130. Cosmic Rays

30. Cosmic Rays
Revised March 2024 by J. Alvarez-Muñiz (Santiago de Compostela U.), Z. Cao (IHEP Beijing),
U.F. Katz (Erlangen U.), P. Mertsch (TTK, RWTH) and C. Spiering (DESY, Zeuthen).

30.1 Theory
Cosmic rays (CRs) are a non-thermal population of particles that pervade the Universe. Theirsalient characteristics can be inferred from their major observational properties: spectrum, composition and arrival directions. For charged CRs, the energies extend from tens of MeV to close to
1 ZeV, the intensity is ∼ 104 m−2 s−1 sr−1 above 1 GeV, but the differential spectrum falls steeply
with energy E, following a power-law dependence E −γ . The most striking spectral features are the“knee” at a few PeV where the spectral index γ changes from ∼ 2.7 to ∼ 3, the “second knee” at∼ 100 PeV with a change to ∼ 3.3 and the “ankle” at a few EeV where γ changes to ∼ 2.5. The
flux is largely suppressed above a few tens of EeV. (More detailed discussion of spectral features
can be found below in Secs. 30.2.1 and 30.2.2.) Charged CRs are composed mostly of protons,
helium, and other nuclei, as well as electrons, positrons and anti-protons. The arrival directions
are mostly isotropic, but below and around the knee interesting O(10−4 . . . 10−3 ) anisotropies dueto the distribution of sources and properties of the Galactic magnetic fields have been observed,
reaching ∼ O(10−1 ) at the highest energies. Gamma-rays can be resolved into those from astrophysical sources (∼ 6660 [1] above 50 MeV, ∼ 300 [2, 3] at TeV energies), plus diffuse fluxes ofgalactic and extra-galactic origin, predominantly showing power-law dependence on energy. The
observation of high-energy neutrinos has opened a new window; while the distribution is largely
isotropic, evidence for two extra-galactic sources as well as for a contribution from the galactic
plane has been found. The energy spectra of charged CRs, diffuse gamma-rays and neutrinos areshown in Fig. 30.1. Combined observations of charged CRs, gamma-rays and neutrinos as well as
gravitational waves (see Sec. 21.2.3) allow for valuable insights into the most extreme astrophysicalenvironments and is referred to as multi-messenger astrophysics. Adding the contribution from all
species results in the all-particle spectrum. While it was believed for a long-time that it was a
featureless power law up to the knee at a few PeV, it has now been recognized that it has much
more structure, mirroring the features in the individual species. These features carry important
information on the acceleration and transport of CRs.
The energy variables used are kinetic energy E, kinetic energy per nucleon, En = E/A fora particle of mass number A, or rigidity R ≡ pc/(Ze) (given in units of volt) for a particle ofcharge number Z, p being the momentum of the particle; the term rigidity refers to the resistanceagainst deflections in a magnetic field B: particles of low (high) rigidity have small (large) gyroradii
rg = R/B. Kinetic energy is closely related to the experimental signatures of a calorimetric
instrument, while rigidity is the most natural one for a spectrometric one. Note also that relativistic
nuclei suffer little energy losses and their transport is prescribed by magnetic fields, thus it can
only depend on rigidity. The intensity J of CRs, also called the diffuse flux, is defined throughthe differential number dN of particles with energy in the interval [E, E + dE], crossing the areadA from a solid angle dΩ in the time dt: dN = J dE dA dΩ dt. Its isotropic part is related to thedifferential density ψ = (4π/v)J, v being the particle speed and to the phase-space density f as
J = p2 f . Note that the intensity can be also defined in reference to particle energy per nucleon or
rigidity. To stress this, often the intensity is written as dJ/dE, dJ/dEn or dJ/dR.
In the detection of CRs, two classes of techniques are distinguished [4]. Direct observations, seeSec. 30.2.1, make use of the interactions of CRs in particle physics detectors (e.g. trackers, spectrometers and calorimeters). Given the limited exposures of such instruments and the steeply falling
spectra, this is currently only realistic below ∼ 100 TeV. In indirect observations, see Sec. 30.2.2,
S. Navas et al. (Particle Data Group), Phys. Rev. D 110, 030001 (2024)
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30. Cosmic Rays

2

103

1/

1/

m2
/s

H

m2
/d

ay

showers of secondary particles initiated by charged CR interactions in natural materials (e.g. air,water or ice) are detected through fluorescence, air-Cherenkov, water-Cherenkov or scintillation
effects. This allows for large instrumented surfaces or volumes. Historically, the two classes of techniques have been employed by two separate communities and we structure the review of charged
CRs accordingly. For detection of gamma-rays, direct observations are relevant mostly below hundreds of GeV; for gamma-rays of higher energies and neutrinos of essentially all energies, indirect
observations are required.

He
O
Fe

101
E 2 dJ/dE [GeV m−2 s−1 sr−1 ]All particle“knee”e+“second knee”
e− + e +10−1“ankle”

Galactic
γ-ray
background

10−3

Diffuse ν background

2

/y
ea

r

Extragalactic
γ-ray background

1/

km

10−5

100

101

102

103

104

105
106
E [GeV]

107

108

109

1010

1011

Figure 30.1: The spectrum of cosmic rays (CRs). Shown are measurements of the intensity ofcharged and neutral CRs, multiplied by kinetic energy squared. The data for the charged CRs [5–34]
have been extracted from the Cosmic Ray Database (CRDB) [35]. Below 104 GeV, the all-particle
spectrum is the sum of spline fits of the most important nuclear species. The diffuse γ-ray fluxes
have been extracted from Refs. [36–38], measurements of the diffuse neutrino background from
Ref. [39]. Energy-integrated intensities are indicated by the various diagonal lines.

Charged CRs are deflected by magnetic fields and so generally speaking the observed events do
not point back to sources. CRs can however reach the earth from galactic and even cosmologicaldistances. Between hundreds of MeV and at least a few PeV, CRs are believed to be of galactic
origin; above a few EeV, the sources are most likely extra-galactic. If CRs with energies in excessof ∼ 1 EeV came from sources in the Galactic disk, the angular distribution at Earth would be very
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30. Cosmic Rays

3

Relative abundance (Si = 106 )1011
Solar system (Lodders, ApJ 591, 1220 (2003))

109
107
105

Cosmic ray flux at Ek/n = 20 GeV/n

H
He
C
B
Be
Li

O
Ne
Mg Si

Fe

S

N

Ar Ca

Ti Cr

Ni

Na Al
P Cl

103

Zn
Mn
Co
Ge
Se Kr
Cu
V
Sr

K

F

101

Sc

Zr

Ga
As Br Rb Y

Mo
Sn Te Xe Ba
RuPdCdCeNdSmGdDy Er Yb

Nb

10−1
5

10

15

20

25

30

35

40

RhAg

In

Sb

45 50
Z

I

Cs La

55

Hf W Os

Pt Hg

Pb

Ir
Pr

60

EuTbHoTmLu Ta Re

65

70

75

Th

Au Tl Bi

80

U

85

90

Figure 30.2: CR abundances compared with solar system ones [58]. Modified from [35].

anisotropic, which is at variance with observations. And if CRs below ∼ 1 PeV were dominantly of
extra-galactic origin, this would result in a gamma-ray flux from objects like the Large Magellanic
Cloud exceeding observations [40]. Direct and indirect observations therefore also largely refer togalactic/extra-galactic sources, respectively. CRs with energies in excess of 1 EeV are referred to
as ultra-high energy cosmic rays (UHECRs).
Sources of non-thermal electromagnetic radiation are routinely observed, see Sec. 30.3, yet
the dominant source of locally measured CRs have not been unambiguously identified. Source
candidates are typically associated with endpoints of stellar evolution or supermassive black holesthat release large amounts of gravitational or rotational energy [41]. In the Galaxy, the prime
candidates are supernova remnants [42] where particles can be shock-accelerated by their blast
waves [43]. Other candidates are star cluster winds [44,45], stellar wind binaries, micro quasars [46](a source powered by accretion from a donor star onto a stellar mass black hole) or even the Galactic
Center [47]. The candidate sources for extra-galactic CRs are Active Galactic Nuclei (AGN) [48],specifically blazars and radio galaxies, gamma-ray bursts [49], starburst galaxies [50,51], pulsars [52]and magnetars [53]. These objects exhibit power-law spectra in electromagnetic radiation, albeit
in limited wavelength ranges. The acceleration mechanisms considered in the literature are shock
acceleration [43], stochastic acceleration [54], and reconnection [55]. A fundamental constraint
on the maximum energy, the so-called Hillas criterion [56], follows from the requirement that thegyroradius must be smaller than the source size.
In the Milky Way, the dominant process in CR transport is diffusion as evidenced by the small
anisotropies in CR arrival directions and by certain abundance ratios of nuclear species. This
diffusive transport bears some resemblance with heat transport in that it smooths the spatial
distribution of CRs. However, in contrast to heat transport, CR diffusion is not due to collisions,but interactions with turbulent magnetic fields. Generally, CRs interact “resonantly” with plasma
waves, that is they get affected only by waves with a wavelength similar to the gyroradius of the CR
particle. If this condition is satisfied, a CR particle will be deflected by the Lorentz force. Many
random deflections lead to a random walk in space, that is diffusion [57].
There is a number of other processes contributing to the transport of charged CRs: momentum
losses, i.e. radiative losses for electrons and positrons [59], ionization and Coulomb losses for nuclei,
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430. Cosmic Rays

electrons and positrons [60]; spallation, that is production of (mostly) lighter nuclei by inelastic
collisions of heavier ones; and other inelastic collisions, e.g. the production of light mesons. We
note that progress in the study of CR transport is often limited by the nuclear interactions since
many cross-sections are poorly known, if at all [61]. The various processes are encoded in the CR
transport equation [62], also referred to as the Parker transport equation [63] in the space physics
community. This partial differential equation is supplemented by the boundary condition of freeescape on the surface of the (often cylindrical) confinement volume. Only in simplified cases canthis equation be solved analytically. The most instructive case is the 1D approximation where only
the direction perpendicular to the Galactic disk is retained. The solution differs for primaries,that is species present and accelerated in the CR sources, and secondaries, which are not present
in CR sources, but produced by inelastic collisions of primaries in the gaseous disk of the Galaxy.
Diffusion in the Galaxy, characterized by a diffusion coefficient κ(R), modifies the source spectrum
q(R), resulting in the steady-state spectrum ψ(R) ∝ q(R)/κ(R). As the production spectrum of
secondaries follows the steady-state spectrum of primaries, q2 (R) ∝ ψ1 (R), the secondary steadystate spectrum is ψ2 (R) ∝ q2 (R)/κ(R) ∝ ψ1 (R)/κ(R). As κ(R) grows with R, secondary spectraψ2 (R) fall more quickly with rigidity than primary spectra ψ1 (R). Unstable secondaries provide
additional constraints on the gas density and residence time of CRs. The solution of the transport
equation in more realistic setups requires numerical codes [64–67].
Protons (iron nuclei) with energies in excess of ∼ 1 EeV (∼ 26 EeV) in a micro-Gauss magnetic
field have gyroradii larger than the typical kiloparsec scales of the Galaxy, thus they cannot be
confined. Their directions are however affected by so-called small-angle scattering, both in the Milky
Way and possibly outside. As far as their spectrum and composition is concerned, protons andheavier nuclei suffer from inelastic collisions with the CMB and the extra-galactic background lightat the highest energies. For protons above 10 EeV, photo-pion production limits the propagation
distances to ∼ 100 Mpc; for nuclei, heavier ones photo-disintegrate to lighter ones, also limiting their
spatial reach. Both processes can lead to a suppression of the flux known as the GZK effect [68, 69]
and produce secondary gamma-rays and neutrinos. Other secondary particles include neutral andcharged pions, which ultimately decay to photons, electrons, positrons and neutrinos, and electronpositron pairs which can also initiate a cascade of photons and lower energy electrons and positrons.
The stable decay products, in particular gamma-rays and neutrinos can be used as an additional
diagnostic tool for the study of the origin and transport of UHECRs.
In many astrophysical environments, the energy density of CRs constitutes a significant fractionof the total or is comparable to that of other ingredients. For instance, on galactic scales, the CR
energy density is of the same order as that of magnetic fields, radiation fields or the turbulent
gas. Due to their pressure, CRs can be dynamically important and shape their environments:
Specifically, CRs contribute to the gravitational support of galaxies and can drive galaxy-scale
outflows. They ionize neutral gas, thus determining coupling of gas and magnetic fields. CRs
can generate turbulence by a variety of streaming instabilities [70, 71], which play a central role inshock acceleration and galactic transport [72]. Finally, CRs also produce diffuse emission throughinteractions with gas and radiation fields, an additional handle for CR studies.
CRs are also important probes of fundamental physics. If dark matter has interactions with theStandard Model, the products of self-annihilation or decay of DM particles can potentially be observed (DM, see Sec. 27.7). This is called DM indirect observation. Generically, one would expect
similar rates of production of particles and antiparticles whereas astrophysical sources predominantly accelerate matter particles. It is therefore advisable to search for signals in CRs positrons,
anti-protons and anti-nuclei [73, 74]. In fact, excesses have been reported of positrons and antiprotons, yet astrophysical pollutions and/or experimental systematic uncertainties can not be excluded. There have also been searches in gamma-rays and neutrinos and a number of studies have
31st May, 2024

30. Cosmic Rays

5

indentified an excess of gamma-rays from the Galactic Center that is compatible with DM particles
of weak-scale mass and weak annihilation cross-section [75]. Another target for exotic searches
in CRs is anti-matter of primordial origin [76]. Most interestingly, the AMS-02 collaboration has
claimed O(10) He candidate events, but whether those are of primordial origin as opposed to
instrumental effects is at this point not clear.

30.2 Charged cosmic rays
30.2.1 Direct observations
Al
×5000

He

N
×300

O
×10

R2.7 dJ/dR [ GV1.7 m−2 s−1 sr−1 ]

10

H
4

103

102

C
×3

Na
×1200

Ne
×5

Li
×30

Mg
×2

AMS02
CALET
DAMPE
NUCLEONPAMELA

Be
×20

Si

B
×2

101

Fe
×0.5

F
×7

100

100

101

102

103 104
R [GV]

105

106

100

101

102

103 104
R [GV]

105

106

Figure 30.3: Rigidity spectra for a selection of CR nuclei. Primary species are shown in the left
panel, (mostly) secondary species in the right panel. The error bars denote the statistical uncertainties, the shaded bars represent the systematic uncertainties. The spectra have been shifted
and multiplied by R2.7 to better bring out spectral features. Here, we have constrained ourselves to data from space-borne experiments of the last ten years, that is AMS-02 [12, 19, 77–79],
CALET [14, 20, 80, 81], DAMPE [11, 17], NUCLEON [9] and PAMELA [6, 82]. Data have been
extracted from [35].
Direct observations [83] cover energies between a few MeV and a few tens of TeV, where CRs
must be of Galactic origin. At energies lower than a few MeV, solar energetic particles [84] are
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630. Cosmic Rays

dominating the flux; above a few tens of TeV, the fluxes are too low to be observed directly andinstead indirect detection techniques [85] need to be used. Besides spectral information, direct
observations enable identification of species on an event-by-event basis, certain experiments evenprovide isotopic discrimination. We present a compilation of direct observations of the most important primary and secondary nuclei in Fig. 30.3. These show broken power-law spectra in rigidity
with J ∝ E −γ in different rigidity ranges. The various changes in spectral slope contain valuable
information on the rigidity-dependence of the diffusion coefficient κ and the primary source spectra
q1 .
Protons are dominating the CR flux by number and by energy below ∼ 10 TeV and theirspectrum has been measured with excellent precision. Measurements of the proton spectrum andother primaries are shown in the left panel of Fig. 30.3. Data from the AMS-02 experiment [12]show a R−2.8 spectrum above ∼ 10 GeV with a break to R−2.7 at ∼ 300 GV. This feature had been
observed by PAMELA earlier [6], and also with CREAM and ATIC for heavier nuclei [86, 87]. Asa reminder, at energies above a few GeV, the measured spectrum can be interpreted as the ratio of
the source spectrum q(R) ∝ R−Γ divided by the diffusion coefficient κ(R) ∝ Rδ . Thus a spectral
index of γ = Γ + δ ' 2.8 can describe the data. On the basis of proton data alone, the degeneracy
between the source spectral index Γ and the spectral index of the diffusion coefficient δ cannot be
broken. Also, the break at ∼ 300 GV could be a break in the source spectrum or in the diffusion
coefficient, but see below. At energies lower than ∼ 10 GeV, the spectrum turns over because ofenergy losses and solar modulation. At energies beyond the reach of AMS-02, both DAMPE and
CALET data show a softening at rigidity ∼ 10 TV [11, 14], confirming earlier indications [86, 87].
Most of the other primary species, that is helium, carbon, nitrogen, oxygen, neon, magnesium
and silicon with the notable exception of iron, also show a spectral break at ∼ 300 GV, but theirspectra are generally harder than the proton one, e.g. γHe < γp , both below and above the break.
Suggested explanations for this difference in spectrum include gradients in the relative circumstellar
abundances of protons and heavier nuclei or invoking different source populations for these twogroups. At ∼ 10 TV a softening break mirrors the feature observed in protons [80]. Above anenergy of ∼ 100 TeV, elemental information is scarse, but a combined analysis of proton and helium
by DAMPE extends to ∼ 300 TeV and indicates another spectral hardening [88]. (Note that thisdata are not included in Fig. 30.3 though.) Such a feature was to be expected to a certain degree inorder to connect to the indirect measurements of proton and helium which start at ∼ 1 PeV. Notethat there exist some 20 % discrepancies between the oxygen and carbon data from AMS-02 [12],CALET [17] and PAMELA experiments [82] in normalization, possibly also in spectral shapes.
Iron constitutes an exception to the otherwise rather similar slopes of primary species heavier
than proton. As is also the case for other nuclei, AMS-02 [19] and CALET [20] disagree on thenormalization by ∼ 20 %, but both measurements of the iron spectrum exhibit spectral shapes
different from the oxygen ones. While the ratio of Fe/O could be accommodated if all nuclei
traversed the same amount of matter (grammage) between source and observer (the so-called slab
model), more realistic models cannot explain the observations [89]. Also, the AMS-02 data on
Fe/O are in tension with earlier measurements [90, 91]. Most interestingly, if extrapolated to lower
energies, the Fe/O could only be accommodated if solar modulation was negligible.
Measurements of stable secondary nuclei contribute two important pieces of information to
the standard scenario of galactic CRs: First, their over-abundance in CRs (with respect to solar
system values, see Fig. 30.2) indicates diffusion as the primary transport process; and second, theirspectral shapes, or rather the difference in spectral shapes between secondaries and primaries allows
inference of the diffusion coefficient. Specifically, at energies where energy losses can be ignored fornuclei, that is above a few GeV, the propagated spectra of primaries ψ1 (R) are approximately ∝R−2.8...−2.7 , which is explained as a softening of the sources spectrum q1 (R). Secondaries, however,
31st May, 2024

730. Cosmic Rays

are produced with a spectrum proportional to the propagated primary spectrum, q2 (R) ∝ ψ1 (R)which also gets further softened by the diffusion coefficient. The difference in spectral index canbe clearly seen when comparing primary with secondary spectra. A compilation of such secondary
spectra from AMS-02 [12, 78, 79], CALET [81] and PAMELA [82] is shown in the right panel ofFig. 30.3. Lithium, beryllium, boron and fluorine can be identified as almost pure secondaries
by their soft spectra. Aluminium, sodium and neon, however, have harder spectra, somewhereintermediate between primaries and secondaries. This can be understood as being due to mixtureof softer secondary contribution from spallation in the interstellar medium (ISM) and a harderprimary source component. Secondaries also exhibit a hardening break at ∼ 300 GV, but thechange in spectral slope is about twice as big [92] when compared to that of the primaries. This
fact serves as evidence for the break being due to a change in the rigidity-dependence of the diffusion
coefficient, as opposed to a break in the source spectrum [93, 94]. Recently, there have been someclaims of excesses in low-energy intensities of Li, F, Al [95], however these claims are somewhat
controversial. We note the importance of composition studies for shedding light on cosmic ray origin.
Unstable isotopes with a lifetime similar to the residence time of CRs can be used to study
galactic propagation. Among these species, 10 Be, 26 Al and 60 Fe have been studied the most as theirrest lifetime is close to the residence time of CRs at GV rigidities. Roughly speaking, the flux ratioof an unstable and a stable secondary that are both produced from similar primary species, reflects
the ratio of production cross-section at high energies (where decay is suppressed by time-dilation).
On the other hand, at low energies, this ratio is suppressed due to the decay of the unstable species.
The transition takes place at energies where the decay time equals the residence time in the Galactic
disk. At present, there is limited information on ratios at energies beyond 1 GeV/nucleon where
the transition for the ratios of the above mentioned unstable nuclei is expected to take place.
CR electrons are also believed to be accelerated in the preferred candidate sources of nuclei,that is, SNRs. Other source candidates are pulsars and pulsar wind nebulae (PWNe); in the simplest models those also accelerate similar amounts of CR positrons. We show a compilation of
the most recent and precise data from AMS-02 [12], CALET [23], DAMPE [21], Fermi-LAT [22],H.E.S.S. [96] and PAMELA [97] on CR electrons, positrons and the sum of electrons and positronsin Fig. 30.4. In addition to the processes at work in the propagation of nuclei, electrons suffer significant radiative losses due to synchrotron emission and inverse Compton scattering. In fact, forthe parameters determined in the standard scenario, the cooling time is shorter than the residence
time above ∼ 10 GeV. For the same source spectral index, the spectra are predicted to be softer
than those of primary nuclei. Indeed, the observed spectrum is roughly ∝ E −3.1 .
If positrons were only produced by spallation in the interstellar medium, the positron spectrum
should be softer than the electron one, however, on the contrary it is markedly harder. Between∼ 10 GeV and ∼ 100 GeV its spectral index γe+ transitions from 3 to 2.7 before a spectral break or
cut-off at a few hundred GeV as shown in Fig. 30.4. The fact that the positron spectrum is harderthan the electron one above a few GeV had first been detected by PAMELA [98] after earlier indications. AMS-02 has now measured the spectrum with great precision up to ∼ 1 TeV [12]. The
origin of the harder positron spectrum remains unclear today. After the discovery by PAMELA,
there had been hope that this was the long sought for signature of self-annihilation or decay of
weakly interacting massive particles (WIMP) dark matter [99]. However, such interpretations arenow severely constrained by observations of gamma-rays, anti-protons and the cosmic microwave
background (CMB, see Chap. 29). Production of e+ in pulsars or PWNe is an astrophysical explanation that had been hypothesized long before the PAMELA observations (e.g. [100]). Recently,
there have been observations of extended emission of high-energy gamma-rays, so-called gammaray halos around PWNe [101], interpreted as evidence of the presence of high-energy electronsand positrons around these objects. Other astrophysical explanations include the production and31st May, 2024

E 3 dJ/dE [GeV2 m−2 s−1 sr−1 ]e− + e +102e−e+e− + e +30. Cosmic Rays

8

AMS02
CALET
DAMPE
Fermi-LAT
H.E.S.S.
PAMELA

e−

e+
101

100

101

102
E [GeV]

103

104

Figure 30.4: Intensities of cosmic ray electrons (squares), positrons (diamonds) and their sum(dots) as a function of kinetic energy E. We have included data from the most recent spaceexperiments AMS-02 [12], CALET [23], DAMPE [21], Fermi-LAT [22] and PAMELA [97] as well
as from the ground-based H.E.S.S. experiment [96]. The spectra have been multiplied by E 3 toenhance the visibility of the spectral features. Data have been extracted from [35].

subsequent acceleration of secondaries in old SNRs [102, 103].
Measurements of the spectra of electrons and positrons are particularly interesting at highenergies. Due to the increasingly important radiative losses, the distance to the sources which
could significantly contribute to the total flux decreases with energy. Estimates at 1 TeV of this
diffusion-loss length are only ' 0.3 kpc. The predicted spectrum therefore becomes rather sensitive
to the exact distances and ages of young, nearby sources which manifest as individual bumps inthe spectrum. Turning this around, observations can be used to search for young, nearby sourcesof CRs. At energies above ∼ 1 TeV, only calorimetric observations are currently available whichcannot discriminate between electrons and positrons. Observations of the all-electron flux, that is
the sum of electron and positron fluxes, find a break at ∼ 1 TeV, displayed in Fig. 30.4. This was
first seen by H.E.S.S. [96] and later confirmed by DAMPE [21] and CALET [23]. The break by
about one power in energy has been interpreted either as due to a break in the spectrum of a large
number of sources, e.g. [104] or as a stochasticity effect from a small population of sources [105].
In the standard scenario of galactic cosmic rays, anti-protons are also produced as secondary
particles, but unlike secondary nuclei or electrons and positrons, their production is kinematicallysuppressed at lower energies. The spectrum of anti-protons observed by PAMELA (Fig. 3 in [106])and AMS-02 (Fig. 62 in [12]) is close to E −2.8 , which is somewhat harder than predicted by earlier
models. More recent models can accommodate the observations, in part due to a re-evaluation of
the production cross-section. Note that there have been claims that the transport parameters obtained when fitting to proton and anti-proton data differ from those obtained by fitting to heavier
nuclei [107]. An alternative explanation for the harder anti-proton spectrum is the accelerationof secondaries in old supernova remnants [103, 108]. At energies of a few GeV, there have been
claims of an excess in the measured anti-proton spectrum. If interpreted as a sign of dark matter
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30. Cosmic Rays

9

Dipole phase [degree]

180
135
90
45
0
315
270
225

Dipole amplitude [10−3 ]

180
102
10
1
0.1
102

103

104

105

106

107
108
E [GeV]

109

1010

1011

1012

ARGO-YBJArtyomovsk
Auger
Auger SD1500
Auger SD750
BaksanBaksan Carpet
Bolivia
Budapest
EAS-TOP
Embudo Cave
HAWC
HobartHonkong
IceCubeIceTopIceTop HE Fe-composition
IceTop HE p-composition
IceTop LE Fe-composition
IceTop LE p-composition
Kamiokande-I/II
KASCADE-Grande
LHAASO-KM2A
Liapootah
London
MACRO
Matsushiro
Mayflower Mine
MilagroMisatoMount Norikura
Musala Peak
NagoyaPlateau Rosa
Poatina
Sakashita
SocorroSuper-Kamiokande
Telescope Array
Tibet
Yakutsk

Figure 30.5: Phase and amplitude of the dipole anisotropy in CRs. Modified from Ref. [35].

annihilation, such an excess could be explained by a weak-scale particle of mass of a few tens of GeV
and annihilation cross-sections close to the thermal relic value. However, the significance of thesignal is relatively low if correlations in the cross-section uncertainties and in the measurements aretaken into account. Considering the spectra of anti-protons together with protons and positrons, itappears that all three have similar spectral indices between ∼ 10 GV and ∼ 300 GV. This is rather
surprising, given that as secondaries positrons and anti-protons should have spectra softer than the
primary protons, due to energy losses and diffusive losses, respectively. In the standard scenario
this cannot be explained and thus must be considered a mere coincidence.
The only astrophysical mechanism for production of anti-nuclei like anti-deuterons (D) or antihelium (3 He or 4 He) is coalescence of anti-nucleons produced in the spallation of primary nuclei inthe interstellar medium. Due to kinematics, however, this is significantly suppressed at energies
below a few GeV, thus rendering this an interesting channel for searches of dark matter, in particular
for relatively light WIMPs with masses of a few GeV or less. The AMS-02 collaboration has reported
some ten candidate events of anti-helium, yet the rate of 3 He or 4 He is incompatible with modelsof coalescence (e.g. [109]). Currently, the most constraining limits on D are from the BESS balloon
flights [110]. This should be improved on by the upcoming GAPS experiment, and also an upgradeof the AMS-02 experiment increasing the acceptance by a factor of three could help clarifying thesituation.
Another important observable in the study of CRs are anisotropies, most commonly definedas the relative directional deviation of the CR intensity from the angular average. As the typical
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1030. Cosmic Rays

anisotropies are at the level of one part in 103 or 104 , high statistics are required. At TeV and
PeV energies, only ground-based experiments have enough statistics, yet they cannot constrain thecomponent of the anisotropy that is aligned with the Earth’s rotation axis. Traditionally, therefore,
only the projection of the true 2D dipole into the equatorial plane has been reported in terms ofan amplitude and phase. We show a compilation [35] in Fig. 30.5. The amplitude is at the level of' 10−4 at energies of hundreds of GeV and increases to ' 10−3 at tens of TeV. At ∼ 100 TeV there
is a dip before the amplitude rises again. Beyond a few PeV upper limits exist at the level of 10−2 .
The Compton-Getting effect [111,112], that is a dipole anisotropy due to the relative motion of thesolar system with respect to the Galactic rest frame has been experimentally confirmed [113]. The
phase is relatively constant at a direction of 45◦ and switches to 250◦ , which is close to the Galactic
Center direction, also around 100 TeV. For a description of anisotropies at the highest energies see
Section 30.2.2. In addition, observations of anisotropies on scales smaller than the dipole have beenreported (see Ref. [114]). These are not expected in standard diffusion theories that only predicta dipole. The leading explanation is the generation due to the specific realization of the turbulent
magnetic field in our Galactic neighbourhood.
30.2.2 Indirect observations
In the energy range above ' 1 PeV the intensity of cosmic rays is so low that it prevents thecollection of a statistically significant sample of these particles in a direct manner with detectors
carried on balloons or satellites. Instead, cosmic rays are detected indirectly through the cascadeof particles they produce in the atmosphere, the so-called extensive air showers (EAS). In this way,
cosmic rays up to and even above 100 EeV have been observed [115, 116], corresponding to abouta hundred million times larger energy than that achieved by particles accelerated in human-madeexperiments.
Extensive Air Showers. Extensive air showers (EAS) are cascades of millions to billions ofsecondary particles initiated by a single primary particle (cosmic ray: proton, neutron or heavier
nucleus; photon; or neutrino) of energy E in the atmosphere. Due to the small density of air
ρ . 10−3 g cm−3 , the shower develops throughout the whole of the atmosphere, and for a primaryparticle of 10 EeV has a lateral spread of ∼ 10 km2 at ground level, hence the name EAS.
When an energetic, E & 1 PeV, cosmic proton or nucleus interacts with a nucleus of air, it
generates between a few and hundreds of secondary particles depending on its energy. On average∼ 30% − 40% of the energy of the primary particle is carried by a leading baryon or nucleus. The
remaining energy is employed in the creation of ultra-relativistic secondary particles, most of themcharged (π ± ) and neutral (π 0 ) pions, with a smaller number of hadrons and heavier mesons such as
charged and neutral kaons, ρ-mesons, etc. The energy of the primary particle rapidly degrades intoa large number of secondaries that can subsequently interact or decay depending on the nature andenergy of the particle and the density of the medium, further contributing to the shower development. If π ± live long enough they can interact with an air nucleus before decaying. At altitudes of afew km where the atmosphere is less dense than at sea level, most π ± with Eπ± & 100 GeV interact
while lower energy π ± decay. Interacting π ± along with the leading baryon and other hadrons,
form a penetrating core of shower particles constituting the hadronic component of the cascade(Fig. 30.6). Charged pions decaying into muons, π + → µ+ + νµ and π − → µ− + ν̄µ , represent themain contribution to the muonic component of the shower (Fig. 30.6), being also responsible for the
production of the bulk of the so-called atmospheric neutrinos. Most muons of energies above a few
GeV travel through the atmosphere without decaying and reach ground, constituting a penetrating
component of the shower. On the other hand, most π 0 s, continuously produced in the hadronic coreof the shower, do not travel long enough distances to interact with an air nucleus unless their energy
31st May, 2024

30. Cosmic Rays

Number of particles / 109

1.0

e+ +e
++
(×50)
hadrons (×50)

0.8photonproton

iron

0.6
0.4
0.2
0

105

AIRES 19.04.08
E = 1 EeV, = 45o

104Particle density [particles/m2]

11

200 400 600 800 1000 1200
Matter traversed in atmosphere [g cm 2]

103

AIRES 19.04.08
E = 1 EeV, = 45ophotoniron

protone+ +e++
hadrons

102
101
100
1
10 10
1

102
103
Distance to shower axis [m]Figure 30.6: Left: Average number of e+ + e− , µ+ + µ− , and hadrons (lines), and their ±1 σdeviation (bands), as a function of matter (in g cm−2 ) crossed in the atmosphere along the shower
axis. The profiles are obtained with AIRES simulations [117] of proton, iron and photon-induced
extensive air showers of energy E = 1 EeV = 1018 eV and zenith angle θ = 45◦ w.r.t. the verticalto ground (at depth 870 g cm−2 ). Right: Lateral development (perpendicular to shower axis) at
ground level of the same components as in the left panel as a function of distance to shower axis.

is well above 1 EeV. Instead, they decay almost immediately π 0 → γγ, initiating electromagnetic
showers. Neutral pions play a significant role in generating the electromagnetic component that
forms the majority of the shower (Fig. 30.6). This is composed of e− and e+ with a mean energy of
10 MeV as a result of photon pair production, as well as secondary photons from bremsstrahlung.
Decaying muons also contribute to the electromagnetic component of the shower. The longitudinal development of the distinct and intertwined shower components, electromagnetic, muonic,
and hadronic, is shown in Fig. 30.6. High-energy primary or secondary photons can occasionallyphotoproduce π ± and initiate a hadronic subcascade resulting in an additional muonic component.
As a cosmic ray shower develops in the atmosphere, the number of particles increases in the longitudinal direction along the shower axis. The amount of matter traversed, X, is measured in unitsof g cm−2 . The shower reaches a maximum size of the electromagnetic component Nmax at a depth
known as Xmax (Fig. 30.6). The number of electrons and positrons declines rapidly after maximum
when their energy reaches the critical energy in air, ∼ 80 MeV, and they lose their remaining energy
dominantly through ionization loss. Since neutrinos do not suffer electromagnetic interactions, andhigh energy muons reach ground level after releasing only a portion of their energy, a fraction of
the energy of the primary initiating the shower is not deposited in the atmosphere. This is theso-called invisible energy that amounts to ≈ 10% − 20% of the shower energy for energies above
0.1 EeV, decreasing with the energy of the primary particle initiating the shower and increasing
with its mass number [118]. At the same time the shower develops in the transverse or lateraldimension to the shower axis, as shown in Fig. 30.6, mainly due to the transverse momentum inhadronic interactions and multiple Coulomb scattering of e− and e+ .
Shower development is driven by the particles carrying most of the energy in the forward regionof the kinematical phase space of the collisions with air nuclei. Particle production is dominated by
non-perturbative QCD which is necessarily treated by using phenomenological approaches. Moreover, particle collisions occurring in the atmosphere at 0.1 EeV are equivalent to center-of-mass
31st May, 2024

1230. Cosmic Rays

energies presently achieved at the LHC, and this energy scales up by a factor of approximately 30
at the highest cosmic ray energies observed. These two facts result in the need for extrapolations
both in energy and phase space when modeling hadronic interactions. The cosmic-ray community
has developed sophisticated simulation packages such as AIRES [117] and CORSIKA [119] to predict EAS observables as a function of primary energy and mass. These programs adopt modelsof hadronic interactions such as SIBYLL [120], QGSJET [121] and EPOS [122], tuned to a large
data set including recent LHC data. Inferring fundamental properties of the primary particle initiating the shower, most notably its mass, requires the use of these air shower simulations. Large
uncertainties remain, both due to theoretical limitations and the lack of data from existing collider
experiments. A toy model to describe electromagnetic showers is due to Heitler [123], while forhadronic showers a model was developed by Matthews [124]. These oversimplified models shed lighton the relation between the main shower observables and the nature of the primaries and predictthat for the electromagnetic component, Nmax ∝ E; Xmax ∝ log E and Xmax ∝ log A−1 with A
the mass number of the primary nucleus; while for the muonic component, Nµ ∝ A(1−β) E β with
β ' 0.85...0.95. These important features of air showers constitute the basis for the identificationof the primary particle with EAS (see next section). Similar features are also obtained in detailedMonte Carlo simulations of EAS development (Fig. 30.6), and have been observed experimentally.

Shower detection and cosmic-ray reconstruction. EAS have been detected with several
techniques. Arrays of conventional particle detectors such as scintillators, water-Cherenkov stations
or underground muon detectors, measure the lateral distribution of the shower front at ground, i.e.,
at a fixed depth. Due to the low cosmic-ray intensity especially at EeV energies (Figs. 30.1 and30.7), the particle detectors are spread over large areas to compensate for the low flux, separated bydistances that range from hundreds of meters to above 1 km. From the times at which the shower
front hits several of these particle detectors, the arrival direction of the cosmic ray is measured
with an accuracy typically better than ∼ 1◦ . Shower arrays measure a shower size parameter,
proportional to the number of secondary particles, that can be related to the energy E of the primary particle. With several types of detectors working together, it becomes possible to effectively
separate the electromagnetic and muonic components of the shower, thereby providing an estimateof the mass of the primary. The main arrays of particle detectors for EAS observation currently
in operation are the surface detector of water-Cherenkov stations of the Pierre Auger Observatory
in Argentina [125] spread over a total area of ∼ 3000 km2 , and the Telescope Array (TA) of scintillators in USA (∼ 700 km2 ) [126]. They typically work with almost 100% duty cycle and havemeasured many properties of the cosmic-ray flux (see next section).
Other arrays can measure the radiation emitted when the shower develops in the atmosphere,
namely, optical Cherenkov radiation, fluorescence light, or radio emission in the MHz to GHz frequency range. Cherenkov detectors measure the forward-beamed incoherent emission at optical
wavelengths. This can be achieved with arrays of individual elements such as at the Yakutsk [127]and Tunka-133 [128] observatories. A fluorescence telescope can monitor a large volume of theatmosphere and detect the isotropic fluorescence radiation emitted by the nitrogen molecules of air
excited by the passage of the charged particles of the shower. The fluorescence radiation is produced in proportion to the energy dissipation and the shower size N (X), allowing a reconstructionof the longitudinal profile of the energy deposit dE/dX of the shower as a function of atmosphericdepth X and, in particular, providing a measurement of Xmax . With the fluorescence
detectionR
technique, the atmosphere is used as a calorimeter, with the integral Ecal = (dE/dX)dX called
the calorimetric energy of the shower. An estimation of the primary energy with the fluorescence
detection technique is obtained by adding to Ecal a correction to account for the invisible energy
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30. Cosmic Rays

introduced above. Fluorescence and optical Cherenkov detectors are limited by operation during
clear and moonless nights which reduces their duty cycle to ' 15%. The main fluorescence detectors
currently in operation are those of the Pierre Auger Observatory [125] and TA [126].
Arrays of detectors of radio emission employ cost-effective elements (antennas) to detect theradiation in the 10’s of MHz to GHz produced by the charged particles in the EAS. Radio emission
is mainly due to two mechanisms: the transverse current induced by the magnetic field of the Earththat travels at the speed of light along shower axis, and the Askaryan effect i.e the radiation emitted
by the excess of negative charge (e− ) that develops in the shower through Compton scattering of
shower photons on e− in the medium, as well as Möller and Bhabha scatterings. The measurementof the radiated energy in radio waves at ground also provides an estimate of the primary energy [129].
In a radio-quiet environment, these detectors can operate with a close to 100% duty cycle, only
limited by thunderstorms and heavy rain. The principal arrays of radio antennas currently operating
include the Auger Engineering Radio Array (AERA) and the ongoing deployment of the AugerPrimeRadio Detector at the site of the Pierre Auger Observatory in Argentina [130], the Tunka-Rex [131]and Yakutsk [132] radio extensions in Russia, the LOw Frequency ARray (LOFAR) with its coredetector in The Netherlands [133], and the Square Kilometer Array (SKA) in Australia [134].
Combining several types of detectors in the same array has proven very fruitful for increasing
the accuracy in event reconstruction and energy calibration. Complementary measurements of thesame event are expected to improve the determination of mass composition of the primary flux
on an event-by-event basis. Projects under construction exploiting the simultaneous use of several
detector kinds include, AugerPrime (water-Cherenkov stations, scintillators, underground muon
detectors, fluorescence detectors and radio antennas) [135], TAx4 (scintillators and fluorescence
detectors) [136], and the IceCube-Gen2 surface array (scintillators and radio antennas) [137]. Other
arrays in the planning stages utilizing radio antennas are GRAND [138] and BEACON [139].
Experimental results. Cosmic rays in the PeV to EeV energy range have been regularly detected for decades, with energies up to > 100 EeV. Despite the progress made in the field in thelast 20 years, the nature and identity of their sources as well as the acceleration mechanisms that
boost the particles to these extreme energies remain open questions. The understanding of CRs is
mainly derived from analyzing their energy spectrum, several observables sensitive to their primarynature, and their arrival direction distribution. This is a challenging task mainly due to the small
flux, with less than 1 particle per km2 per year above 30 EeV (see Fig. 30.1), but also because theproperties of CRs in this energy range can only be inferred indirectly from measurements of the
EAS whose description relies on extrapolations of particle physics properties at energies several
orders of magnitude above those achieved in terrestrial accelerators. Last but not least, since CRs
are charged they are deflected by the galactic and intergalactic magnetic fields and their arrival
directions at Earth point back only approximately to their actual sources.
Energy spectrum: The cosmic-ray spectrum observed at Earth (Fig. 30.1, with Fig. 30.7 highlighting the highest energies) can be characterized by a series of power-law functions proportional
to E −γ with γ ∈ (' 2.5, ' 5.0) the spectral index that changes with energy. The production
mechanism of CRs, mainly the unknown maximum CR energy achievable, CR composition andspectral index at the sources; the source type and distribution in the Universe; and the propagation through the Galaxy and the intergalactic space, all leave distinct imprints on the spectrum
giving rise to several observable features. The differential flux over 5 orders of magnitude in energy
is shown in Fig. 30.7. The flux has been multiplied by E 3 to highlight the deviations from a pure
power law with a single value of γ. Several features are apparent, namely: a steepening at ' 5 PeV
known as the knee (Fig. 30.1); another steepening around 100 PeV dubbed the second knee; the31st May, 2024

30. Cosmic Rays

14

107

108

E [GeV]
109

1010

1011

1038
2nd kneeinstepankle

sys.
E - Augersys.
E - TA

ssion

1037

suppreE3 dJ/dE (eV2 km 2 yr 1 sr 1)

106

Telescope Array
Pierre Auger
1015

1016

1017

1018
E [eV]

1019

1020

Figure 30.7: Measurements of the all-particle CR flux from Telescope Array (TA) [140] (bluetriangles) and the Pierre Auger Observatory [33, 141] (black circles). The direction and magnitude
sysof the systematic uncertainty on the flux due to the energy scale (σE) for TA and Auger is indicatedby the corresponding arrows. For a comprehensive compilation of measurements see [142].

ankle, a flattening of the spectrum at around 5 EeV; a recently discovered feature corresponding
to a further flattening starting at 10 EeV dubbed the instep; and the suppression of the spectrum
starting around 50 EeV. These features are thought to be correlated with the observed changes on
the average CR composition (see Primary composition below).
Cosmic-ray experiments have systematic differences in their energy scales and this manifests
itself in differences in the measured spectrum, not only on the energy axis but also on the normalization when the flux is scaled with a power of the energy. The diagonal uncertainty bars
in Fig. 30.7 serve to visualize the impact of these systematic differences on the spectrum. In theenergy range above ∼ 100 PeV the fluorescence technique is used to determine the primary cosmicray energy, with the atmosphere where the EAS develops functioning as a calorimeter. In the twostate-of-the-art experiments for UHECRs, the Pierre Auger Observatory and the Telescope Array, a
sub-sample of events is recorded simultaneously with the fluorescence (FD) and the surface detector(SD) arrays. With the SD, a shower size parameter is measured and calibrated against the energy
measured with the FD. This approach provides a more direct method for determining cosmic-ray
energy without relying on simulations. Differences in the energy scale between Auger and TA remain, however, primarily due to the use of different measurements of the amount fluorescence lightemitted per unit of energy deposited, and to the different models for the invisible energy in EAS
adopted. When these systematic uncertainties are accounted for, the spectra of the Pierre Auger
Observatory and TA have been shown to agree within 5%, except in the energy region near theend of the instep feature and at the suppression.
Primary composition: The main observable sensitive to CR composition is the depth in the atmosphere along shower axis (Xmax ) at which the number of particles in the shower is maximum. Observatories capable of detecting Cherenkov and/or fluorescence light induced by the passage of the
EAS through the atmosphere, can measure Xmax on an event-by-event basis. With sufficient statis31st May, 2024

30. Cosmic Rays

15.5
900
850
800
750
700
650
600
550
500
70
60
50
40
30
20
10
0

16.0

16.5

17.0

17.5

log10(E/eV)
18.0 18.5

19.0

Telescope Array (FD)
Pierre Auger (FD)
Pierre Auger (SD)Yakutsk
Tunka

19.5

20.0
proton20.5

iron

SIBYLL 2.3c
EPOS-LHCQGSJETII.04
E (GeV)
proton(Xmax) (g cm 2)

Xmax (g cm 2)

15

iron

107

108

109
E (GeV)

1010

1011

Figure 30.8: Measurements of hXmax i (top) and σ(Xmax ) (bottom) obtained by the Telescope Array [143, 144], Pierre Auger Observatory [145, 146], Yakutsk [127] and Tunka [147]
UHECR detectors, compared to predictions for proton and iron nuclei using the hadronic models
SIBYLL2.3c [148], EPOS-LHC [122] and QGSJET-II.04 [121]. Detection techniques: fluorescence(FD), Cherenkov (Yakutsk, Tunka, and TA below ' 1 EeV), and using the surface detector arrayof the Auger Observatory (SD). For a compilation including experiments using the radio techniquesee [142] and also [149].

tics, the distributions of Xmax can be determined from which the average value hXmax i and its fluctuations σ(Xmax ) are obtained. A comparison with the hXmax i and σ(Xmax ) as predicted in simulations of EAS for different primaries and energies, as well as fits to the Xmax distributions lead to thedetermination of the mean fractions of primary protons, helium, carbon-nitrogen-oxygen and iron in
the cosmic-ray flux at Earth. However, the interpretation of any mass-sensitive observable relies onmodeling hadronic interactions up to the highest energies where there are no data from terrestrial
accelerators, and this introduces a considerable uncertainty in the determination of the mass. Also,
due to intrinsic shower-to-shower fluctuations (see Fig. 30.6), an event-by-event determination of
the mass of the primaries is not currently possible. Despite these limitations, the measurements presented in Fig. 30.8 alongside the predictions of EAS simulations for proton and iron primaries, reveal
a broad trend toward a lighter composition at the knee, within the energy range of a few PeV. This isfollowed by a gradual rise in the average logarithm of the primary cosmic-ray mass, eventually leading to a heavier composition at around 100 PeV, although notable differences between experiments
31st May, 2024

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30. Cosmic Rays

exist. As the energy increases from 100 PeV up to ∼ 2 EeV the measurements point consistently toa predominantly light composition with a large fraction of primary protons. Above that energy, thedata from the largest statistical sample of events collected with the FD of the Pierre Auger Observatory indicate that the composition is mixed with the mean mass steadily growing. This observation
is further supported by the shower-to-shower fluctuations of Xmax also shown in Fig. 30.8. Though
the data of the Telescope Array seem in apparent tension with this picture, they have been shown
to be compatible with the results of the Pierre Auger and Yakutsk Observatories [150] within thecurrent levels of statistics and understanding of systematic uncertainties. In particular, TA data
are compatible with the mixed composition inferred by the Pierre Auger Collaboration [142].
The small duty cycle of the fluorescence technique combined with the steeply falling spectrum
above ' 50 EeV prevents a statistically significant determination of the composition in this energy
range. Information on the distribution of nuclear masses can be obtained with the surface arrays
alone that work with a high duty cycle. Exploiting the arrival times of particles in the SD stations, that are known to contain information on the penetration of the shower in the atmosphere,measurements of Xmax with the Pierre Auger Observatory were extended up to 100 EeV as shownin Fig. 30.8, after calibration of the mass-sensitivity of the SD with the measurements of Xmax
with FD at lower energy. Other novel methods such as those based on deep learning analysis
techniques are also being explored [151]. Additionally, the arrays of radio detectors are also sensitive to Xmax through the measurement of the shape of the radio emission footprint on the groundinduced mainly by the electromagnetic component of the EAS. The radio technique demonstrates
considerable potential in this respect and scalability, making it a cost-effective possibility for future
UHECR detectors [149, 152].
Arrival directions: Anisotropies in the arrival direction of CRs are a key to discovering theirsources. This is in principle feasible if the charges of the CRs and the galactic and extragalacticmagnetic fields are well-enough determined. UHECRs are subject to the GZK effect, the energy lossof protons and heavier nuclei in interactions with the cosmic background. This imposes a horizon
to possible sources of ∼ 250 Mpc for protons and Fe nuclei, but shorter for nuclei in between thesetwo, for instance ∼ 5 Mpc for He and ∼ 100 Mpc for Si at energies above ' 50 EeV [153]. Having
only a limited range of source distances contributing to the signal makes it potentially feasible toidentify sources or infer their properties statistically.
The Pierre Auger Collaboration has discovered a large-scale dipolar anisotropy at energies above
8 EeV with 6.9σ significance [154]. The amplitude of the dipolar anisotropy is d = 0.073+0.010−0.008 andthe dipole points at a direction that is ∼ 115◦ away from the Galactic Center, evidencing the extragalactic origin of UHECRs above this energy threshold. The dipole direction is not aligned with any
obvious individual source, or with the expected CMB dipole, and is instead consistent with the local
distribution of stellar mass (2MASS Redshift Survey), after accounting for the deflections expectedin the Galactic magnetic field. A compelling feature is the growth of the amplitude of the dipolewith energy in agreement with the expectation that particles of higher rigidity are less deflectedby magnetic fields. Combining the Pierre Auger Observatory data set in the southern hemisphereand the smaller statistical sample of events from Telescope Array in the north, a full-sky coverageis achieved. The combined results regarding the dipolar anisotropy are compatible with the Pierre
Auger Observatory-only results with no evidence of the existence of a quadrupole component. At
energies between ∼ 10 PeV and ∼ 1 EeV the amplitude of the dipole is smaller (Fig. 30.5, bottom
panel), but there is a trend for its direction to change from pointing close to the Galactic Center(GC) at low energy towards a direction away from the GC (Fig. 30.5, top panel) in the EeV energy
range. This suggests that there is a transition between the galactic and extragalactic origin of
UHECRs around the ankle in the spectrum, at a few EeV.
Hints of correlation of arrival direction of UHECRs with potential sources have been confirmed
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30. Cosmic Rays

in several analyses [142, 154, 155]. With data from the Pierre Auger Observatory a 4σ excess of
events above 38 EeV was found in a region of angular radius ' 27◦ centered on the radio galaxy
Centaurus A (CenA) [154]. The Telescope Array Collaboration has also reported an excess of
events with energies above 57 EeV (the so-called hot spot) in the northern sky in the directionof R.A. = 144.0◦ , Dec. = 40.5◦ , with a 2.8σ significance and in an angular window of 25◦ [155].
Correlations with catalogs of potential UHECR sources have also been found. The sky viewed fromthe Pierre Auger Observatory is better modeled with a ' 10% flux excess in the directions of nearby
starburst galaxies with a significance of 3.8σ and an energy threshold of 38 EeV with the correlation
driven by the region of CenA where two prominent starburst galaxies are also located [154].
Despite the comprehensive observations made, it remains challenging to definitively ascertain
the origin of UHECRs, primarily due to their deviation caused by the insufficiently constrained
galactic and extragalactic magnetic fields. However, the constructed CR observatories designed
to detect extensive air showers have the potential to also identify neutral particles of comparable
energies. These include neutrinos, neutrons, and photons. Such searches can be made provided
that methods are devised to separate photon and neutrino-induced EAS from those produced by
the more abundant charged CRs, or in the case of neutrons if excesses in the sky are found. No
photon or neutrino candidates have been clearly identified in the energy range around and above
100 PeV and upper limits to their flux have been obtained (see Fig. 30.13). UHECR observatories
are thus also multi-messenger observatories of neutral particles [156]. These can be combined withgravitational wave detection and conventional radio, optical, X-ray and gamma-ray astronomy togreatly improve our knowledge about the most powerful objects in the Universe, as happened withthe discovery of gravitational and electromagnetic radiation from the binary neutron star merger
system in 2017 [157], with no neutrinos identified in temporal and spatial coincidence with it [158].

Astrophysical interpretation. A coherent picture of the nature and sources of CRs is emerging from the observations of the spectrum, composition and arrival directions, with many open
questions. Cosmic rays below ' 10 PeV most likely have a galactic origin. The observed dipolar anisotropy in arrival directions imply that above 8 EeV they have their origin in extragalactic
sources. One likely scenario is that the transition takes place at a few EeV, a hypothesis supported by the observed phase of the dipolar anisotropy changing around that energy from pointing to near the Galactic Center towards away from it (Fig. 30.5). Cosmic-ray rigidity Ze determines the maximum energy at which different particle species can be accelerated in the sources
Emax (Z) = Z × Emax (Z = 1). As a consequence, protons would cutoff first in the spectrum, followed by helium, carbon ... up to iron. The observed increase with energy of the mass below thesecond knee could be interpreted as the signature of the end of the Galactic contribution dominating below the second knee [159]. As energy increases above a few times 100 PeV, the composition
starts to become lighter. This could signify the emergence of an extragalactic component because
no correlation with the densely populated Galactic plane is observed. A combined fit of the Pierre
Auger Observatory measurements of the UHECR energy spectrum and composition [160] is compatible with the existence of this extragalactic component along with a second one at higher energy
responsible for the sharp change in spectral index at the ankle feature in the spectrum at ' 5 EeV.
Observations above the ankle suggest that each accelerated nuclear species from protons to iron,dominates in a narrow energy band of the UHECR spectrum produced through a combination of
the individual composition peaks. In particular, the instep reflects the interplay between the flux
contributions of the helium and carbon-nitrogen-oxygen components injected at the source with
their distinct cutoff energies, all shaped by nuclear photodisintegration on background light during
the propagation. This is consistent with the suppression above ' 50 EeV attributable to the Emax
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30. Cosmic Rays

reachable at the cosmic accelerators along with the GZK and photodisintegration propagation effects. This comprehensive and unified understanding is continually evolving as additional data
accumulates. Multi-messenger observations of the expected secondary neutrino and gamma-ray
fluxes, or the lack thereof, will provide valuable constraints.
Hadronic interactions and Extensive Air Showers. EAS detectors probe energy and phasespace regions of hadronic interactions currently not accessible with terrestrial accelerators, although
only in a very indirect manner. The tail of the distribution of Xmax is sensitive to the attenuation
length of primary p in the atmosphere, and the inelastic p-air cross-section can be inferred. In thismanner, measurements of the p-air cross-section have been obtained at equivalent center-of-mass√
pp collision energy, spp > 40 TeV, and are in agreement with model predictions within systematic
uncertainties [142]. The muonic component in the air shower is generally used as a probe of
the hadronic interactions during the shower development. Various measurements of muons withenergies in the ' 100 MeV to ' 10 GeV range produced in EAS, have revealed that hadronic models
of multiparticle production fall short in predicting the observed number of muons above cosmic-ray
energies of ' 100 PeV [161]. On the other hand, the simulated shower-to-shower fluctuations in themuon number that are particularly sensitive to the first hadronic interactions in the shower, arein good agreement with the measurements [162]. This indicates that the shortage in the numberof simulated muons builds-up in multiple soft-QCD processes throughout the EAS development
rather than being driven by only the first few and highest-energy interactions of the EAS. This
constrains possible explanations of the so-called Muon Puzzle based on new physics beyond theStandard Model.

30.3 Gamma Rays
There is a well-studied flux of cosmic gamma rays (defined here as having energy greater than
1 MeV) present at the top of the atmosphere. Known as the diffuse gamma-ray flux, it has beenmeasured with multiple space and ground-based instruments across a broad range of energy. On
top of the diffuse one, many discrete sources have been found with either a steady gamma-ray flux
or variability of many types.
30.3.1 Observational Instruments: Space borne and Ground based
Space borne γ-ray detectors, including AGILE [163], DAMPE [164], CALET [165], mainly
Fermi-LAT [166], cover the energy range above 10 MeV up to 100 GeV. With the wide Field-ofView (FoV), they effectively survey the whole sky for steady γ-ray sources, and monitor all typesof transient phenomena such as flares of Active Galactic Nuclei (AGN) and γ-ray bursts (GRBs).
Above 100 GeV, ground-based Imaging Air Cherenkov telescope (IACT) experiments H.E.S.S [167],
MAGIC [168], VERITAS [169] and CTA-LST [170] are very effective observational instruments.
Using the stereo measurement technique, the IACT arrays achieve the angular resolution of thearrival direction of γ-rays at the level of 3 arc minute which is necessary for the high precision measurements of discrete sources. The small Field-of-View (FoV) of the telescopes and low-operation
duty cycle make the all-sky surveys for new sources difficult. Only H.E.S.S scanned the region
along the Galactic plane around the Galactic Center [171], as shown in Figure 30.9. Non-imaging
Cherenkov light technique is also developed trying to cover wider FoV, e.g. in the TAIGA experiment [172]. The most suitable detectors for all-sky surveys are extensive air shower detector arrays
at high altitudes, such as ARGO-YBJ [173], ASγ [174], HAWC [175] and LHAASO [176]. They
are operated with very high duty cycle, typically > 95%, have compatible sensitivity for discrete
sources to IACT telescopes in much wider FoV in the same energy band, and higher sensitivity
at higher energies above 10 TeV. In Table 30.1, the main features of the major facilities in γ-ray
astronomy are listed.
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19
Instrument

energyrange

Effective
area (m2 )sensitivity(milli-CU† )energyresolution (%)

PSF
(◦ )

FoV
(sr)

duty
cycle (%)

Fermi-LATa)
H.E.S.S.b)
MAGICc)VERITASd)
CTA-LST1e)
ASγ f )
ARGO-YBJg)
HAWCh)LHAASO-WCDAi)
LHAASO-KM2Ai)

20 MeV - 300 GeV
10 GeV - 50 TeV≥ 30 GeV
50 GeV - 50 TeV
20 GeV - 300 GeV
10 TeV - 1 PeV
50 GeV - 10 TeV
100 GeV - 100 TeV
100 GeV - 20 TeV
10 TeV - 4 PeV∼ 0.95
∼ 105
∼ 105
∼ 105
∼ 104
∼ 7 × 104
∼ 0.8 × 104∼ 3 × 104
∼ 0.8 × 105∼ 106

10 - 30
∼5
∼7
∼5
∼ 10
∼ 200
∼ 300
∼ 50
∼ 12
∼ 12

8 - 1815
16
10 - 15
10 - 30
20 - 40>13
20 - 50∼33
15 - 400.15 - 3.5< 0.1≤ 0.070.08 - 0.13
0.05 - 0.1
∼ 0.8
∼ 0.5
∼ 0.690.2 - 0.84
0.2 - 0.6

∼ 2.4
∼ 0.03
0.02
0.02
0.02
∼ 2.0
∼ 2.0
> 1.5
∼ 2.0
∼ 2.0

∼ 60
∼10
∼18
10-14
∼10
90
86
95
95
95

Table 30.1: Facilities for γ-ray detection and their specifications in reference a) [166], b) [177], c) [178], d) [179], e) [170], f ) [174], g) [173], h) [175],i) [176]. † milli-CU = 10−3 Crab Unit.

30.3.2 Diffuse Gamma Rays
The majority of photons detected at high energies are characterized as diffuse emission thatis not resolved as discrete sources. The observations of the diffuse emission are mainly carriedout by wide FoV detectors, including space missions, OSO-3 [180], SAS-2 [181], COS-B [182],
CGRO/EGRET [183], and Fermi-LAT [184] at energies below 1 TeV, and ground-based experiments
Milagro [185], H.E.S.S [171], ARGO-YBJ [186], ASγ [187] and LHAASO [37] at energies up to 1
PeV. Evident in Figure 30.9, the dominant component comes from the plane of the Galaxy (i.e., |b| .
10◦ , and is referred as the Galactic Diffuse Emission (GDE). Precise measurement of the GDE flux
strongly depends on the subtraction of the contamination from discrete sources most of which arefound spatially extended. With significantly improved sensitivity of source detection, Fermi-LAT
and LHAASO largely reduce the contamination by removing the regions associated with known
sources. In case of LHAASO, the flux in the Galactic plane with longitudes of 15◦ < l < 235◦ andlatitudes of |b| < 5◦ is well measured [37].
Three components are expected in GDE, namely γ-rays from the decay of neutral pions produced
via inelastic collisions between energetic cosmic ray nuclei and the interstellar medium (ISM);
bremsstrahlung radiation of electrons and positrons in ISM; and inverse Compton scattering ofelectrons and positrons off the interstellar radiation field. Possible annihilation or decay of dark
matter (DM) particles might also give rise to diffuse γ-rays particularly in the densest region of
the Galaxy. Therefore, GDE serves not only as a very important tool to probe the production,
propagation, and interaction of cosmic rays, but also as a route to search for DM in any excess overthe expectation, which is based on assumptions of the cosmic-ray spatial distribution, composition,energy spectrum and on the ISM column density along the line-of-sight. The search for DM also
depends on the fraction of the contribution by the unresolved dim discrete sources in the GDE.
Unfortunately, all of the assumptions have their own large uncertainties at present.
Evidence of an isotropic component of diffuse γ-ray emission, presumably of extragalacticallyoriginated, was obtained with the measurement of its spectrum by CGRO/EGRET [188] and FermiLAT [189]. The Fermi-LAT spectrum covers the energy range from 0.1 GeV to 820 GeV and iswell described by a power-law with an exponential cutoff. It is consistent with a scenario of adiscrete source population, such as blazars with power-law spectral shape, dominating the emission
and experiencing attenuation due to the extragalactic background light (EBL) [189]. Contributions
from the cascade of very-high-energy gamma rays and UHECRs are not ruled out as a fraction of
31st May, 2024

20

30. Cosmic Rays

Figure 30.9: The GeV γ-ray sky maps surveyed by Fermi-LAT [184], LHAASO [3] and H.E.S.S[171] from 1 GeV to 100 TeV and above.

the extragalactic diffuse emission.
30.3.3 Discrete Gamma Ray Sources
As a neutral component of cosmic rays, γ-rays directly reach the earth from their sources, thus
allowing us to identify the origin of the photons by association with known celestial objects orevents. As shown in Figure 30.9, the source-associated contributions are revealed directly by thebright spots whose sizes are due to the point-spread-function (PSF) of the instruments and the
intrinsic spatial extensions of the sources. It is also clearly shown that the sources are divided into
two groups: Galactic and extragalactic.
Galactic Sources More than 6600 sources have been found emitting γ-rays in the Milky Way.
Most of them have steady photon emissions over a wide energy range above 0.1 GeV up to 2 PeV. 43
of them have emission of γ-rays above 0.1 PeV referred as PeVatrons since the parent particles thatemitted the photons must be accelerated above 1 PeV on average in the source regions. Variabilityof the photon fluxes has also been observed from known objects such as pulsars and binary systems
or transient phenomena.
A. Sources with steady emissions are the majority of Galactic γ-ray emitters which are well
documented in reviews [190], [191], [192] and in γ-ray source catalogs [193] (for < 100 MeV), 4FLCT(for 0.1-300 GeV) by Fermi-LAT [194], TeV-Catalog available on-line (http://tevcat.uchicago.edu)
and the newly released 1LHAASO (for 1-2000 TeV) by LHAASO [3]. All associations with known
celestial objects, such as SNRs, PWNe, young massive-star clusters (YMC) are discussed in the corresponding catalog papers (e.g. individual catalogs collected in http://tevcat.uchicago.edu). Mostof the sources, particularly for their high-energy emission above tens of TeV, remain unidentified.
Among the identified ones, the Crab [195] and RX J1713-3946 [196] are the most extensively studied
objects and constitute paradigmatic examples of PWNe and SNRs.
The Crab has a compact PWN powered by the rotation energy of the pulsar in its heart.
Electrons and positrons in the wind are accelerated at the termination shocks and emit γ-rays
through synchrotron radiation at energies lower than 0.1 GeV. Simultaneously, accelerated electronsand positrons boost soft background photons, such as those in the cosmic microwave background,to energies well above 1 GeV via inverse Compton scattering. Figure 30.10 shows the spectralenergy density (SED) of the Crab nebula with a fit using a simple one-zone leptonic model. It
31st May, 2024

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30. Cosmic Rays

Figure 30.10: Spectral energy density (SED) of photons from the Crab from sub-µeV to 1.1
PeV. Above 1 TeV, data are collected from 7 experiments listed in legend in the upper panel. The
lower panel shows the deviation between data and the model based on a widely accepted one-zone
leptonic origin in the nebula. Only Fermi-LAT and LHAASO data are shown for simplicity. Inset
is the X-ray image of the nebula by Chandra [197].

generally describes the radiation of the nebula over energies up to Eγ ∼ 1.1 PeV, implying thatelectrons and positrons are confined in a small region of ' 0.2 pc by a magnetic field of intensity
B ' 110 µG and are accelerated to energies as high as ' 2.3 PeV. This requires a surprisingly
high acceleration rate, η = ¯/B = 0.14(B/100µG)(Eγ /1 PeV)1.54 PeV, at the level of 15%, where¯ is projection of the electric field averaged over the particle trajectory. This rate is 3 ordersof magnitude higher than that in the normal shock environment such as in SNRs, revealing theexistence of a so-called ‘extreme accelerator’ in the middle of the nebula [195]. The flux of photons
above 0.8 PeV indicates some deviation from the pure leptonic scenario implying that a hadronic
component might be responsible. It could be a hint of the super PeVatron which may contributeto the Galactic cosmic rays above the knee [195] (see Fig. 30.1).
RX J1713.7-3946 is one of the brightest objects in the TeV sky, and is the first SNR shell
to be confirmed as a TeV gamma-ray source [196]. The detailed TeV morphology reveals a shellstructure similar to the X-ray observations, indicating that particles are accelerated to very highenergy therein. The TeV gamma-ray spectrum extends to nearly 100 TeV. It is not determined
yet whether the gamma-rays are produced via Inverse Compton scattering of relativistic electrons(leptonic process), or via neutral pion decay with the pions produced in the inelastic scatteringof CR protons with ambient gas (hadronic process) [198]. Nevertheless, the spectral information
demonstrates the efficient acceleration of charged particles to energies beyond 100 TeV in thisobject. The latest H.E.S.S observations also found that the TeV gamma-ray emission region extends
significantly beyond the X-ray emitting shell [199], which may be due to either the escape of particles
from the shell or to particle acceleration in the shock precursor region.
B. Variable sources Crab flares, binaries and pulsars are observed in the Galactic γ-ray sky.
Their activity varies on timescales from a fraction of one second (pulsars), to days (Crab Nebula,
Novae), weeks, months or even years (γ-ray binaries). Various analysis pipelines are developed
mainly by the LAT collaboration to search for and monitor γ-ray transients.
The Crab Nebula shows flare activities on a timescale of days [200]. The instability is observed
only in GeV band by AGILE and Fermi/LAT. The flaring mechanism is still unclear with a couple
31st May, 2024

22

30. Cosmic Raysof models being under debate.
Each γ-ray binary is composed of a compact object (pulsar or black hole) and a massive star.
Their γ-ray emissions characterized by the orbital modulation, with time scales ranging from 3.9days (LS 5039) to ∼ 47 years (PSR J2032+4127). Microquasars are also binary systems thatlaunch powerful jets from the compact objects by accreting matter from their companions. Three
microquasars have been detected namely, Cyg X-1, Cyg X-3, and SS 433. They have shown γray activities correlated with orbital motion [201], jet precession [202], X-ray state changes [203],and flares [204]. Eta Carinae is the only colliding wind binary firmly detected, showing orbital
modulation in the γ-ray emission in a period of 5.54 years [205].
Pulsars show steady pulsation on their spin periods ranging from several milliseconds to seconds
in GeV band [206], thereby qualifying as γ-ray pulsars. Only the Crab and Vela pulsar are pulsatingin TeV [207] [208]. PSR J2021+4026 is observed for the γ-ray flux variability on time scales of several
years [209], making it the only variable γ-ray pulsar. Many millisecond pulsars themselves are γ-ray
pulsars showing periodic variability in milliseconds [210]. γ-ray eclipses and orbital modulations
have been detected in several binaries hosting millisecond pulsars, usually on the time scale of hours
to days, arising from the intra binary shock between the pulsar wind and stellar wind [211] [212].
Millisecond pulsars could transit between spin-down-powered state and accretion-powered state.
Variability in the γ-ray flux is observed accompanying these changes [213].
Novae outbursts have been detected in γ-rays, arising from the particle acceleration at shocks
and last for months [214]. RS Ophiuchi is the first nova with its outburst detected in TeV up to 1
month [215].
Extragalactic Sources The majority of extragalactic γ-ray sources are active galactic nuclei(AGN). The fourth catalog of AGNs (4LAC) by LAT for 8 year observations contains 2863 objects
located at high Galactic latitudes (|b| > 10◦ ) while 344 others were found at lower latitudes [216].
98% of them are blazars. The blazar population consists of Flat Spectrum Radio Quasars (FSRQs),
BL Lac-type objects and unknown types [216]. The Data Release 3 adds 587 more blazars and
4 radio galaxies to the catalog [217]. More than 70 blazars and a few radio galaxies are detectedin the very high-energy (VHE) band, namely photon energy greater than 0.1 TeV, by imaging
atmospheric Cherenkov telescopes (IACT) (http://tevcat.uchicago.edu).
Blazars belong to a class of AGN where the jets are oriented at a relatively small angle withrespect to the line of sight. This specific viewing angle allows us to observe the emission from thosejets with significant Doppler boosting. The photon flux in the jets may enhance significantly withrespect to that in quiet states, a phenomenon referred to as blazar flares. They are simultaneously
observed over a wide energy band from radio to VHE γ-rays with timescales ranging from a few
minutes to year [218] [219]. The broad-band SED of blazars typically shows two humps of nonthermal radiation. The one in the lower energy range from radio to X-rays is generally attributed
to synchrotron emission from relativistic electrons and positrons in the jet, while the origin of thehump at higher energies is still under debate. Possible emission mechanisms are the IC scatteringof accelerated leptons off low energy photons, which are inside jets or from outside regions [220], or
decay of neutral pions produced in collisions of accelerated protons against ambient matter [221],or some combination of the two processes.
The ground-based EAS experiments are suitable γ-ray detectors for monitoring the flares of
AGNs with the advantages of large FoV and full duty cycle of operation. The ARGO-YBJ collaboration reported a long-term continuous monitoring of Mrk 421 and Mrk 501 [222–224], the twobrightest blazars in the TeV sky. The γ-ray flux shows a good long-term correlation with that in
the X-ray band. HAWC detected the persistent emission from those two AGNs [225]. Recently, the31st May, 2024

30. Cosmic Rays

23

1

10-9

0.4
0.2
0

-0.2

10-9

-10

10

10-11
Flare 4 (2010)
OVRO
RXTE-ASM
MAXI-GSC
Swift-BAT
Fermi-LAT
ARGO-YBJ
SSC model
SSC model for S1

-12

10

10-13

-0.4
-30

-20

-10

0
Lag [Day]

10

20

30

E2dN/dE (erg cm-2 s-1)

0.6

E2dN/dE (erg cm-2 s-1)

Correlation coefficient

0.8

10-14
10-17

-15

10

-13

10

10-11

-9

10
10-7
Energy (TeV)

-10

10

Flare 2 (2010)
OVRO
Swift-UVOT
Swift-XRT
RXTE-ASM
MAXI-GSC
Swift-BAT
Fermi-LAT
ARGO-YBJTACTIC (MJD=55243)
VERITAS (MJD=55244)
SSC model
SSC model for S1

10-11

-12

10

10-13

-5

10

-3

10

10-1

10

10-14
10-17

-15

10

-13

10

10-11

-9

10
10-7
Energy (TeV)

-5

10

-3

10

10-1

10

Figure 30.11: The multi wavelength analysis of Mrk 421 involving measurements over wide energy
range from radio to TeV γ-ray during 4.5 years when ARGO-YBJ and LAT were operated [224].
The discrete correlation function between the light curves in X-ray band and TeV γ-ray band is
calculated and clearly shows no time lag between emissions in the two bands [224] (left panel). The
SED significantly changes from steady states (grey solid lines in middle and right panels) to flaring
states depending on the strength of flares. Comparing a small flare in the middle panel and a larger
one in right panel, the later has harder SED in VHE band. [224].

LHAASO collaboration reported eight sources detected at Galactic latitude |b| > 12◦ , among whichsome are AGNs, including well-known emitters, such as the radio galaxy M87, VER J0521+211
and 1ES 1215+303 [3].
Using data for 4.5 years when ARGO-YBJ and Fermi-LAT simultaneously operated from 2008
to 2013, the ARGO-YBJ collaboration realized the long-term multi wavelength observation of
Mrk 421 in all bands of radio, optical, X-ray, GeV, and TeV gamma-rays [224]. The well-known
correlation [226] between the photon fluxs in X-ray band and TeV γ-ray band is investigated in aquantitative way, namely the discrete correlation function between the light curves in two energy
bands being calculated. No time lag in the scale of days is found(see Figure 30.11). This is regarded
as evidence of favoring the one-zone Self-Synchrotron Compton scattering scenario [222].
Flares happened in that time window are systematically analyzed and clear correlation between
the strength of flares and features of the SEDs are observed as an example shown in Figure 30.11.
Detailed investigation of SEDs implies that various particle acceleration mechanisms, such as relativistic diffusive shock acceleration, might be responsible for different flares. A similar analysis iscarried out with data during outbursts of Mrk 501. The SEDs in the VHE band are observed to beharder during flares than that in the quite period. The detection of energetic photons above 10 TeV
and the hardness of the SED hint some exceeds over the expectation of one-zone SSC model [223].
Gamma-Ray Bursts (GRBs)
GRBs are violent explosions observed in distant galaxies, characterized by a rapid flash of γ-rays
lasting from a fraction of a second up to several hundreds of seconds. The emission from GRBs
occurs in two stages, namely the prompt emission phase and the afterglow phase, as can be seenin Figure 30.12.
In the second catalog of Fermi/LAT-detected GRBs, covering the first 10 yr of operations, 169
GRBs are detected above 100 MeV [231]. The high-energy emission generally lasts much longer
than the prompt keV-MeV emission. The widely discussed scenario for the extended GeV emission
is synchrotron radiation by relativistic electrons that are accelerated in shocks resulting from theinteraction of the jet with the surrounding medium [232, 233].
VHE emission has been detected from just a few GRBs by IACTs during the afterglow decay
phase. MAGIC slewed to the direction of GRB 190114C only ' 60 seconds after the trigger
31st May, 2024

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30. Cosmic Rays

Figure 30.12: The typical multi-wavelength measurement of the light curves of the γ-ray burst
GRB 221009A in the GeV band [227] (top left) and in the TeV band [228] (bottom left). The
clear different structures of the brightness variation patterns indicate the different origins of thesynchrotron radiation and inverse Compton scattering of leptons accelerated by the internal andexternal shock waves, respectively. The spectral energy distributions of the GRB 190114C and
GRB 1908129A, respectively measured by MAGIC [229] (top right) and H.E.S.S [230] (bottom
right). The Self-Synchrotron Compton scattering model of the afterglow is marginally supported
in the observations covering a wide energy band from X-rays to TeV γ-rays.

and detected photons above 300 GeV from the burst for the first 20 minutes [234]. This VHE
emission is explained by inverse Compton up-scattering of synchrotron photons by high energy
electrons in the external shock [229], as shown in the right-upper panel of Figure 30.12. Two otherevents, GRB 180720B and GRB 190829A, were also detected during the afterglow decay phase by
H.E.S.S [230, 235], the unexpected SED is shown in the right-lower panel of Figure 30.12.
The brightest-of-all-time GRB 221009A serendipitously occurred within the FoV of LHAASO.
More than 64,000 photons (above 0.2 TeV) were detected within the first 3000 seconds by LHAASOWCDA [228]. The detection covers both the prompt emission phase and the early afterglow in the
TeV band, revealing the onset of afterglow emission in the TeV band for the first time, as shown in
the left panels of Figure 30.12. In addition, the unprecedented photon statistics of the TeV emission
enabled identifying a jet break in the light curve, indicating an opening angle of GRB 221009A of∼ 0.8◦ . This is consistent with the brightest core of a structured jet, explaining the unexpectedhigh isotropic equivalent energy of this GRB. LHAASO-KM2A registered more than 140 photons
with energies above 3 TeV from GRB 221009A (to be published). The intrinsic energy spectrumof gamma-rays is well fitted by a power law after correcting for EBL absorption, with the highest
energy photon above 13 TeV traveling over a distance with red shift z ∼ 0.152(TBP).
31st May, 2024

30. Cosmic Rays

25

Tests on Lorentz Invariance Violation (LIV) Tests on LIV are feasible and thus, limits canbe set using the highest energetic photons collected from remote sources. Any tiny violation of theinvariance leads the fundamental dissipation relation to be rewritten [236] as E 2 = m2 c4 + p2 c2 (1 +A1 pc/Mp c2 + A2 (pc/Mp c2 )2 + ...), where E, p are the energy and momentum of a particle with themass m, the Mp is the Plank scale and A1 , A2 are theoretic parameters of the violation at thefirst and second order levels. This must lead instability of photons that may decay on their way
to the Earth [237]. The first order violation effect due to the decay channel γ → e+ + e− has notbeen found at energies ∼5 orders of magnitudes higher than the Planck scale, regarded as the null
evidence of the quantum gravitational effect. However, the limit due to second-order effect caused
by decay channel γ → 3γ is still found still ∼3 orders of magnitudes below the Planck scale, using
the latest observations of photons up to 1.4 PeV from the Cygnus X direction [238].

30.4 Neutrinos
In contrast to charged particles, neutrinos are not deflected by electromagnetic fields and thus
point back to their origin, making them appealing messengers for astronomical observations. In
addition, neutrinos of cosmic origin, or produced in the atmosphere of the Earth, allow us to study
particle physics in a kinematic regime not accessible to date to accelerator experiments. In thefollowing, we will consider neutrinos with energies at the GeV energy scale and above.
30.4.1 Production of high-energy neutrinos
High-energy neutrinos can be produced in hadronic interactions in a variety of astrophysicalobjects (astrophysical or cosmic neutrinos), in scattering of extremely energetic protons (p) withthe cosmic microwave background (cosmogenic neutrinos) and by cosmic-ray interactions in the
Earth’s atmosphere (atmospheric neutrinos). The main production chain is (A denoting atomic
nuclei and X a hadronic system)p(A) + p(A, γ) → π ± + X

with subsequent decays

π → µ νµ and µ → e νµ νe ,(30.1)

resulting in a ratio νe : νµ : ντ = 1 : 2 : 0 (not distinguishing here between ν and ν). If the source
density is high, muons can lose most of their energy before decaying, yielding a ratio 0 : 1 : 0 in
the extreme case. If protons were kept in the source region by magnetic fields without interacting,and only neutrons could escape and then decay via n → p + e− + ν e , the ratio would be 1 : 0 : 0.
Over cosmic distances, flavor mixing turns these ratios to 0.30:0.36:0.34 for the first source scenario(1:2:0), 0.17:0.45:0.37 for the second (0:1:0) and 0.55:0.17:0.28 for the third scenario (1:0:0) [239].
30.4.2 Measurement methods
Most experiments targeting high-energy cosmic neutrinos are based on the detection of Cherenkov
light induced by charged secondary particles produced in neutrino interactions. This includes underground detectors like Super-Kamiokande with its fiducial volume of 22.5 × 103 m3 (see Sect.
36.3.1) and underwater/ice detectors like ANTARES, KM3NeT or IceCube, the latter with a volume of 109 m3 (see Sect. 36.3.2). Neutrinos with energies exceeding some tens of PeV can be also
detected via the coherent emission of Cherenkov radiation at radio wavelengths in ice or other radiotransparent media (e.g. ANITA or RNO-G, see Sect. 36.3.3). Neutrinos with EeV energies could be
identified via extensive air showers starting too deep in the atmosphere to be due to particles withstrong or electromagnetic interaction. Alternatively, they could be detected via slightly upwarddirected air showers from the decay of tau leptons generated in interactions of Earth-skimming or
mountain-traversing ντ [240]. These signatures could be observed by cosmic-ray experiments suchas the Pierre Auger Observatory [241].
31st May, 2024

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30. Cosmic Rays

30.4.3 Diffuse fluxes
Atmospheric neutrinos The flux of atmospheric neutrinos as measured by different experiments is shown in Fig. 30.13. The production chain for conventional atmospheric neutrinos follows
eq. (30.1), with an observed ratio νe : νµ = 1 : 2 at energies of a few GeV (where almost all muonsdecay in the atmosphere), and a ratio below 1 : 10 at TeV energies, where muons reach the groundbefore decaying. The flux of muon neutrinos with energies below 100 GeV from the lower hemisphere is reduced due to neutrino oscillations, reducing the νe : νµ ratio at the lowest energies.
The flux of νe is obtained by subtracting the number of neutral-current muon neutrino interactions (as deduced from the measured charged-current muon neutrino reactions) from the numberof contained events without a muon track and converting the resulting Eνe distribution into the νeflux using the differential cross sections for CC and NC νe -nucleon scattering. The conventional
atmospheric neutrino flux dominates in the GeV to TeV region, following an Eν−3.7 power law.
Prompt atmospheric neutrinos are produced by the decay of hadrons containing a charm or
bottom quark, the production of which is strongly suppressed. Since they are produced early inthe air shower and decay before losing energy, however, the energy spectrum of prompt neutrinos
is expected to be harder (Eν−2.7 ) and to dominate the atmospheric neutrino flux at its highest
energies. The corresponding theoretical prediction has large uncertainties related to the cosmic-ray
spectrum and mass composition, the model for heavy-flavor production, and the parton distributionfunctions [242]. At present, experimental measurements only provide upper limits for the prompt
flux (see e.g. Fig. 30.14 where the prompt component was fitted to zero).
Diffuse extragalactic neutrino flux In 2013, a diffuse and isotropic flux of neutrinos of astrophysical origin was discovered with the IceCube Neutrino Observatory. The flux was identified
with the so-called HESE (high-energy starting events) selection as an excess of neutrino events
at high energies over atmospheric neutrinos and a background of misreconstructed atmosphericmuons (see Fig. 30.14, for the 7.5-year HESE sample [251]). Similar high-energy excesses were also
identified for tracks entering the detector from outside [252], and for fully contained cascade events.
Evidence for this flux has meanwhile also been reported by ANTARES [253] and Baikal-GVD [254],
albeit with much lower significance. The measured fluxes are consistent with a parameterizationas power-law functions proportional to Eν−γ , with the normalization factor and the spectral index
γ as parameters. The resulting γ values vary from 2.2 to 2.5 for different event classes covering
different energy ranges.
Different production mechanisms result in different neutrino flavor compositions at sources and,after neutrino oscillations over astrophysical distances, at the Earth. An IceCube study of the event
topologies [239] slightly favors νe : νµ : ντ = 1 : 2 : 0 at the source (pion decay according to eq. (30.1)
versus 0 : 1 : 0 (damped muons) and disfavors a 1 : 0 : 0 scenario (neutron decay).
A single event with energy 6.05 ± 0.72 PeV has been detected in IceCube [247]. It is compatible
with having been generated by the resonant process ν̄e + e− → W − → hadrons at Eν = 6.3 PeV(Glashow resonance) [255]. A statistically significant observation of the Glashow resonance would
reveal the presence of electron antineutrinos in the astrophysical flux and could provide information
about their production process: the expected ratio ν̄e : νe depends on the mass composition ofcosmic-rays and also on the photon density and the magnetic field strength of the source [256].
Cosmogenic neutrinos Cosmogenic neutrinos stem from the decay of charged pions generated ininteractions of ultra-high-energy cosmic rays with cosmic microwave (a) and infrared (b) backgroundradiation (p + γ → n + π + ) [257] and from the decays of neutrons produced in photodisintegration
processes [258, 259] (c). The neutrino flux at EeV energies is expected to be dominated by (a) and31st May, 2024

30. Cosmic Rays

E 2 dΦ ν + ν̄ /dE (GeV cm −2 s −1 sr −1 )27

IceCube 2021 - Astrophysical ν̄e
IceCube 2023 - Astrophysical all-flavor
IceCube 2018 - UHE limits
Auger 2022 - UHE limits
Allowed region for cosmogenic neutrinos

10 2
10 4
10 6
10 8
10 10
10 1

Atmospheric ν
Astrophysical νSuperK 2016 - νe
SuperK 2016 - νµ
ANTARES 2021 - νe
ANTARES 2021 - νµ
IceCube 2015 - νe
IceCube 2015 - νµ

101

103
105
Neutrino energy (GeV)

Upper limits

107

109

Figure 30.13: Measured energy spectra of atmospheric and cosmic diffuse neutrino fluxes. Experimental limits at highest energy are compared to model predictions for cosmogenic neutrinos [160].
All fluxes are normalized to one flavor (ν + ν), assuming a ratio ν : ν = 1 and, for cosmic neutrinos,
a ratio νe : νµ : ντ = 1 : 1 : 1 at Earth. Data sources: SuperK 2016 [243]; ANTARES 2021 [244];
IceCube 2015 νe [245]; IceCube 2015 νµ [246]; IceCube 2021 astrophysical ν̄e (ν + ν flux derived
from a single candidate event for the Glashow resonance) [247]; IceCube 2023 astrophysical all
flavor [39]. The limits at the highest energies are taken from [248] (IceCube) and [249] (Auger).
They are shown in the energy bins used for the corresponding analyses and have been adjusted tobin widths of one decade. The region allowed for the expected cosmogenic neutrino fluxes is takenfrom [250] (see also Fig. 36.10).

(c).
Measurement methods and experimental data are described in Sect. 36.3.3. and Fig. 36.10. The
expected flux can be estimated from the measured spectrum and composition of charged cosmic
rays, using the CMB density and the well measured properties of proton and nuclear interactions
with photons at a center-of-mass energy in the GeV range. The current uncertainty of thesepredictions exceeds one order of magnitude. Figure 30.13 reproduces the presently tightest limits
and compares them to the region for which cosmogenic neutrino fluxes would be consistent withthose limits (as of 2019) and cosmic-ray analyses [250].
Neutrinos from the Galactic Plane The Milky Way is an emitter across the electromagnetic
spectrum ranging from radio to gamma-rays. A large part of the observed gamma-ray flux isbelieved to consist of photons from the decays of π 0 s produced by cosmic rays colliding with theinterstellar medium. The TeV diffuse neutrino flux from the corresponding π ± decays along the
Galactic plane has been estimated with different models, ranging from a simple extrapolation of
Fermi-LAT gamma-ray data to higher energies, to more sophisticated approaches (see e.g. [260]).
First hints for a TeV neutrino emission from the Galactic Ridge have been reported by the
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Figure 30.14: Measured (data points) and expected (histograms) distributions of the depositedenergy measured in the IceCube detector for events passing the HESE selection, which strongly
suppresses down-going atmospheric neutrinos by vetoing accompanying muons. The cosmic neutrino flux has been assumed to follow an unbroken power law in Eν . Its normalization and spectral
index, as well as the normalizations of the conventional and prompt atmospheric neutrino and theatmospheric muon contributions were fitted to the data, where only the region above 60 TeV wasused to constrain the cosmic neutrino flux.

ANTARES collaboration [261]. IceCube has measured the flux of galactic neutrinos with a significance of 4.5σ against the only-background-hypothesis [262]. Figure 30.15 shows a map of the
Galactic plane with the point-by-point pre-trial significance of the IceCube neutrino observations.
While the overall signal is consistent with the modeled diffuse emission from the Galactic plane,
a significant part could also arise from a population of unresolved point sources. All individual"warm spots", however, are statistically consistent with background fluctuations.

Figure 30.15: The Milky Way plane in neutrinos (Galactic coordinates, with the origin beingat the Galactic Center). Shown is the pre-trial significance of the IceCube observations using acascade neutrino event sample, calculated from an all-sky scan for point-like sources [262]. Contours
indicate the regions that contain 20% and 50% of the predicted diffuse neutrino emission according
to an extrapolation of Fermi-LAT results. Grey lines indicate the Northern-Southern sky horizon
line.

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30.4.4 Neutrinos from astrophysical point sources
Most point source candidates include Active Galactic Nuclei (AGN). In particular, blazars –AGN that have jets pointing towards the observer – are thought to be likely sources. In 2017, a spatial and temporal correlation was found between a flare of the electromagnetic emission from blazar
TXS 0506+056 and the high-energy neutrino event IC170922A, detected by IceCube. An alert wassent to other observatories and a follow-up campaign in multiple wavelengths was started. At the
moment of neutrino detection, the blazar was flaring in gamma rays, with an accidental coincidence
excluded at the 3σ level [263]. Subsequent analyses of archival data revealed an excess in neutrino
events with a significance of 3.5σ with respect to the expected atmospheric background, coincident
with the position of TXS 0506+056, albeit not correlated with an electromagnetic flare [264].
In another analysis, the positions of 110 gamma-ray sources selected a priori were analyzed individually for a possible surplus of neutrinos over atmospheric and cosmic background expectations.
An excess of 79+22−20 neutrinos was found in the direction of the nearby AGN NGC 1068 (not a blazar,
but a Seyfert-2 galaxy), at a significance of 4.2σ (see figure 30.16). The excess is spatially consistent
with the direction of the strongest clustering of neutrinos in the Northern sky. The inferred flux
exceeds the potential TeV gamma-ray flux by at least an order of magnitude [265], suggesting thatthe sight to the gamma-ray generation region is obscured, as expected for Seyfert-2 galaxies.

Figure 30.16: Left: The sky region around the most significant spot in the Northern Hemisphereand NGC 1068. Shown is a fine scan of the region around the hottest spot, marked by a white cross.
The red circle shows the position of NGC 1068. The solid and dashed contours show the 68% and
95% confidence regions of the hot spot localization. Right: Distribution of the squared angulardistance between NGC 1068 and the reconstructed event direction. Figures taken from [265].

Other potential sources include starburst galaxies, galaxy clusters, supernovae remnants (steadyemission) as well as Gamma Ray Bursts (GRBs) and Tidal Disruption Events, TDEs (transientemission). Indeed, using data from IceCube and the Zwicky Transient Facility ZTF, hints for acorrelation of high-energy muon neutrinos with TDEs have been reported [266].
30.4.5 Results on particle physics
Investigating the attenuation of high-energy neutrinos as a function of energy and their path
length through the Earth, the first measurement of the neutrino-nucleon cross section at energies
between a few tens of TeV and ≈ 1 PeV (corresponding to center-of-mass energies between a few
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30. Cosmic Rays

100 GeV and about 1.4 TeV) has been achieved [267], giving access in deep-inelastic scattering in a
kinematic region currently not accessible to accelerator-based experiments.
The study of atmospheric high-energy neutrinos allows for the investigation of oscillation physics(see Sect. 14) at higher energies and over longer baselines than Earth-bound experiments. Constraints (sin2 θ23 = 0.51 ± 0.050 and ∆m232 = (2.41 ± 0.07) × 10−3 eV2 ) have been obtained with
IceCube and are compatible with corresponding results from accelerator experiments [268]. Both
IceCube and KM3NeT/ORCA are also sensitive to ντ appearance [269]. The KM3NeT/ORCA
detector (under construction, see Sect. 36.3.2) is furthermore expected to provide sensitivity to theneutrino mass hierarchy.
Also, Beyond-Standard-Model (BSM) physics is being tested. For instance, constraints by
IceCube on 2/4 mixing (the fourth state being a sterile neutrino) are comparable to constraints fromaccelerator experiments [270]. Neutrinos may have BSM interactions, and if the coupling strengths
are weak or if heavy mediators are involved, these interactions may only manifest themselves inthe HE and UHE neutrino sector. Corresponding constraints from IceCube have been publishedin [271]. Also, possible oscillation-like effects induced by quantum gravity are investigated [272].
Acknowledgement Many thanks to team members, Prof. Q. Yuan, R.Z. Yang, J. Li, X.Y.
Wang, S.Z. Chen and Dr. S.Q. Xu, L. Nie, R.F. Xu, who made substantial contributions to theγ-ray part of this section. We are grateful to C. Haack and L. Schumacher for their invaluable help
in producing Fig. 30.13.
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