposited energies (a) deposited deposited energies (b) arrival directions Fig. 17. Left Panel: Deposited energies, by neutrinos interacting inside IceCube, Figure 4: Deposited energies and arrival directions of events and and expected contribudeposited energies andexpected arrival directions Figure 4:six Deposited energies arrival directions of4:observed observed events contribu129 Figure 4: in Deposited energies and and arrival directions of observed events and expected observed years of data. The greyfigure region shows uncertainties on contribu sum ofof observed events and expected contrib from backgrounds astrophysical neutrinos. Atmospheric backgrounds (estimated tions from backgrounds andbackgrounds astrophysical neutrinos. Atmospheric muon backgrounds (estimate tions backgrounds and astrophysical neutrinos. Atmospheric (estimated tions fromfrom backgrounds and astrophysical neutrinos. Atmospheric muon backgrounds (estimated alltions backgrounds. Theand atmospheric muon flux (blue) andmuon itsmuon uncertainty is computed from data) are in Atmospheric neutrino backgrounds shown in blue blue withwith 1s unceruncerfrom data) shown in red. Atmospheric neutrino from data) are shown in red. Atmospheric neutrino backgrounds are shown in blue 1s uncerfrom data) are shown shown in red. red. Atmospheric neutrino backgrounds are shown in with 1s from simulation to overcome statistical limitations in are ourare background measurement andbackgrounds are shown in blue with 1s unce tainties shown as gray band. For scale, 90% CL upper bound on charm tainties on prediction shown asneutrino a gray band. For tainties on prediction prediction shown a gray band. For scale, 90% CL upper bound on charm charm tainties onmatch prediction shown as aaas gray band. For scale, 90% CL upper bound on scaled toon total measured background rate. The atmospheric flux is scale, 90% CL upper bound on char component of atmospheric neutrinos is as The best-fit astrophysical specof line. atmospheric neutrinos is shown as a magenta line. The best-fit astrophysical spe component of atmospheric neutrinos is of shown asmagenta a magenta best-fit astrophysical component of previous atmospheric neutrinos is shown shown as aacomponent magenta line. TheThe best-fit astrophysical specderived from measurements both π,line. K, and charm components ofspec131 tra an power-law model) are shown gray. solidsolid line assumes single tra (assuming anthe unbroken power-law model) are shown in gray. The solid line assumes a sing tra (assuming an unbroken power-law model) are shown in gray. The line assumes single atmospheric spectrum. Also shown are fitsin spectrum, assuming aasimple tra (assuming (assuming an unbroken unbroken power-law model) aretwo shown into gray. The solid line assumes aa single power-law model, whereas dashed line assumes aa(dashed two power-law model, using spectrum power-law model, whereas dashed line assumes power-law (solid gray) and broken power-law gray). Right Panel: The same a two power-law model, using spectru power-law model, whereas dashed line assumes a two power-law model, using spectrum power-law model, whereas a dashed line assumes two power-law model, using spectrum derived [10] as prior for high-energy component. events above 60 TeV TeV are considered considered data andin now showing distribution of events deposited energy above derivedonly in Only [10] as awith prior for component. Only events above 60 TeV are considere derived in [10] as a prior for high-energy component. events above 60 high-energy TeV are considered derived inmodels, [10] as aabut prior for high-energy component. Only events above 60 are 60in infit. declination. At South Pole, in angle δ is equivalent to declination fit. in fit. intev fit. distribution in zenith angle θ related by identity, δ = θ π/2. It is clearly visible that data is flat in Sourn Hemisphere, as expected from contribution of anlike isotropic astrophysical flux. events in We removed events (two coincident muons from unrelated air likeand in sample. We removed eventsair 32 air and 55 (two coincident muons from unrelated a events in sample. sample. removed events (two coincident muons from unrelated likelike events in sample. We We removed events 32 and and 55events (two coincident muons from unrelated showers) and 28 with sub-threshold hits in array) for purposes of all all clustering and 28array) (event sub-threshold hits in IceTop array) for purposes of all clusterin showers) 28 (event sub-threshold in IceTop IceTop forwith purposes of clustering all clustering showers) andand 28 (event (event withwith sub-threshold hits hits in showers) IceTop array) for purposes of analyses. This test (see Fig. 5) significant evidence clustering with p-values of 44% 44% analyses. Thisof Fig.with 5) with did not yield significant analyses. 5) not did not yield significant evidence of(see clustering p-values of 44% evidence of clustering with p-values of 44 analyses. ThisThis test test (see(see Fig.Fig. 5) did did not yield yield significant evidence oftest clustering p-values of Eand > 200 TeV in upgoing ν + ν data set accumulate near horizon µ µ µ and 77% for shower-only and all-events tests, respectively. We also performed a gala 77% for shower-only and all-events tests, respectively. We also performed a galacand 77% for shower-only and all-events tests, respectively. We also performed a galacand 77% for shower-only and all-events tests, respectively. We also performed a galacplane clustering test(p-value using a 23.4%) fixed width of aa2.5a around plane (p-value 23.4%) and using plane clustering test using aa fixed width of around plane (p-value 23.4%) and using intic Norrn Hemisphere. Elsewhere, muon neutrinos are increasingly tic plane clustering test using a fixed width of tic 2.5 around plane and using tic plane clustering test using fixed width of around plane (p-value 23.4%) and using variable-width scanof (p-value 17.4%). All because above p-values are corrected for trials. variable-width (p-value 17.4%). All above p-values corrected for trials. variable-width (p-value 17.4%). All above p-values are corrected for trials. variable-width scan (p-value 17.4%). Allreaching above p-values are corrected for trials. absorbed in scan scan Earth before are vicinity detector of ir relatively large high-energy cross sections. This causes apparent 6. Future Plans 6. Plans 6. Future Plans 6. Future Future Plans anisotropy of events in Norrn Hemisphere. Also HESE events Modified inthreshold IceCube have managed to reduce energy threshold for a sele Modified analysis strategies in IceCube have managed to energy threshold for aafor selecmodified analysis strategies in IceCube managed toanalysis reduce energy a selecmodified analysis strategies in IceCube havehave managed to reduce reduce strategies energy threshold for selecwith energy of E >to 100 suffer from absorption tion ofable starting even furr in order to tion of starting events even furr in order to observed observed flux andin itsbe of starting events furr in order tobetter be TeV better able toevents describe observed flux and itsbetter able to describe observed flux and i tiontion ofdeposited starting events eveneven furr indep order to be be better able to describe describe flux and its but atfirst thistwo timeyears y only properties [7], but at time y have only been applied to first two years of data used forbeen properties [7], at this y only been applied to ofhave data used for applied to first two years of data used f Earth and refore mostly detected when originating in Sourn properties [7],are but but at this this timetime y havehave only beenproperties applied to[7], first two years of data used for this study. lower-threshold this study. Corresponding lower-threshold datasets, using full set of data collected by IceCube IceCube study. Corresponding lower-threshold datasets, using full setdata of data collected by datasets, IceCube thisthis study. Corresponding lower-threshold datasets, using Corresponding full setarrival of collected by Hemisphere. After correcting for absorption, directions of cos-using full set of data collected by IceCub will become available soon [11]. Inors addition, combined fits of this dataset and ors like th will become available soon [11]. In combined fits of this dataset and ors likelike become available In addition, combined of this dataset and willwill become available soonsoon [11].[11]. In addition, addition, combined fits fits of this dataset and ors like mic neutrinos are isotropic, suggesting extragalactic sources. In fact, no through-going muon through-going muon channel [10] are in [11]. through-going muon channel are currently in preparation [11]. channel [10] are currently in preparation [11]. through-going muon channel [10][10] are currently currently in preparation preparation [11]. correlation of arrival directions of highest energy shown in with respect to systematics when compare Due to simplicity andevents, robustness of this search Due to and robustness of search with respect to when compared to simplicity simplicity robustness of this search with respect to systematics when compared DueDue to simplicity andand robustness of this this search with respect to systematics systematics when compared Fig. 19, with potential sources or source classes has reached level of triggering and providing input for follow-u to more detailed searches, it is well suited towards to more detailed searches, it is well suited towards triggering and providing input for follow-up to more detailed searches, is well suited towards triggering providing input for follow-up to more detailed searches, it isitwell suited towards triggering and and providing input for follow-up 3σ The absence of strong anisotropies 7 in arrival direction of IceCube 60 data disfavors scenarios with strong Galactic emission. However, limited number of events and low angular resolution of cascade-dominated

53 July 9, :42 ws-rv9x6 Book Title trisep halzen page 53 High-Energy Astrophysical Neutrinos 53 IceCube Preliminary Fig. 18. Unfolded spectrum for six years of HESE neutrino events starting inside detector. The yellow and red bands show 1σ uncertainties on result of a twopower-law fit. Superimposed is best fit to eight years of upgoing muon neutrino data (pink). Note consistency of red and pink bands. Figure from Ref. 129 samples can hide this type of emission. At a minimum, it is possible that some of data originates in Galactic sources. Various Galactic scenarios have been considered for diffuse neutrino flux in TeV-PeV energy range, including diffuse emission from Galactic CRs, joint emission of Galactic CR sources, or very extended emission from Fermi bubbles 137,146,147 or Galactic halo. 148,149 More exotic scenarios consider dark matter decay in Galactic dark matter halo. Most of se scenarios also predict production of pionic PeV gamma rays. These gamma rays are absorbed via pair production in scattering off CMB photons with an absorption length of about 10 kpc. Therefore, observation of PeV gamma rays would be a smoking gun of Galactic PeV neutrino emission. 137,157 However, isotropic arrival direction of neutrinos would be a natural consequence of extragalactic source populations. A plethora of models have been considered, including galaxies with intense star formation, cores of active galactic nuclei (AGNs), low-luminosity AGNs, 169,170 quasar-driven outflows, 171 blazars, low-power gamma-ray bursts (GRBs), 78, choked GRBs, 83,183,184 cannonball GRBs, 185 intergalactic shocks, 186 galaxy clusters, 159, tidal disruption events, or cosmogenic neutrinos. 121,122 We will discuss in following how we can use multimessenger information to pinpoint true origin of neutrino emission.

54 July 9, :42 ws-rv9x6 Book Title trisep halzen page Francis Halzen Arrival directions of most energetic neutrino events (HESE 6yr (magenta) & n µ + n µ 8yr (red)) North South absorption >90% o Galactic Plane o 1098 Galactic -90 o Fig. 19. Mollweide projection in Galactic coordinates of arrival direction of neutrino events. We show results of eight-year upgoing track analysis 129 with reconstructed muon energy E µ 200 TeV ( ). The events of six-year high-energy starting event (HESE) analysis with deposited energy larger than 100 TeV (tracks and cascades ) are also shown. 129,195,196 The thin circles indicate median angular resolution of cascade events ( ). The blue-shaded region indicates zenith-dependent range where Earth absorption of 100 TeV neutrinos becomes important, reaching more than 90% close to nadir. The dashed line indicates horizon and star ( ) Galactic Center. We highlight four most energetic events in both analyses by ir deposited energy (magenta numbers) and reconstructed muon energy (red number). 6. Multimessenger Interfaces The most important message emerging from IceCube measurements is not apparent yet: prominent and surprisingly important role of protons relative to electrons in nonrmal universe. To illustrate this point, we show in Fig. 20 observed neutrino flux φ in terms of product E 2 φ, which is a measure of its energy density. One can see that cosmic energy density of high-energy neutrinos is comparable to that of γ-rays observed with Fermi satellite 105 (blue data) and to that of ultra-highenergy (UHE) cosmic rays (above 10 9 GeV) observed, e.g., by Auger observatory 197 (green data). This might indicate a common origin of signal and provides excellent conditions for multi-messenger studies. A challenge to most galactic and extragalactic scenarios is large neutrino flux in range of TeV, which implies an equally high intensity of gamma rays from decay of neutral pions produced along with charged pions that are source of observed neutrino flux. 20 For extragalactic scenarios, this gamma-ray emission is not directly ob-

55 July 9, :42 ws-rv9x6 Book Title trisep halzen page 55 High-Energy Astrophysical Neutrinos 55 served because of strong absorption of photons by e + e pair production in extragalactic background light (EBL) and CMB. The high-energy leptons initiate electromagnetic showers of repeated inverse-compton scattering and pair production in CMB that eventually yield photons that contribute to Fermi γ-ray observations in GeV-TeV range. The extragalactic γ-ray background observed by Fermi 105 has contributions from identified point-like sources on top of an isotropic γ-ray background (IGRB) shown in Fig. 20. This IGRB is expected to consist mostly of emission from same class of γ-ray sources that are individually below Fermi s point-source detection threshold (see, e.g., Ref. 198 ). A significant contribution of γ-rays associated with IceCube s neutrino observation would have somewhat surprising implication that indeed many extragalactic γ-ray sources are also neutrino emitters, while none has been detected so far. Anor intriguing observation is that high-energy neutrinos observed at IceCube could be related to sources of UHE CRs. The simple argument is as follows: UHE CR sources can be embedded in environments that act as storage rooms for cosmic rays with energies far below ankle (E CR 1EeV). This energy-dependent trapping can be achieved via cosmic ray diffusion in magnetic fields. While se cosmic rays are trapped, y can produce γ-rays and neutrinos via collisions with gas. If conditions are right, this mechanism can be so efficient that total energy stored in low-energy cosmic rays is converted to that of γ-rays and neutrinos. These calorimetric conditions can be achieved in starburst galaxies 158 or galaxy clusters. 187 We will discuss se multimessenger relations in more detail next IceCube Neutrinos and Fermi Photons Photons are produced in association with neutrinos when accelerated cosmic rays produce neutral and charged pions in interactions with photons or nuclei. Targets include strong radiation fields that may be associated with accelerator as well as concentrations of matter or molecular clouds in ir vicinity. Additionally, pions can be produced in interaction of cosmic rays with EBL when propagating through interstellar or intergalactic background. A high-energy flux of neutrinos is produced in subsequent decay of charged pions via π + µ + + ν µ followed by µ + e + +ν e + ν µ and charge conjugate processes. High-energy gamma rays result from decay of neutral pions, π 0 γ + γ. Pionic gamma

56 July 9, :42 ws-rv9x6 Book Title trisep halzen page Francis Halzen E 2 φ [GeV cm 2 s 1 sr 1 ] isotropic γ-ray background (Fermi) A γ-rays from π 0 decay HESE (7yr) π ± / π 0 production high-energy neutrinos (IceCube) calorimetric limit proton (E 2 ) B ν µ + ν µ (8yr) ultra-high energy cosmic rays (Auger) cosmogenic ν + ν GZK mechanism C energy E [GeV] Fig. 20. The spectral flux (φ) of neutrinos inferred from eight-year upgoing track analysis (red fit) and six-year HESE analysis (magenta fit) compared to flux of unresolved extragalactic γ-ray sources 105 (blue data) and ultra-high-energy cosmic rays 197 (green data). The neutrino spectra are indicated by best-fit power-law (solid line) and 1σ uncertainty range (shaded range). We highlight various multimessenger interfaces: A: The joined production of charged pions (π ± ) and neutral pions (π 0 ) in cosmic-ray interactions leads to emission of neutrinos (dashed blue) and γ-rays (solid blue), respectively. B: Cosmic ray emission models (solid green) of most energetic cosmic rays imply a maximal flux (calorimetric limit) of neutrinos from same sources (green dashed). C: The same cosmic ray model predicts emission of cosmogenic neutrinos from collision with cosmic background photons (GZK mechanism). rays and neutrinos carry, on average, 1/2 and 1/4 of energy of parent pion, respectively. With se approximations, neutrino production rate Q να (units of GeV 1 s 1 ) can be related to one for charged pions as E ν Q να (E ν ) 3 [E π Q π ±(E π )] Eπ 4E ν. (76) α Similarly, production rate of pionic gamma-rays is related to one for neutral pions as E γ Q γ (E γ ) 2 [E π Q π 0(E π )] Eπ 2E γ. (77) Note, that relative production rates of pionic gamma rays and neutrinos only depend on ratio of charged-to-neutral pions produced in cosmic-ray interactions, denoted by K π = N π ±/N π 0. Pion production of cosmic rays in interactions with photons can proceed resonantly in processes p + γ + π 0 + p and p + γ + π + + n. These channels produce charged and neutral pions with probabilities 2/3 and 1/3, respectively. However, additional contribution of nonresonant pion production

57 July 9, :42 ws-rv9x6 Book Title trisep halzen page 57 High-Energy Astrophysical Neutrinos 57 changes this ratio to approximately 1/2 and 1/2. In contrast, cosmic rays interacting with matter, e.g., hydrogen in Galactic disk, produce equal numbers of pions of all three charges: p + p N π [ π 0 + π + + π ] + X, where N π is pion multiplicity. From above arguments we have K π 2 for cosmic ray interactions with gas (pp) and K π 1 for interactions with photons (pγ). With this approximation we can combine Eqs. (76) and (77) to derive a simple relation between pionic gamma-ray and neutrino production rates: 1 3 α E 2 νq να (E ν ) K π 4 [ E 2 γ Q γ (E γ ) ] E γ=2e ν. (78) The prefactor 1/4 accounts for energy ratio E ν / E γ 1/2 and two gamma rays produced in neutral pion decay. This powerful relation relates pionic neutrinos and gamma rays without any reference to cosmic ray beam; it simply reflects fact that a π 0 produces two γ rays for every charged pion producing a ν µ + ν µ pair, which cannot be separated by current experiments. Before applying this relation to a cosmic accelerator, we have to be aware of fact that, unlike neutrinos, gamma rays interact with photons of cosmic microwave background before reaching Earth. The resulting electromagnetic shower subdivides initial photon energy, resulting in multiple photons in GeV-TeV energy range by time photons reach Earth. Calculating cascaded gamma-ray flux accompanying IceCube neutrinos is straightforward. 107,199 As an illustration, we show a model of γ-ray and neutrino emission as blue lines in Fig. 20. We assume that underlying π 0 / π ± production follows from cosmic-ray interactions with gas in universe. In this way, initial emission spectrum of γ-rays and neutrinos from pion decay is almost identical to spectrum of cosmic rays (assumed to be a power law, E Γ ), after accounting for different normalizations and energy scales. The flux of neutrinos arriving at Earth (blue dashed line) follows this initial CR emission spectrum. However, observable flux of γ-rays (blue solid lines) is strongly attenuated above 100 GeV by interactions with extragalactic background photons. The overall normalisation of emission is chosen in a way that model does not exceed isotropic γ-ray background observed by Fermi satellite (blue data). This implies an upper limit on neutrino flux shown as blue dashed line. Interestingly, neutrino data shown

58 July 9, :42 ws-rv9x6 Book Title trisep halzen page Francis Halzen in Fig. 20 saturates this limit above 100 TeV. Moreover, HESE data that extends to lower energies is only marginally consistent with upper bound implied by model (blue dashed line). This example shows that multi-messenger studies of γ-ray and neutrino data are powerful tools to study neutrino production mechanism and to constrain neutrino source models. 159 The matching energy densities of extragalactic gamma-ray flux detected by Fermi and high-energy neutrino flux measured by IceCube suggest that, rar than detecting some exotic sources, it is more likely that IceCube to a large extent observes same universe astronomers do. Clearly, an extreme universe modeled exclusively on basis of electromagnetic processes is no longer realistic. The finding implies that a large fraction, possibly most, of energy in nonrmal universe originates in hadronic processes, indicating a larger role than previously thought. The high intensity of neutrino flux below 100 TeV in comparison to Fermi data might indicate that se sources are even more efficient neutrino than gamma-ray sources. 164,200 IceCube is developing methods, most promisingly real-time multiwavelength observations in cooperation with astronomical telescopes, to identify sources and build on discovery of cosmic neutrinos to launch a new era in astronomy. 201,202 We will return to a coincident observation of a flaring blazar on September 22, 2017, furr on IceCube Neutrinos and Ultra-High-Energy Cosmic Rays The charged pion production rate Q π ± is proportional to density of cosmic-ray nucleons in beam that produces pions, Q N, by a bolometric proportionality factor f π 1. For a target with nucleon density n and extension l, efficiency factor for producing pions is f π 1 exp( κlσn), where cross section σ and inelasticity, i.e., average relative energy loss of leading nucleon, refer to eir pγ or pp interactions. The pion production efficiency f π normalizes conversion of cosmic-ray energy into pion energy on target as: E 2 πq π ±(E π ) f π K π 1 + K π [ E 2 N Q N (E N ) ] E N =E π/κ π. (79) We already introduced pion ratio K π in previous section, with K π 2 for pp and K π 1 for pγ interactions. The factor κ π denotes average inelasticity per pion that depends on average pion multiplicity N π. For,

59 July 9, :42 ws-rv9x6 Book Title trisep halzen page 59 High-Energy Astrophysical Neutrinos 59 both, pp and pγ interactions this can be approximated as κ π = κ/n π 0.2. The average energy per pion is n E π = κ π E N and average energy of pionic leptons relative to nucleon is E ν E π /4 = (κ π /4)E N 0.05E N. In general, CR nucleon emission rate, Q N, depends on composition of UHE CRs and can be related to spectra c of nuclei with mass number A as Q N (E N ) = A A2 Q A (AE N ). In following we will derive a upper limit on diffuse neutrino fluxes under assumption that UHE CRs are dominated by protons. 69,70 The local emission rate density, Q = ρ 0 Q, at se energies is insensitive to luminosity evolution [ of sources at high redshift and can be estimated to be at level of E 2 p Q p (E p ) ] ( ) ev 1044 erg/mpc 3 /yr Note, that CR composition measurements indicate that mass composition above ankle also requires a contribution of heavier nuclei. However, estimated local UHE CR power density based on proton models is a good proxy for that of UHE CR models including heavy nuclei, as long as spectral index is close to Γ 2. For instance, a recent analysis of Auger 74 provides a solution with spectral index Γ 2.04 and a combined nucleon density of [EN 2 Q N (E N )] ev erg/mpc 3 /yr. For calculation of (quasi-)diffuse neutrino spectra we start from contribution of individual sources. A neutrino point-source (PS) at redshift z with spectral emission rate Q να contributes a flux (in units GeV 1 cm 2 s 1 and summed over flavors) φ PS (1 + z)2 ν (E ν ) = 4πd 2 L (z) Q να ((1 + z)e ν ), (80) where d L is luminosity distance. For standard ΛCDM cosmological model, 68 this is simply given by redshift integral α z dz d L (z) = (1 + z) H(z ). (81) Here, Hubble parameter H has a local value of c/h Gpc and scales with redshift as H 2 (z) = H 2 0 [(1 + z) 3 Ω m + Ω Λ ], with Ω m 0.3 and Ω Λ 0.7. Note that extra factor (1 + z) 2 appearing in Eq. (80) follows from definition of luminosity distance and accounts for relation of energy flux to differential neutrino flux φ. The diffuse c Note that integrated number of nucleons is linear to mass number, deq N (E) = A A deq A (E). 0

60 July 9, :42 ws-rv9x6 Book Title trisep halzen page Francis Halzen neutrino flux from extragalactic sources is given by integral over comoving volume dv c = 4π(d L /(1 + z)) 2 dz/h(z). Weighting each neutrino source by its density per co-moving volume ρ(z) gives (see, e.g., Ref. 203 ): φ ν (E ν ) = c 4π 0 dz H(z) ρ(z) Q να ((1 + z)e ν ). (82) α In following, we will assume that neutrino emission rate Q να follows a power law E Γ. The flavor-averaged neutrino flux can n be written as 1 3 α Eνφ 2 να (E ν ) = c ξ z 1 4π H 0 3 EνQ 2 να (E ν ), (83) where Q να = ρ 0 Q να is neutrino emission rate density and we introduced redshift factor ξ z = 0 α (1 + z) Γ ρ(z) dz. (84) ΩΛ + (1 + z) 3 Ω m ρ 0 A spectral index of Γ 2.0 and no source evolution in local (z < 2) universe, ρ(z) = ρ 0, yields ξ z 0.5. For sources following starformation rate, ρ(z) = (1 + z) 3 for z < 1.5 and ρ(z) = ( ) 3 for 1.5 < z < 4, with same spectral index yields ξ z 2.6. We already introduced this simplified treatment of integration of sources in an evolving universe in section 4.1. We can now derive observed diffuse neutrino flux related to sources of UHE CRs. Combining Eqs. (76) and (79) to relate local neutrino emission rate density to CR nucleon rate density, we arrive at diffuse (per flavor) neutrino flux via Eq. (83): 1 3 α ( ) ( Eνφ 2 να (E ν ) ξz [EpQ 2 p (E p )] Ep=10 f 19.5 ev π erg/mpc 3 /yr ) GeV cm s sr. (85) Here, we have assumed pp interactions with K π = 2. The calorimetric limit, f π 1, of Eq. (90) corresponds to Waxman Bahcall (WB) upper limit on neutrino production in UHE CR sources. 69,70 As mentioned in introduction of this section, se calorimetric conditions can be achieved by a rigidity-dependent cosmic ray trapping considered, e.g., in starburst galaxies 158 or galaxy clusters. 187 It is intriguing that observed intensity of diffuse neutrinos is close to level of WB bound. A more precise correspondence is illustrated by green lines in Fig. 20 showing a model of UHECR protons that

61 July 9, :42 ws-rv9x6 Book Title trisep halzen page 61 High-Energy Astrophysical Neutrinos 61 could account for most energetic cosmic rays (green data). Note, that cosmic ray data below GeV is not accounted for by this model and must be supplied by additional sources, not discussed here. If we now consider case that UHECR sources are embedded in calorimeters, we can derive maximal neutrino emission (green dashed line) from low-energy tail of proton model. Interestingly, observed neutrino flux saturates this calorimetric limit. It is refore feasible that UHECRs and neutrinos observed with IceCube have a common origin. If this is case, neutrino spectrum beyond 200 TeV should reflect energydependent release of cosmic rays from calorimeters. Future studies of neutrino spectrum beyond 1 PeV can provide supporting evidence for CR calorimeter. In particular, transition to a thin environment (f π 1), that is a necessary condition of UHE CR emission, implies a break or cutoff in neutrino spectrum. Note that proton model in Fig. 20 also contributes to flux of EeV neutrinos shown as a dotted green line. Ultra-high energy CRs are strongly attenuated by resonant interactions with background photons, as first pointed out by Greisen, Zatsepin and Kuzmin 96,97 (GZK). This GZK mechanism is responsible for suppression of UHECR proton flux beyond GeV ( GZK cutoff ) in Fig. 20 (green solid line) and predicts a detectable flux of cosmogenic neutrinos 24 (green dotted line). The proton fraction of UHE CRs at E ev can be probed by EHE neutrino observatories at level of 10% if (all flavor) EeV sensitivity reaches E 2 φ 10 9 GeV/cm 2 /s/sr and if sources follow evolution of star formation rate. The low energy tail of same population of UHE CR protons can be responsible for observed neutrino emission below 10 PeV assuming a calorimetric environment Pinpointing Astrophysical Sources of Cosmic Neutrinos The flux of neutrinos measured by IceCube provides a constraint on flux from individual sources that it is composed of. We can investigate under what circumstances IceCube can detect neutrino emission from individual, presumably nearby, point sources that contribute to quasi-diffuse emission. Eq. (83) relates average luminosity of individual neutrino sources to diffuse flux that is measured by experiment to be at level of E 2 φ ν 10 8 GeVcm 2 s 1 sr 1 for energies in excess of 100 TeV; see Fig. 18. From measurement, we can infer average

62 July 9, :42 ws-rv9x6 Book Title trisep halzen page Francis Halzen 10 2 effective local density ρ eff [Mpc 3 ] LL AGN Starburst FR-I excluded by non-observation of closest source in Norrn Hemisphere Galaxy Clusters FR-II (E 2 φ PS < TeV/cm 2 /s) BL Lac diffuse flux (ξ z = 2.6) diffuse flux (ξ z = 0.5) FSRQ neutrino luminosity L ν[erg/s] Fig. 21. The effective local density and (maximal) neutrino luminosity of various neutrino source candidates from Ref. 204 The green solid (green dotted) line shows local density and luminosity of population of sources responsible for diffuse neutrino flux of E 2 φ 10 8 GeV cm 2 s 1 sr 1 observed with IceCube, assuming source evolution following star-formation rate (ξ z 2.6) or no source evolution (ξ z 0.5), respectively. The grey-shaded area indicates source populations that are excluded by nonobservation of point sources in Norrn Hemisphere (f sky 0.5) with discovery potential E 2 φ PS TeV cm 2 s emission from a single source 203 depending on local density of sources, 1 ( ) 1 ( ) 1 E 2 3 νq να (E ν ) ξz ρ Mpc 3 erg s 1. (86) α For a homogenous distribution of sources, we expect, within partial field of view f sky of full sky, one source within a distance d 1 determined by f sky 4πd 3 1/3 ρ 0 = 1. In or words, d 1 defines volume containing one nearby source for a homogeneous source density ρ 0. Defining φ 1 as flux of a source at distance d 1, given by Eq. (80) with z 0 and d L d 1, we can write probability distribution p(φ) of finding closest source of population with a flux φ as (for details see App. of Ref. 203 ) p(φ) = 3 ( ) 3 1 φ1 2 e ( φ 1 φ ) 3 2. (87) 2 φ φ The average flux from closest source is n φ 2.7φ 1, with median φ med 1.3φ 1. Applying this to closest source introduced above, we

63 July 9, :42 ws-rv9x6 Book Title trisep halzen page 63 High-Energy Astrophysical Neutrinos 63 obtain its per-flavor flux: 1 3 Eνφ 2 να α ( fsky 0.5 ) 2 ( ) 3 1 ( ξ z 2.6 ρ Mpc 3 ) 1 3 TeV cm 2 s 1. (88) Interestingly, this value is not far from IceCube s point-source discovery potential at level of TeV cm 2 s 1 in Norrn Hemisphere. 205 In Figure 21, we show local density and luminosity of orized neutrino sources. 204 The grey-shaded region is excluded by failure to observe se sources as individual point sources, assuming discovery potential of IceCube in Norrn Hemisphere given in caption. The green lines show combination of density and luminosity for sources at level of observed IceCube flux, assuming a source density evolution following star formation rate (solid line) or no evolution (dotted line). We conclude that IceCube is presently sensitive to source populations with local source densities smaller than, conservatively, 10 8 Mpc 3. Much lower local densities, like BL Lacs FSRQs, are challenged by nonobservation of individual sources. Some source classes, like Fanaroff-Riley (FR) radio galaxies, have an estimated neutrino luminosity that is likely too low for observed flux. Note that se estimates depend on evolution parameter ξ z, and refore exact sensitivity estimate depends on redshift evolution of source luminosity density. In addition, this simple estimate can be refined by considering not only closest source of population but combined emission of known local sources; see, e.g., Ref. 203 Is it possible that sources of extragalactic cosmic rays are mselves neutrino sources? From measured cosmic-ray spectrum, one can derive that emission rate density of nucleons is at level of 71,72 L p = ρ 0 E 2 pq p (E p ) (1 2) erg Mpc 3 yr 1. (89) Combining this with Eq.25 we can derive diffuse neutrino flux: 1 E 2 ξ z K π 3 νφ να (E ν ) f π (2 4) 10 8 GeV cm 2 s 1 sr. (90) 1 + K π α Here, ξ z is evolution factor previously introduced. The equation has been rewritten and some notation adjusted in order to accommodate both pp and γp interactions. Counting particles we derive that 1 3 E ν Q να (E ν ) = E π Q π, (91) α

64 July 9, :42 ws-rv9x6 Book Title trisep halzen page Francis Halzen from which relation for energy follows by multiplying both sides with E ν ; an additional factor of 1/4 multiplies right-hand side by ratio of neutrino to pion energy within approximations routinely used throughout. The requirement f π 1 limits neutrino production by actual sources of cosmic rays as pointed out by seminal work by Waxman and Bahcall. 69 For optically thin sources, f π 1, neutrino production is only a small by-product of acceleration process. The energy loss associated with pion production must not limit sources ability to accelerate cosmic rays. On or hand, optically thick sources, f π 1, may be efficient neutrino emitters. Realistic sources of this type need different zones, one zone for acceleration process (f π 1) and a second zone for efficient conversion of cosmic rays to neutrinos (f π 1). 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 ξ z 2.4 and K π 1 2, upper bound resulting from Eq. (90) and f π = 1 is at level of neutrino flux observed by IceCube. Therefore, it is possible that observed extragalactic cosmic rays and neutrinos have 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 calorimetric environment can be introduced by energy dependent diffusion. If D(E) is diffusion coefficient, n timescale of escape from calorimeter is given by solution to 6D(E)t = d 2, where d is effective size of region. Typically, we have D(E) E δ with δ In following, we again consider case of protons. Taking σ pp cm 2 at E p = 100 PeV and diffusion coefficient of D(E p ) D GeV (E p /1GeV) 1/3, pp thickness can be expressed as τ pp ctn gas σ pp or ( ) 2 ( ) 1 ( ) 1/3 d DGeV Ep ( n ) τ pp pc cm 2 /s 10 PeV 100cm 3. (92) Here, we have used feasible parameters of starburst galaxies. 158,159 Therefore, depending on calorimetric environment, it is possible that flux below a few PeV is efficiently converted to neutrinos and contributes to TeV PeV diffuse emission observed by IceCube.

65 July 9, :42 ws-rv9x6 Book Title trisep halzen page 65 High-Energy Astrophysical Neutrinos Are Blazars Sources of Cosmic Neutrinos (and Extragalactic Cosmic rays)? The qualitative matching of energy densities of photons and neutrinos, discussed in previous section, suggests that unidentified neutrino sources contributing to diffuse flux might have already been observed as strong gamma-ray emitters. Theoretical models 206,207 and recent data analyses show that Fermi s extragalactic gamma-ray flux is dominated by blazars. A dedicated IceCube study 211 of Fermi-observed blazars showed no evidence of neutrino emission from se source candidates. However, inferred limit on ir quasi-diffuse flux leaves room for a significant contribution to IceCube s diffuse neutrino flux at 10% level and increasing towards PeV. This hyposis is corroborated by recent observation of flaring blazar TXS in direction of a very high energy IceCube neutrino. IceCube detects one well-localized muon neutrino every few minutes as an up-going track event. These events are dominated by low-energy atmospheric neutrinos. IceCube recently installed an automatic filter that selects in real time rare very high energy events that are potentially cosmic in origin and sends astronomical coordinates to Gamma-ray Coordinate Network for possible follow-up by astronomical telescopes. The tenth such alert, IceCube A, 212 on September 22, 2017, reported a wellreconstructed muon neutrino with energy exceeding 180 TeV (most likely energy 290 TeV) and, refore, with a significant probability of originating in outer space rar than in Earth s atmosphere. What makes this alert special is that telescopes detected enhanced gamma-ray activity from a flaring blazar aligned with cosmic neutrino to within The source is a known blazar, TXS , and its redshift has been subsequently measured to be z Originally detected by NASA s Fermi 214 and Swift 215 satellite telescopes, alert was followed up by MAGIC air Cherenkov telescope. 216 MAGIC detected gamma rays with energies exceeding 100 GeV. Several or telescopes subsequently observed flaring blazar. Given where to look, IceCube searched in archival neutrino data, up to and including October 2017, for evidence of neutrino emission at location of TXS With a redshift of 0.34, we can conclude that source is a TeV blazar. Several or telescopes subsequently observed flaring blazar. It is important to realize that nearby blazars like Markarian sources are at a redshift that is ten times smaller, and refore TXS ,

66 July 9, :42 ws-rv9x6 Book Title trisep halzen page Francis Halzen with a similar flux despite greater distance, is one of most luminous sources in Universe. It must belong to a special class of sources that accelerate proton beams revealed by neutrino. That source belongs to a subclass is also consistent with fact that multiple attempts have not found a correlation between arrival directions of cosmic neutrinos previously observed by IceCube and various Fermi blazar catalogues that are dominated by vanilla nearby sources. Given where to look, IceCube searched its archival neutrino data up to and including October 2017, for evidence of neutrino emission at location of TXS When searching sky for point sources of neutrinos, two analyses have been routinely performed: one looking for a steady emission and one that searches for flares over a variety of timescales. Evidence was found for a spectacular burst of 14 high-energy neutrinos in 110 days. It dominates flux of source over last 9.5 years for which we have data. It is interesting to note that a subset of blazars, around 1 10 % of all blazars, bursting once in 10 years at levels of TXS, can accommodate diffuse cosmic neutrino flux observed by IceCube. The energy of neutrino flux generated by flaring blazars is at same level as flux in extragalactic cosmic rays, Waxman-Bahcall bound. It is important to note striking fact that all high-energy spectra, for both photons and neutrinos and for both 2014 and 2017 bursts, are consistent with a hard E 2 spectrum, which is expected for a cosmic accelerator. In fact, gamma-ray spectrum flattens beyond that during 110-day period of 2014 burst. This, combined with low probability for coincident observation of Fermi and IceCube, significance of 2014 neutrino flare, and detection of TeV emission by MAGIC, puts discovery of first comic ray accelerator beyond question. Here, we discuss how identification of TXS help us understand total diffuse neutrino flux measured by IceCube and how it is tied to production rate of very high-energy cosmic rays. In order to calculate flux of high-energy neutrinos from a population of sources, we adopt calculation of flux introduced in 6 to relate diffuse neutrino flux to energy injection rate of cosmic rays and ir efficiency to transfer energy from protons (Cosmic rays). Considering a population of sources, with neutrino luminosity L ν, diffuse neutrino flux could be obtained by E 2 dn de = 1 4π d 3 r L ν 4πr 2 ρ (93)

67 July 9, :42 ws-rv9x6 Book Title trisep halzen page 67 High-Energy Astrophysical Neutrinos 67 which can be simplified into E 2 dn de = c 4π t HξL ν ρ (94) As we plan to work out diffuse neutrino flux from time dependent (flaring) source, similar to TXS, and within assumption that a fraction of sources contribute to neutrino flux, we revise equation to account for duration of flare, total time of observation, and fraction of sources. Therefore, corresponding to TeVcm 2 s 1 sr 1 = F 4π E 2 dn de = c 4π t HξL ν ρ t T F (95) ( RH 3 Gpc ( )( )( ξ 1 ρ 10 8 Mpc 3 L ν erg/s )( t 10 yr 110 d T obs ) ) (96) which results in F = In summary, a special class of BL Lac blazars like TXS, that undergo 110 day duration flares would be describing observed diffuse flux of high-energy cosmic neutrinos. The high-energy neutrino flaring sources constitute 5% of sources. The energetics in neutrino production from se sources has to be consistent with flux of very(ultra) high-energy cosmic rays. Equivalently, E 2 dn de c ( ) 1 4π 2 (1 de e fπ ) ξt H, (97) dt The cosmic rays injection rate at energies above ev is (1 2) erg Mpc 3 yr 1. Comparing results of Equation 96, we can find pion efficiency of neutrino source ( L ν erg/s )( ρ 10 8 Mpc (1 e fπ ) )( t 110 d )( ) 10 yr F T obs 0.05 de/dt (1 2) erg Mpc 3 yr 1 (98) This corresponds to f π > 0.8. In section on blazar jets we discussed how this can be achieved with a proton beam with low boost factor interacting with blue photons in active galaxy. The jet producing neutrinos is not transparent to TeV photons, only to photons with tens of GeV which is indeed what is observed in 2014 flare in Fermi data. It is also worth noting that on July 31, 2016, IceCube sent out a similar neutrino alert. The AGILE collaboration, which operates an orbiting X-ray

68 July 9, :42 ws-rv9x6 Book Title trisep halzen page Francis Halzen and gamma-ray telescope, reported a day-long blazar flare in direction of neutrino, one day before neutrino detection. 218 Before automatic alerts, in April 2016, TANAMI collaboration argued for association of highest energy IceCube event at time, dubbed Big Bird, with flaring blazar PKS B Finally, AMANDA, IceCube s predecessor, observed three neutrinos in coincidence with a rare flare of blazar 1ES , detected by Whipple telescope in However, se detections did not reach significance of observations triggered by IceCube A. As discussed in previous sections, absence of a strong anisotropy of neutrino arrival directions raises possibility that cosmic neutrinos originate from a number of relatively weak extragalactic sources. It is indeed important to keep in mind that interaction rate of a neutrino is so low that it travels unattenuated over cosmic distances through tenuous matter and radiation backgrounds of Universe. This makes identification of individual point sources contributing to IceCube flux challenging. 203, Even so, it is also important to realize that IceCube is capable of localizing sources by observing multiple neutrinos originating in same location. Not having observed neutrino clusters in present data raises question of how many events are required to make such a model-independent identification possible. The answer to this question suggests construction of a next-generation detector that instruments a ten times larger volume of ice Beyond Astronomy IceCube was designed as a discovery instrument that covers a range of areas in multidisciplinary science. Examples include search for Galactic supernova explosions and study of neutrinos mselves. With higher energies and high-statistics data samples, opportunities for neutrino physics are varied Searching for Dark Matter Neutrino telescopes are powerful tools in search for particle nature of dark matter. By using deepest ice and a higher density of optical sensors, IceCube s DeepCore subarray lowers threshold of detector to 10 GeV over a significant fraction of detector volume; see Fig. 3.

69 July 9, :42 ws-rv9x6 Book Title trisep halzen page 69 High-Energy Astrophysical Neutrinos 69 It was initially proposed as a way to enhance IceCube s capabilities for detecting lower mass dark matter particles. It is worth noting that AMANDA detector, forerunner and proof of concept for IceCube, received a significant fraction of its initial funding to search for dark matter. Also, in this context, some have considered isotropic arrival directions of cosmic neutrinos to be a clue that y originate in Galactic halo as a result of decay of PeV-energy dark matter particles, a speculation that at this point is perfectly consistent with observations , More traditionally, IceCube and ANTARES search for dark matter by looking for annihilation of weakly interacting massive particles (WIMPs) wherever y have accumulated to a high density: in Sun, 228,229 in Milky Way, and in nearby galaxies. 233 For instance, WIMPs are swept up by Sun as solar system moves about Galactic halo. Though interacting weakly, y will occasionally scatter elastically with nuclei in Sun and lose sufficient momentum to become gravitationally bound. Over lifetime of Sun, WIMPs may accumulate to a density where equilibrium is established between ir capture and annihilation. The annihilation of se WIMPs to final states that can decay to neutrinos represents an indirect signature of halo dark matter. This WIMP annihilation signal is revealed by neutrinos that escape Sun with minimal absorption. The neutrinos are, for instance, decay products of heavy quarks and weak bosons resulting from annihilation of WIMPs into χχ τ τ, b b, or W + W. Neutrino telescopes are sensitive to such neutrinos because of ir relatively high energy, above 20 GeV at this point, reflecting mass of decaying WIMP. The beauty of indirect detection technique using neutrinos originating from Sun is that astrophysics of problem is understood. The source in Sun has built up over solar time, sampling dark matter throughout galaxy. Therefore, any possible structure in halo has been averaged out. Given a WIMP mass and properties, one can unambiguously predict signal in a neutrino telescope; if not observed, model is ruled out. This is in contrast to or indirect searches whose sensitivity depends critically on structure of halo dark matter; observation requires cuspy structure near Galactic center or clustering on appropriate scales elsewhere. Observation necessitates not only appropriate WIMP properties but also favorable astrophysical circumstances. IceCube has established world-leading limits on WIMPs with significant spin-dependent interactions with protons because y result in strong concentrations inside Sun, a nearby and readily identifiable source. 234,235

70 July 9, :42 ws-rv9x6 Book Title trisep halzen page Francis Halzen An excess of neutrinos, of GeV or higher energy, over atmospheric neutrino background in direction of Sun is signature of dark matter. There is no alternative astrophysical explanation of such a signal, which represents a smoking gun for dark matter particles. In most WIMP scenarios, cross sections for WIMP capture and for WIMP annihilation are large enough so that an equilibrium between capture and annihilation would have been achieved within age of solar system. 236 In this case, limits on neutrinos from Sun can be expressed in terms of capture cross section. If equilibrium is not reached, weaker limits can still be derived. The current IceCube limits 228,234,235 are shown in Fig. 22. These are derived from three years of muon neutrino observations; no excess of neutrinos over atmospheric flux has been found in direction of Sun. By including events that start inside DeepCore, mass range for WIMP search could be extended down to 20 GeV, which overlaps some of allowed region from DAMA experiment. 237 Since exact branching ratios of WIMP annihilation into different channels is model-dependent, experiments usually choose two annihilation channels that give extreme neutrino spectra to show ir results. Annihilation into b b is chosen as a representative case producing a soft neutrino spectrum, and annihilation into W + W or τ τ as a hard spectrum. Assuming a 100% branching ratio to each of se channels brackets expected neutrino spectrum for any model with branching to more channels. IceCube and Super-K reach bounds at cm 2 level, covering WIMP mass range, between two experiments, from a few GeV to 100 TeV. Because of A 2 coherence factor for scattering on heavy nuclei with atomic number A, direct detection experiments have an advantage over IceCube for case of spin-independent interactions. They thus achieve superior limits to IceCube Neutrino Oscillations The first IceCube neutrino oscillation analysis 245 used data from 79- string detector from May 2010 to May The analysis was based entirely on ν µ -induced muons from below horizon. By taking advantage of DeepCore subarray of IceCube, neutrino oscillations were observed over an energy range that includes oscillation minimum of around 25 GeV for propagation through diameter of Earth. Data were divided into two samples, muon tracks reconstructed using entire IceCube detector

71 July 9, :42 ws-rv9x6 Book Title trisep halzen page 71 High-Energy Astrophysical Neutrinos 71 Fig. 22. Upper limits at 90% confidence level on spin-dependent neutralino-proton cross section assuming that neutrinos are produced by b b, τ τ, and W + W annihilation. Limits from IceCube, 228,234,235 Super-K, 238 and ANTARES 239,240 are shown. Full lines refer to limits on annihilation channel and dashed lines to b b channel. Direct search results from PICO 241 and tentative signal regions (green-shaded area) are included for comparison. The purple-shaded region indicates allowed parameter space in MSSM supersymmetric dark matter models that are not ruled out by or experiments. (E ν > 100 GeV) and events starting in DeepCore (20 < E ν < 100 GeV). The low-energy sample consisted of 719 events, while high-energy sample included 39,638 events. The high-energy sample, in which standard oscillations do not affect rates, was used for calibration. A deficit was observed in low-energy sample, where approximately 25% more events would have been detected in absence of oscillations. Taking systematic uncertainties into account, including ±0.05 in spectral index of atmospheric neutrino flux at production, no-oscillation hyposis was rejected at more than 5σ. The fitted values of oscillation parameters in a two-flavor fit are m 2 32 = ev 2 and sin 2 2θ 23 > For comparison, a recent global three-flavor analysis 246 gives 2.4 ev 2 and 0.95 respectively, with a range of ±5% at 1σ and a slight dependence on mass hierarchy. While measured oscillation parameters agree with previous experiments, it is important to realize that y have been measured at a characteristic energy that is higher. The measurement is refore also

72 July 9, :42 ws-rv9x6 Book Title trisep halzen page Francis Halzen ν µ muon-suppressed pion decay (0:1:0) 25% 75% 50% pion & muon decay (1:2:0) 50% oscillation-averaged 25% neutron decay (1:0:0) 75% 25% 50% 75% ν τ ν e Fig. 23. Neutrino flavor phase space after oscillation. We use best-fit oscillation parameters sin 2 θ 12 = 0.304, sin 2 θ 23 = 0.577, sin 2 θ 13 = , and δ = 251 following Ref. 247 updated after Neutrino Each position in triangle parametrizes a general initial flavor ratio (ν e : ν µ : ν τ ). We also indicate specific ratios for neutron decay and pion production. The inner triangle is corresponding observable phase space after decoherence of neutrino flavor state over large times or distances. sensitive to any new neutrino physics, an important consideration when precision of IceCube measurements will be significantly improved. The above results will significantly improve with development of analysis techniques that are optimized to selection and analysis of low-energy events. Recently, IceCube has also contributed world-best limits on existence of ev-mass sterile neutrinos New Neutrino Physics Various authors have studied implications of IceCube s HESE (highenergy starting event) topologies with astrophysical and/or exotic production mechanisms Figure 23 shows general neutrino flavor phase space ν e :ν µ :ν τ and expected intrinsic flavor ratio in astrophysical sources from neutron decay (triangle), pion+muon decay (circle), and muon-damped pion decay (square). The observable neutrino flavor ratio is expected to be averaged over many oscillations. This leaves only a very narrow range for possible flavor composition, which is shown as line

73 July 9, :42 ws-rv9x6 Book Title trisep halzen page 73 High-Energy Astrophysical Neutrinos 73 in center of Fig. 23. The corresponding observable flavor ratios of three astrophysical production mechanisms are also indicated. The final parameter space is very close to tri-bi-maximal approximation of mixing angles, which predicts that final flavor ratio depends only on initial electron neutrino ratio x = N νe /N νtot and (2/3+x):(7/6 x/2):(7/6 x/2). The precise relation between HESE topologies and flavor composition is nontrivial, since atmospheric backgrounds and detector effects have to be taken into account properly. In a recent IceCube analysis, 135 it was shown that observation of tracks and cascades is consistent with most astrophysical scenarios within uncertainties. At sub-pev energies (before ν τ events can be distinguished from single cascades), observation is mostly degenerate in terms of total ν e + ν τ ratio, except for contribution of prompt tau decays into muons. The expected fraction for tracks out of total number events is about 7/24 x/8, where we take into account that CC interactions are about three times larger than neutral current interactions at se energies. The uncertainty of inferred intrinsic electron-neutrino fraction x is hence about eight times higher than uncertainty of track fraction. The situation becomes even more challenging if we include backgrounds and systematic uncertainties. The situation of flavor identification improves at super-pev neutrino energies. On one hand, decay length of τ produced in CC ν τ interactions becomes resolvable by detector and can in principle be distinguished from tracks and cascade events as argued before. On or hand, electron antineutrinos, ν e, can resonantly interact with in-ice electrons via Glashow resonance, ν e e W, at neutrino energies of about 6.3 PeV. This could be observable as a peak in cascade spectrum, depending on relative contribution of ν e after oscillation. In principle, this will allow us to answer basic question of wher cosmic neutrinos are photo- or hadro-produced in source with different neutrino-to-antineutrino ratios. 256, Supernovae and Solar Flares In addition to normal acquisition of events that reconstruct as tracks or cascades in deep array of IceCube and as air showers in IceTop, rates at which PMT voltages cross thresholds of discriminators in DOMs are continuously monitored. Typical rates for DOMs in deep ice are 500 Hz (including correlated afterpulses), most of which is noise. Typical rates in high-gain DOMs of IceTop are 2-5 khz, most of

74 July 9, :42 ws-rv9x6 Book Title trisep halzen page Francis Halzen which is induced by low-energy photons, electrons and muons entering tanks. A sudden increase in total summed counting rate of deep DOMs would signify a potential supernova explosion in Galaxy. Supernova neutrinos of 10 MeV interacting within a few meters of a DOM would generate enough hits to cause a sharp increase in summed counting rate followed by a characteristic decline. 258 IceCube records a DC current that tracks time evolution of supernova in microsecond time bins. However, detector records time of every photoelectron with nanosecond precision and binning can refore be improved offline. This will improve capability to identify deleptonization burst. The additional measurement of rate of neutrino events producing two photons is sensitive to energy of supernova neutrinos. In IceTop, sudden changes in rates occur in response to solar events. Forbush decreases, in which plasma from a solar flare abruptly reduces rate of cosmic rays entering atmosphere, are frequently detected and can be analyzed. More rare are sudden increases caused by solar energetic particles that enter atmosphere with sufficient energy to generate secondary cosmic rays that reach IceTop tanks. The event of December 13, 2006, was measured with sixteen tanks (eight stations) n in operation. 259 The flare of May 17, 2012, is currently being analyzed IceCube, Facility During its construction phase, IceCube demonstrated a significant potential for facilitating a range of or research. For example, a dust logger provided measurements with millimeter precision that are valuable for event reconstruction in IceCube but that also provide a record of surface winds over more than 100,000 years. 260 Already during construction of AMANDA, antennas forming RICE detector were deployed in some holes to expand target volume in search for cosmogenic neutrinos. 261 An acoustic test setup of receivers in upper portion of four IceCube holes was deployed in 2007 to explore acoustic technique for detecting ultra-high-energy neutrinos. A retrievable transmitter (pinger) was submerged briefly in several newly prepared holes at various depths and distances from receivers to measure attenuation of sound in ice. The attenuation length of 300 m is significantly less than had been expected. 262 The Askaryan Radio Array (ARA) 263 plans to take advantage of kilometer-scale attenuation for radio signals in

75 July 9, :42 ws-rv9x6 Book Title trisep halzen page 75 High-Energy Astrophysical Neutrinos 75 ice to construct a detector with a 200 km 2 effective area, which should be sufficient to determine level of production of cosmogenic neutrinos, which at present is highly uncertain. The initially deployed ARA detectors send data to computers housed in IceCube Lab (ICL) for staging and transmission to north. The DM-Ice experiment 264 proposes to repeat DAMA experiment in quiet environment of Antarctic ice. An interesting feature of observation is fact that seasonal modulation of muon rate has opposite phase relative to motion of Earth through gas of dark matter as compared to a detector in Norrn Hemisphere. A test detector to explore noise environment for DM-Ice was deployed at bottom of an IceCube string in December Its computers and data transmission are also hosted in ICL. The enhancement of low-energy capabilities of IceCube provided by DeepCore subarray has led to PINGU proposal 265 to deploy an additional 40 strings within existing DeepCore detector. This would lower threshold to below 5 GeV (< 25 m muon track length in ice). In this energy range, matter effects in Earth lead to resonant oscillations of ν µ ν e ( ν µ ν e ) for normal (inverted) hierarchy 266 that depend on zenith angle. By taking advantage of fact that neutrino cross section is larger than that for antineutrinos, coupled with excess of ν µ compared to ν µ, a measurement sensitive to neutrino mass hierarchy is possible on a relatively short timescale. PINGU would also have sensitivity to ν µ disappearance, ν τ appearance, and maximal mixing. The lower energy threshold would also enhance indirect searches for dark matter with IceCube as well as sensitivity to neutrinos from supernova explosions. In addition, re is potential for neutrino tomography of Earth with PINGU From Discovery to Astronomy, and more... Accelerators of CRs produce neutrino fluxes limited in energy to roughly 5% of maximal energy of protons or nuclei. For Galactic neutrino sources, we expect neutrino spectra with a cutoff of a few hundred TeV. Detection of se neutrinos requires optimized sensitivities in TeV range. At se energies, atmospheric muon background limits field of view of neutrino telescopes to downward hemisphere. With IceCube focusing on high energies, a second kilometer-scale neutrino telescope in Norrn Hemisphere would ideally be optimized to observe Galactic

76 July 9, :42 ws-rv9x6 Book Title trisep halzen page Francis Halzen center and largest part of Galactic plane. Following pioneering work of DUMAND, 8 several neutrino telescope projects were initiated in Mediterranean in 1990s In 2008, construction of ANTARES detector off coast of France was completed. With an instrumented volume at about one percent of a cubic kilometer, ANTARES reaches roughly same sensitivity as AMANDA and is currently most sensitive observatory for high-energy neutrinos in Norrn Hemisphere. It has demonstrated feasibility of neutrino detection in deep sea and has provided a wealth of technical experience and design solutions for deep-sea components. While less sensitive than IceCube to a diffuse extragalactic neutrino flux, ANTARES has demonstrated its competitive sensitivity to neutrino emission from Galactic center 232,267 and extragalactic neutrino sources in Sourn Hemisphere. 268 The important synergy between Mediterranean and Antarctic neutrino telescopes has been demonstrated recently by first joint study of continuous neutrino sources 269 as well as neutrino follow-up campaigns of gravitational waves. 270 An international collaboration has started construction of a multi-cubickilometer neutrino telescope in Mediterranean Sea, KM3NeT. 271 Major progress has been made in establishing reliability and costeffectiveness of design. This includes development of a digital optical module that incorporates 31 3-inch photomultipliers instead of one large photomultiplier tube. The advantages are a tripling of photocathode area per optical module, a segmentation of photocathode allowing for a clean identification of coincident Cherenkov photons, some directional sensitivity, and a reduction of overall number of penetrators and connectors, which are expensive and failure-prone. For all photomultiplier signals exceeding noise level, time-over-threshold information is digitized and time-stamped by electronic modules housed inside optical modules. This information is sent via optical fibers to shore, where data stream will be filtered online for event candidates. KM3NeT in its second phase 271 will consist of two ARCA units for astrophysical neutrino observations, each consisting of 115 strings (detection units) carrying more than 2,000 optical modules, and one ORCA detector studying fundamental neutrino physics with atmospheric neutrinos. The detection units are anchored to 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

77 July 9, :42 ws-rv9x6 Book Title trisep halzen page 77 High-Energy Astrophysical Neutrinos 77 Fig. 24. The KM3NeT The KM3NeT optical optical module module. (fromthe Ref. KM3NeT 271 ). The infrastructure optical module consists of a glass sphere with comprises a diameter several ofthousand 42 cm, housing identical optical 31 photosensors modules arranged (yellowish disks). The glass sphere can withstand in three-dimensional pressure spatial ofarrays water located and in is transparent deep waters to faint light that must be detected of to Mediterranean see neutrinos. Sea. The spacing between optical modules is different for ARCA and ORCA detectors to optimally detect neutrinos with targeted energies. Each Sicily). optical module consists of a glass sphere with a diameter of A parallel effort 42 cm, housing is underway 31 photo-sensors in Lake (yellowish Baikal disks). with The glassconstruction of sphere can withstand pressure of water and is transparent to faint light that must be detected to see deep underwater neutrino telescope Baikal-GVD (Gigaton Volume De- neutrinos. tector). 272 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 eight strings consists of three sections with 12 optical modules. Deployment of a second cluster was completed in spring Furr progress requires larger instruments. IceCube refore proposes as a next step capitalizing on opportunity of instrumenting 10 km 3 of glacial ice at South Pole and reby improving on IceCube s sensitive volume by an order of magnitude. 273 This large gain is made possible by unique optical properties of Antarctic glacier revealed by construction of IceCube. As a consequence of extremely long photon absorption lengths in deep Antarctic ice, spacing between strings of light sensors can be increased from 125 to over 250 meters without significant loss of performance of instrument. The instrumented volume can refore grow by one order of magnitude while keeping construction budget of a next-generation instrument at level of cost of current IceCube detector. The new facility will increase event rates of cosmic events from hundreds to thousands over several years. 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