11institutetext: APC, Paris, France

# High-energy astroparticle physics

D. Semikoz

###### Abstract

In these three lectures I discuss the present status of high-energy
astroparticle physics including Ultra-High-Energy Cosmic Rays (UHECR), high-
energy gamma rays, and neutrinos. The first lecture is devoted to ultra-high-
energy cosmic rays. After a brief introduction to UHECR I discuss the
acceleration of charged particles to highest energies in the astrophysical
objects, their propagation in the intergalactic space, recent observational
results by the Auger and HiRes experiments, anisotropies of UHECR arrival
directions, and secondary gamma rays produced by UHECR. In the second lecture
I review recent results on TeV gamma rays. After a short introduction to
detection techniques, I discuss recent exciting results of the H.E.S.S.,
MAGIC, and Milagro experiments on the point-like and diffuse sources of TeV
gamma rays. A special section is devoted to the detection of extragalactic
magnetic fields with TeV gamma-ray measurements. Finally, in the third lecture
I discuss Ultra-High-Energy (UHE) neutrinos. I review three different UHE
neutrino detection techniques and show the present status of searches for
diffuse neutrino flux and point sources of neutrinos.

##  0.1 Ultra-high-energy cosmic rays

###  0.1.1 Introduction

Figure 1:  Left: The cosmic ray spectrum $I(E)$ as function of kinetic energy
$E$, compiled using results from the LEAP, proton, Akeno, and HiRes
experiments [2, 3]. The energy region influenced by the Sun is marked in
yellow and an $1/E^{2.7}$ power-law is also shown. Right: The same spectrum at
high energies $E>10^{11}$ eV multiplied by $E^{3}$ [4]. Spectrum changes are
called the ‘knee’ at $10^{15}$ eV and the ‘ankle’ at $10^{19}$ eV.

Particles coming from space to the atmosphere of the Earth historically were
called cosmic rays. Most cosmic rays, however, are not ‘rays’ or photons, but
charged particles, protons and nuclei. Real high-energy gamma rays coming from
space to the Earth are only a small fraction of total flux, and they will be
discussed in Section 0.2. The measured spectrum of cosmic rays from 100 GeV to
highest energies $E>10^{20}$ eV is presented in Fig. 1 (left). The yellow
strip at low energies presents the contribution of the Sun. The remaining
spectrum can be fitted with a single power law $1/E^{2.7}$ up to highest
energies. The main contribution to it above 100 GeV gives galactic sources.
After multiplication of the spectrum on the energy cube, one can see changes
of power law in Fig. 1 (right). At $E>10^{15}$ eV the spectrum becomes
steeper. This change in the spectrum called the ‘knee’ and associated energy
$E=10^{15}$ eV is the maximum energy up to which galactic sources accelerate
cosmic rays. The next change of the spectrum is located at $E=3\cdot 10^{18}$
eV and has two possible interpretations. Either this is the place where
extragalactic sources start to dominate or it is the result of pair-
production energy loss by extragalactic protons (see Section 0.1.3). At the
end of the spectrum there is a cutoff, which was not seen in the old
experiments presented in Fig. 1 (right) due to small statistics, but it was
observed recently by the HiRes [3] and Auger [5] experiments.

In this lecture I briefly discuss the theory and observations of Ultra-High
Energy Cosmic Rays (UHECR), the highest-energy particles measured on Earth
with energy $E>10^{18}$ eV. Such particles, protons and nuclei, can be
accelerated in astrophysical objects, propagate through intergalactic space,
losing energy in the interactions with Cosmic Microwave Background (CMB).
UHECR are charged particles. Therefore they are also deflected in the Galactic
and intergalactic magnetic fields on the way from the source to the Earth. For
a more detailed introduction to UHECR I recommend recent lectures by M.
Kachelriess [6].

There are several important scales commonly used in astroparticle physics.
Distance is usually measured in parsecs, $\rm{1\leavevmode\nobreak\ pc}=3\cdot
10^{18}$ cm. Corresponding larger units are kiloparsec
$\rm{1\leavevmode\nobreak\ kpc}=10^{3}\rm{\leavevmode\nobreak\ pc}$ and
megaparsec $\rm{1\leavevmode\nobreak\ Mpc}=10^{6}\rm{\leavevmode\nobreak\
pc}$. Energy at highest energies is usually expressed in units of
$\rm{EeV}=10^{18}$ eV.

The plan of this lecture is as follows. In Section 0.1.2 I shall discuss
possible acceleration mechanisms of cosmic rays and astrophysical objects
which potentially can be their sources. In Section 0.1.3 I present the main
energy loss processes for UHECR particles and briefly discuss their deflection
in the magnetic fields. In Section 0.1.4 I sum up recent observational results
from the Pierre Auger Observatory and other experiments. In Section 0.1.5
results on anisotropy at highest energy are discussed. In Section 0.1.6 I
review expectations on secondary photons and neutrinos from UHECR protons.
Results are summed up in Section 0.1.7.

###  0.1.2 Acceleration

There are several possible acceleration mechanisms that can work in
astrophysical objects. These include first-order Fermi acceleration on the
shocks in plasma or acceleration in the potential difference, which we call
one-shot acceleration below. However, in any case, the Larmor radius of a
particle does not exceed the accelerator size, otherwise the particle escapes
from the accelerator and cannot gain energy further. This criterion is called
the Hillas condition [7] and sets the limit

${\cal E}\leq{\cal E}_{\rm H}=qBR$ (1)

for the energy ${\cal E}$ gained by a particle with charge $q$ in the region
of size $R$ with the magnetic field $B$.

Figure 2:  The Hillas plot with constraints from geometry and radiation losses
for $10^{20}$ eV protons (left) and iron (right). The thick line represents
the lower boundary of the area allowed by the Hillas criterion, Eq. (1).
Shaded areas are allowed by the radiation-loss constraints as well: light grey
corresponds to one-shot acceleration in the curvature-dominated regime only;
grey allows also for one-shot acceleration in the synchrotron-dominated
regime; dark grey allows for both one-shot and diffusive (e.g., shock)
acceleration.

The maximum energy of the accelerated particle can be restricted even more
than required by Eq. (1) if one takes into account energy losses during
acceleration. Unavoidable losses come from particle emission in the external
magnetic field, which can be either synchrotron-dominated if the velocity of
the particle is not parallel to the magnetic field, or curvature-dominated in
the opposite case.

In Fig. 2 in the plane magnetic field versus acceleration region size, the
Hillas condition Eq. (1) is shown by a thick black line. The left figure is
for protons and the right one for iron nuclei. Possible acceleration in
different astrophysical objects is shown with thin solid figures. Notations
are the following: NS are neutron stars, GRB are gamma-ray bursts, BH are
black holes, AD are accretion disks, jets are jets in active galaxies, K and
HS are knots and hot spots in the jets, L are lobes of radio galaxies,
clusters are clusters of galaxies, starbursts are starburst galaxies, voids
are voids in large-scale structure. Additional notations in brackets are
subtypes of active galaxies: Sy for Seyfert galaxies, BL for BL Lac galaxies
and RG for radio galaxies. Only objects above the Hillas line have the
potential possibility to accelerate particles to $10^{20}$ eV. This is a
necessary condition, but not enough for a specific acceleration mechanism. As
seen from Fig. 2, for example, neutron stars cannot accelerate particles to
highest energies under any condition, while shock acceleration would work only
for objects presented in the dark grey corner of this plot.

###  0.1.3 Propagation

Owing to expansion of the Universe, particles which come from sources at
redshift $z$ lose their energy as

$E_{P}\rightarrow E^{\prime}_{P}=E_{P}/(1+z)\leavevmode\nobreak\ .$ (2)

A typical energy loss distance, i.e., distance at which particles lose a
significant part of their energy for this process, is of the order of $z\sim
1$ (50% of energy), i.e., $R\sim 3\leavevmode\nobreak\ \mbox{Gpc}=10^{28}$ cm.

As well as during propagation in the intergalactic space, protons lose energy
due to two other main processes of interactions with Cosmic Microwave
Background (CMB) photons. Those are electron–positron pair production and pion
production. In both processes massive particles have to be produced and they
have threshold energy. Since the typical energy of CMB photons is very small,
$\epsilon_{CMB}=6\times 10^{-4}$ eV, the threshold for those processes is very
high. Only at energies above $E_{th}=m_{e}^{2}/\epsilon_{CMB}\sim 10^{15}$ eV
does the electron–positron pair-production process become important:

$P+\gamma_{CMB}\rightarrow P+e^{+}+e^{-}.$ (3)

The typical energy loss distance for this process is

$R=\frac{M_{P}}{2m_{e}}\frac{1}{\sigma_{P{e^{+}e^{-}}}n_{CMB}}=600\leavevmode\nobreak\
\mbox{Mpc}=2\times 10^{27}\leavevmode\nobreak\ \mbox{cm}\leavevmode\nobreak\
,$ (4)

where $n_{CMB}=400/\mbox{cm}^{3}$ is the density of CMB photons,
$\sigma_{P{e^{+}e^{-}}}\approx 10^{-27}/\mbox{cm}^{2}$ is the proton-pair
production cross-section. The factor $M_{P}/2m_{e}$ comes here from the fact
that in every interaction a proton loses only a tiny fraction of its energy
proportional to the proton/electron mass ratio.

Figure 3:  Left: Nucleon interaction length as function of energy from Ref.
[8]. Attenuation due to pion production Eq. (5) presented by the thick solid
line, the same for pair production Eq. (3) presented by the thin solid line.
Right: Horizon (maximal distance) from which protons with given or higher
energy can arrive. Lines for 10%, 30%, 50%, 70% and 90% of events are shown
[9].

At energies above threshold $E_{th}\approx
m_{\pi}M_{P}/\epsilon_{CMB}=10^{20}$ eV, the pion production process dominates
energy losses. This process for cosmic rays was first considered by Greizen,
Zatsepin, and Kuzmin in 1966 [10] and is now named the GZK process.

$P+\gamma_{CMB}\rightarrow\left\\{\begin{array}[]{c}P+\pi^{0}+\sum_{i}\pi_{i}\\\
N+\pi^{+}+\sum_{i}\pi_{i}\end{array}\right.$ (5)

The typical energy loss distance for this process is

$R=\frac{M_{P}}{m_{\pi}}\frac{1}{\sigma_{P\gamma}n_{CMB}}=100\leavevmode\nobreak\
\mbox{Mpc}=3\times 10^{26}\leavevmode\nobreak\ \mbox{cm}\leavevmode\nobreak\
,$ (6)

where $\sigma_{P\gamma}\approx 6\times 10^{-28}/\mbox{cm}^{2}$ is the proton
pion production cross-section. The factor $M_{P}/m_{\pi}$ comes here from the
fact that in every interaction the proton loses only 15–20% of its energy
proportional to the proton/pion mass ratio. Note that at higher energies the
dominating process in Eq. (5) is multi-pion production, in which the proton
loses 50% of its energy in every interaction, however, the cross-section for
this process $\sigma_{\sum\pi}=10^{-28}/\mbox{cm}^{2}$ is a factor 6 lower
than single pion production.

None of the above processes allows a proton with high energy to come from a
very large distance. The distance from which protons can come as a function of
energy is presented in Fig. 3 (left) [8]. The interaction length for pion
production [Eq. (5)] is shown by the dashed line. Attenuation due to pion
production [Eq. (6)] is presented by the thick solid line, the same for pair
production [Eq. (3)] is presented by the thin solid line. Figure 3 (left)
shows the average distance travelled by a single particle. However, for
searches of UHECR sources the important question is the maximum distance or
horizon from which UHECR can come to the detector. In Fig. 3 (right) we
present the horizon as a function of minimal proton energy. The lines 10%,
30%, 50%, 70% and 90% show the fraction of events which come from a given
distance. For example, 90% of events with $E>10^{20}$ eV should come from
distances $R<100$ Mpc. This distance is sometimes called the GZK distance,
because energy losses in this case are dominated by the GZK process of Eq.
(5).

The dominant loss process for nuclei of energy $E\raise
1.29167pt\hbox{$\;>$\kern-7.5pt\raise-4.73611pt\hbox{$\sim\;$}}10^{19}\,$eV is
photodisintegration $A+\gamma\to(A-1)+N$ in the CMB and the infrared
background due to the giant dipole resonance [11]. The threshold for this
reaction follows from the binding energy per nucleon, $\sim 10\>$MeV. Photo-
disintegration leads to a suppression of the flux of nuclei above an energy
that varies between $3\times 10^{19}\>$eV for He and $8\times 10^{19}\>$eV for
Fe.

Figure 4:  Sky map of the UHECR proton deflections for energy $E=40$ EeV in
two different models of Galactic magnetic field from Ref. [12]. The colours
show deflections from 0 to 10 degrees.

Figure 5:  Fraction of the sky in which the deflection in the extra-Galactic
magnetic field is bigger than the given value. Left: Constraint simulation of
K. Dolag et al. [13]. Right: Simulation of Sigl et al. [14].

Since UHECR are charged particles, they not only lose energy in the
interactions with background photons, but also when deflected by Galactic and
intergalactic magnetic fields.

The magnetic field of the Milky Way galaxy is conventionally modelled as a sum
of the regular and turbulent components of the field in the disk and halo of
the Galaxy. This means that the deflection in the Galactic field $\theta_{\rm
Gal}$ is a superposition of at least four terms:

$\theta_{\rm Gal}=\theta_{\rm Disk}^{\rm regular}+\theta_{\rm Disk}^{\rm
turbulent}+\theta_{\rm Halo}^{\rm regular}+\theta_{\rm Halo}^{\rm
turbulent}\leavevmode\nobreak\ .$ (7)

The deflection angle of UHECR in a regular magnetic field after propagation of
distance $D$ is given by:

$\theta^{\rm regular}\simeq\frac{ZeB_{\bot}D}{E_{\rm UHECR}}\simeq
5^{\circ}Z\left[\frac{E_{\rm UHECR}}{4\cdot 10^{19}\mbox{
eV}}\right]^{-1}\left[\frac{B_{\bot}}{2\cdot 10^{-6}\mbox{
G}}\right]\left[\frac{D}{2\mbox{ kpc}}\right]\leavevmode\nobreak\ ,$ (8)

where where $B_{\bot}$ is the magnetic field component orthogonal to the line
of sight, $E_{\rm UHECR}$ is the particle energy, and $Z$ is the atomic
charge. In the case of deflection by the turbulent field on the distance $D$
much larger than the correlation length of the field $\lambda_{B}$ and where
the deflection angle is small, the deflection is given by

$\displaystyle\theta^{\rm turb}$ $\displaystyle\simeq$
$\displaystyle\frac{1}{\sqrt{2}}\frac{ZeB_{\bot}\sqrt{D\lambda_{B}}}{E_{\rm
UHECR}}\simeq 1.2^{\circ}Z\left[\frac{E_{\rm UHECR}}{4\cdot 10^{19}\mbox{
eV}}\right]^{-1}\left[\frac{B_{\bot}}{4\cdot 10^{-6}\mbox{
G}}\right]\left[\frac{D}{2\mbox{
kpc}}\right]^{1/2}\left[\frac{\lambda_{B}}{50\mbox{ pc}}\right]^{1/2}$ (9)

The deflection angles by regular and turbulent components of Galactic Disk and
Halo, $\theta^{\rm Disk}_{\rm regular}$ and $\theta^{\rm Disk}_{\rm
turbulent}$ are given by Eqs. (8), (9). Contributions of the Halo fields
$\theta^{\rm Halo}_{\rm regular}$ and $\theta^{\rm Halo}_{\rm turbulent}$ are
less certain, but the result in deflections is usually assumed to be less than
the one for disk fields.

Deflections of UHECR by the regular field in the disk $\theta_{\rm Disk}^{\rm
regular}$ have been studied in many theoretical models. A sky map of the
deflections of UHECR with $E=40$ EeV in two different models is presented in
Fig. 4. Despite both models being consistent on average with the expectation
of Eq. (8), predictions in any given direction are strongly model-dependent.

Extragalactic magnetic fields are unknown except in the centres of galaxy
clusters. Therefore one has to use theoretical models for the evolution of the
magnetic fields. In such models magnetic fields follow the formation of large-
scale structures. Because the structure of extragalactic magnetic fields is
very non-trivial with very large fields near large-scale structures and tiny
fields in the voids, one cannot use Eq. (9) everywhere. Instead one can
introduce a fraction of the sky with deflections lower than a given value.
Unfortunately, modern models give a very broad range of predictions. In Fig. 5
we show calculations by two groups that show very different results. The group
of K. Dolag et al. made constraint simulations of local large-scale structures
within 100 Mpc around the Earth [13]. This means that all big structures such
as clusters of galaxies are located in exactly the same places as in the real
sky. Also the density of points in this simulation is adaptive with more
points at clusters and fewer on filaments. The results of this simulation are
shown in Fig. 5 (left). According to this simulation, at 100 Mpc from the
Earth only in 2% of the sky are deflections bigger than
$\theta^{EGMF}=1^{\circ}$. Those places are centres of galaxy clusters. In
contrast the simulation of G. Sigl et al. [14] uses a uniform grid with more
points on filaments and fewer on clusters. Unfortunately this simulation is
not constrained and thus cannot be directly compared to local large-scale
structures. In this simulation $\theta^{EGMF}>50^{\circ}$ in 60% of the sky.

Let us note here that propagation energy losses are extremely important for
the understanding of experimental results on spectrum and composition
discussed in the next section. Deflections in turn are a key issue in the
anisotropy studies in Section 0.1.5.

###  0.1.4 Observations

In this section we shall discuss the present status of UHECR observations.

Figure 6:  Extensive air shower produced by a UHECR particle in the atmosphere

We start with the detection of UHECR in the atmosphere. The typical column
density of the atmosphere is 1000 g/cm2 and in 1g there are $N=10^{24}$
protons, while a strong cross-section is $\sigma_{PP}\sim
10^{-25}\leavevmode\nobreak\ \mbox{cm}^{2}$. Thus UHECR protons or nuclei
should interact within the atmosphere many times before they reach the Earth’s
surface. In these interactions it would produce extensive air showers. An
example of such a shower is illustrated in Fig. 6. After first interaction the
primary proton or nuclei would produce a large number of pions. Neutral pions
would start an electromagnetic cascade, while charge pions would produce
muons. At the maximum of shower development one expects $N=10^{9-10}$
particles distributed in an area with a radius of a few kilometres. At this
point the shower mostly consists of 10 MeV electrons and photons and only
5–10% of its energy is in muons. If the shower is not vertical, the column
density increases as $1/\cos(\theta_{zenith})$ and reaches 2000 g/cm2 for
$\theta_{zenith}=60^{\circ}$. At such a depth all electromagnetic components
of the shower disappear and the shower would consist of muons only. Another
way to detect the shower is to look for fluorescent UV light of nitrogen atoms
in the atmosphere. This method is called ‘calorimetric’ and gives a
3-dimensional image of the shower. The main problem with this method is that
detection is possible only on a moonless night, making the duty cycle of such
detectors possible only 10–15% of the time. Finally one can detect direct
Cherenkov light of the charged particles, but since this light is concentrated
only within the central kilometre of the shower, one cannot use this technique
at highest energies.

Figure 7:  Pierre Auger Observatory detector with more than 1600 water tanks
and 4 fluorescence telescopes (see Ref. [15] for details)  Figure 8:  Energy
spectrum of UHECR as a function of energy measured by the Pierre Auger
Observatory and model predictions for iron nuclei (blue) and protons (red) [5]

The Pierre Auger Observatory (Auger) is the largest UHECR detector in the
world at the moment with an area of 3000 km2. Such a big area is required to
collect enough statistics with UHECR at highest energies $E>60$ EeV, because
the flux of such UHECR is tiny, one particle per 100 km2 per year. Auger is
located on the plateau at an altitude of 1000 metres in the Mendoza province
of Argentina. The ground detector consists of 1600 water tanks distributed 1.5
km from each other as presented in Fig. 7. Also there are four fluorescence
telescopes pointed at the atmosphere above the ground detectors as shown in
Fig. 7. Detection of 10% of showers both by fluorescence detectors (FD) and by
ground detectors guarantees a good quality of events and at the same time
allows one to calibrate the ground detectors by FD.

In Fig. 8 we show a recent energy spectrum which was measured by Auger before
31 March 2009 [5]. The steeply falling flux of UHECR is multiplied by $E^{3}$
in order to show details of the spectrum. The total systematic energy error is
22% and is shown in the top right corner of the figure. For energy bins with
$E<3\cdot 10^{19}$ eV statistical errors are not important, while at highest
energies $E>60$ EeV the shape of the spectrum is still uncertain and more
statistics are needed. On the other hand, the suppression of the spectrum is
statistically significant and is clearly seen in Fig. 8.

This is an important experimental result, since it is independent confirmation
of similar observations made by the HiRes experiment [3]. Thus cutoff in the
energy spectrum exists. However, there are several questions to be answered
before one can tell that this really is a GZK cutoff. First, is this cutoff
due to the maximum energy of sources, or to energy losses? In Section 0.1.2 we
have seen that indeed the maximum energy for many types of sources is close to
$10^{20}$ eV. The ultimate answer to this question would be the detection of
several sources at different distances with cutoff following expectations of
energy losses.

Figure 9:  Left: Measurement of shower development by signals in the
fluorescence detectors as a function of depth in the atmosphere. The maximum
of shower development in this example is $X_{max}=753\leavevmode\nobreak\
g/\mbox{cm}^{2}$ [16]. Right: Average $X_{max}$ of showers measured by HiRes
and Auger and $RMS$ of $X_{max}$ measured by Auger in 2009 [17].

Second, is the chemical composition of UHECR proton-dominated at those
energies? Since in our Galaxy all elements up to iron are accelerated to
energies around the knee $E=10^{15}$ eV, the same situation can exist in
astrophysical objects which accelerate to highest energies. Experimental
answers to this question can be found in the future even by Auger, but already
current data show that the composition becomes heavy at high energies. Indeed,
recent Auger results from Refs. [16, 17] are shown in Fig. 9. In Fig. 9 (left)
we present the shape of the shower development in the atmosphere as seen by a
fluorescence telescope. The signal is proportional to the number of electrons
and positrons in the shower. Signals grow due to the development of
electromagnetic cascades. The maximum of the signal corresponds to the maximum
development of the cascade in the atmosphere. After that the shower loses its
energy due to dissipation effects. The depth of the atmosphere corresponding
to the maximum of the shower development is called $X_{max}$. For the example
presented, this maximum is at $X_{max}$ = 753 g/cm2 and the energy of the
event is $E=1.6\cdot 10^{19}$ eV [16]. At the same energy, protons on average
interact much deeper in the atmosphere than heavy nuclei.

Figure 10:  The layout around the Interaction Point 1 (IP1) of the LHC. The
structure at the centre indicates the ATLAS detector surrounding the collision
point. The LHCf detectors are installed in the instrumentation slot of the
TANs located $\pm 140$ m from IP1. Two independent detectors, LHCf Arm1 and
LHCf Arm2 are installed at either side of IP1[18].

On the top panel of Fig. 9 (right) one can see the results of the most common
hadronic models presented with red lines for protons and with blue lines for
iron. The example event in Fig. 9 (left) is definitely proton-like. The
averaged $X_{max}$ values in each bin are presented in the same figure for
both the Auger and HiRes experiments. Both results are consistent with each
other showing a relatively light composition from $10^{18}$ eV to $10^{19}$
eV. However, Auger shows heavier composition at highest energies.

The main problem when measuring the composition with $X_{max}$ is its strong
model dependence, as seen on the top panel of Fig. 9 (right). There are two
complementary ways out. One is to use a composition-sensitive parameter that
weakly depends on the model choice. Such a parameter is
$RMS(X_{max})=\sqrt{\langle X_{max}^{2}\rangle-\langle X_{max}\rangle^{2}}$,
presented in the lower panel of Fig. 9 (right). One can see that according to
this measurement the composition becomes heavier at high energy. Another
important way is to test models and find the best one. For this purpose a
dedicated experiment LHC forward (LHCf) was constructed at CERN. The idea of
this experiment is to measure the neutral particles emitted in the very
forward region of LHC collisions at low luminosity. The configuration of this
experiment is presented in Fig. 10. Data required for testing the hadronic
models will be collected in the first scientific runs of the LHC [18]. Thus in
the near future we shall have better knowledge of hadronic models and more
understanding of the composition of UHECR at highest energy. At present the
Auger results indicate heavy composition; this was not confirmed by
independent measurements and the fraction of light nuclei in the data remains
uncertain.

This is a very important question for searches of UHECR sources, which we
shall discuss in the next section.

###  0.1.5 Anisotropy

Figure 11:  Left: Sky map of arrival directions of UHECR with $E>40$ EeV in
old experiments. Right: Probability that this anisotropy is a function of
angular distance between events [19].

Since for every UHECR event the arrival direction is detected, for tens of
years many attempts were made to find sources of UHECR in the experimental
data. Unfortunately none of them has been confirmed so far. There are two ways
to look for the sources. One is to look for the data itself and try to find
anisotropy in autocorrelation factions. The second is to pick up a catalogue
of possible sources and look for the cross-correlations with this catalogue.
This second way always requires confirmation by an independent data set, since
completeness of the catalogue is a very complicated issue and it is difficult
to estimate the probability due to the parameter choice a posteriori.

Here we start with autocorrelations. In the left panel of Fig. 11 one can see
the sky map with the arrival direction of events with $E>40$ EeV in several
old experiments, including SUGAR, AGASA, HiRes, Yakutsk, Havera Park, Volcano
Ranch, and Fly’s Eye. On the right panel of the same figure one can see the
probability that autocorrelations between selected events are by chance within
a given angle. One can see that the probability is minimal at angles 20–25
degrees. After penalization on the choice of angle, the probability that this
happened by chance is $P=0.3$% [19]. This clustering of events on rather
moderate scales can be due to the location of the sources in the Large Scale
Structure.

Figure 12:  Probability of autocorrelations as a function of energy and
angular distance between events, see Ref. [20]

The same probability in the first Auger data is presented in Fig. 12 as a
function of both energy and angle. One can see that for exactly the same
energy $E=40$ EeV and angle $\theta=20^{\circ}$–$25^{\circ}$ the probability
is $P\sim 10^{-2}$. However, recent results with larger statistics did not
show more significant anisotropy at such energies [21]. This makes the
situation with anisotropy in the data less clear.

Figure 13:  Left: Sky map of arrival directions of 27 UHECR with $E>57$ EeV
measured by the Pierre Auger Observatory before August 2007 in galactic
coordinates (circles) and 472 nearby AGNs (red stars) [22]. Blue contours show
the Auger exposure. Right: Likelihood ratio for events after formulation of
the prescription. Period II is for data on the left panel. Period III is for
new data up to March 2009 [21].

Now let us discuss correlations with astrophysical objects. First Auger data
have shown strong correlations with nearby active galaxies called Active
Galactic Nuclei (AGN). Namely, 12 out of 14 events with E > 57 EeV were
correlated within $\theta<3.1^{\circ}$ from 472 AGNs from the Veron catalogue
with distances $R<75$ Mpc. This correlation was considered by the Auger
Collaboration as a formal way to study the deviation of cosmic rays from
isotropic distribution. Data from Period I was tested with the prescription
during Period II, where 13 new events were detected, out of which 9 obeyed
prescription parameters. The prescription was fulfilled, i.e., the observed
sky was considered anisotropic at the 99% confidence level [22]. Data used in
this publication and shown in Fig. 13 (left) correspond to Periods I (not
shown) and II shown in Fig. 13 (right) before the vertical line. Unfortunately
this correlation was not confirmed in the later data [Period III in Fig. 13
(right)].

Figure 14:  Angular distribution of events around the Cen A galaxy in Auger
data compared to isotropic ones

It does not mean that all anisotropy signals in Auger have completely
disappeared. There is still a remaining excess of events around the Cen A
galaxy on scales of 20 degrees, see Fig. 14. This anisotropy has to be tested
by future data.

###  0.1.6 Secondary photons and neutrinos from UHECR

Figure 15:  Left:  Fluxes of protons and secondary photons as a function of
energy. Primary protons with spectrum $1/E^{2.6}$ and maximum energy
$E_{max}=10^{21}$ eV are shown by the thin red line. Secondary protons fit the
UHECR spectrum from $E>10^{18}$ eV (thick red line). Secondary photons from
all reactions are shown by the blue dashed line and from pion production only,
Eq. (5) by the magenta line. Right: Fluxes of UHECR and secondary photons in
the case of iron nuclei primaries with spectrum $1/E^{2.1}$ and maximum energy
$E_{max}=10^{21}$ eV. The remaining iron nuclei are shown by the green line.
Secondary protons by the magenta line. Secondary photons by the blue line.
Figure 16:  Contribution of secondary photons from UHECR to the extragalactic
gamma-ray background as a function of energy and other possible sources which
contribute to the same background [23]

As was discussed in Section 0.1.3, protons lose their energy in pair
production and pair production reactions. Since secondary pions quickly decay,
secondary photons and neutrinos are produced. Neutrinos propagate to the Earth
without interactions on the way, but photons cannot. They start to interact
with background photons and produce pairs. Electrons and positrons in turn up-
scatter CMB photons or produce synchrotron radiation:

$\displaystyle\gamma+\gamma_{background}$ $\displaystyle\rightarrow$
$\displaystyle e^{+}+e^{-}$ $\displaystyle e^{\pm}+\gamma_{background}$
$\displaystyle\rightarrow$ $\displaystyle e^{\pm}+\gamma$ (10) $\displaystyle
e^{\pm}+B$ $\displaystyle\rightarrow$ $\displaystyle e^{\pm}+\gamma_{synch}$

The sequence of processes in Eq. (0.1.6) is called an electromagnetic cascade.
At energies above $10^{15}$ eV the cascade proceeds on the CMB background
(400/cm3), but at lower energies pair production on CMB is impossible. At such
energies the cascade continues on a much less abundant infrared background
(1/cm3) and at lower energies on optical background (0.01/cm3). Then it stops
at the multi-GeV energies of gamma rays.

In Fig. 15 we plot primary cosmic-ray and secondary photon fluxes from primary
protons (left) and iron (right) from Ref. [23]. Secondary protons after
interaction fit the UHECR spectrum from $E>10^{18}$ eV in Fig. 15 (left).
Secondary photons cascade down to the GeV region. Only a small fraction of
photons come from the pion production reaction (magenta dotted line). Most of
the photons generated are from the $e^{+}e^{-}$ production reaction with total
flux shown by the dash-dotted blue line. The number of secondary protons is
much lower in the case of iron primaries, as shown by the dotted magenta line
in Fig. 15 (right). As a result, the secondary photon flux in the GeV region
is much smaller in this case, on the level of 0.2% of the EGRET measurement.
Also very high energy photons are absent in this case due to low maximum
proton energy.

Figure 17:  Left: Example of GZK photon flux from Ref. [24]. UHECR protons fit
the HiRes spectrum. Secondary neutrinos are shown by a green line. The
remaining secondary photons are in the range between the blue lines. Right:
Experimental upper limits on the photon fraction in the UHECR spectrum from
Ref. [21].

In Fig. 16 we compare the range of the electromagnetic cascade fluxes from
UHECR with other possible astrophysical contributions in the EGRET band. Note
that most of the uncertainty of the UHECR cascade flux comes from an unknown
source evolution. The scatter for a given class of sources is thus much
smaller, as seen from Fig. 16 for the case of AGNs.

In Fig. 17 (left) we plot the possible range of GZK gamma-ray fluxes for a
given proton flux which fit the UHECR spectrum. The range of fluxes comes from
the variation of possible values of the extragalactic magnetic field and the
range of the models for extragalactic radio background. Also on the same
figure the corresponding neutrino flux is shown by a green line. In Fig. 17
(right) we show the experimental upper limits on the fraction of photons in
the UHECR flux. The range of possible GZK photon fluxes corresponds to protons
with a range of power law injection spectra and source evolution fitting the
UHECR spectrum. One can note that the current best upper limits of Auger are
still above the range of expected theoretical values. On the other hand,
existing limits already exclude some exotic models.

###  0.1.7 Summary

In the first lecture we briefly discussed many aspects of UHECR physics.

Observed cosmic rays have energies up to $10^{20}$ eV. Acceleration in
astrophysical objects to such energies is a very non-trivial task and there
are no objects in our Galaxy which can do this job. There are very few classes
of exceptionally powerful objects in the Universe, some of which can be real
sources of UHECR. Accelerated particles lose their energy in interactions with
the CMB background and are also deflected by electromagnetic fields during
their propagation from sources to the Earth.

There are three important experimental challenges in UHECR physics: the
spectrum of cosmic rays, the chemical composition of cosmic rays, and the
search for anisotropies in the sky with the ultimate goal of finding UHECR
sources.

The cutoff in the energy spectrum at highest energies $E>6\cdot 10^{19}$ eV
has now been established by two independent experiments, HiRes and Auger.

The most striking result of 2009 was evidence of heavy composition, shown by
the Auger experiment at highest energies, Fig. 9. This result still needs
independent confirmation. Also the interpretation of composition measurements
is affected by uncertainty in the hadronic models. This question can be
clarified in the near future by the LHCf experiment.

Finally, most challenging is the search for UHECR sources. The last result in
this direction was made by Auger in 2007. They found that the sky is
anisotropic at the highest energies, at least at the 99% C.L., by looking at
the correlations with nearby AGNs. Unfortunately those correlations were not
confirmed in the new data, and the only anisotropy excess remaining in the
Auger data at the highest energies is an excess around the Cen A galaxy, see
Fig. 14.

During energy losses the UHECR protons produce secondary photons and
neutrinos. Most of the secondary photons cascade down to the GeV energies,
where this contributes to the diffuse extragalactic background. An
experimental search for the remaining gamma rays at highest energies
$E>10^{18}$ eV is challenging and existing upper limits are just above
theoretical predictions, see Fig. 17.

Thus there are many unsolved problems in UHECR physics. They require both
theoretical and experimental efforts in the near and more distant future.

##  0.2 High-energy gamma rays

###  0.2.1 Introduction

In this lecture I shall discuss the theory of TeV gamma rays and recent
observations made in this field. I shall give a brief introduction to the
experimental detection techniques and present some selected results on the
subject. For more detailed study I would like to recommend the recent review
by F. Aharonian, J. Buckley, T. Kifune, and G. Sinnis [25].

Relativistic particles can travel with a speed larger than the speed of light
in the medium $V>V_{M}=c/n$. Here $n>1$ is the refractive index of the medium.
This index in the air is $n_{\mbox{a}}=1.008$ and in water
$n_{\mbox{w}}=1.33$.

The charged particles polarize the molecules of the medium, which then return
rapidly to their ground state, emitting prompt radiation called Cherenkov
radiation. This radiation is emitted under a constant Cherenkov angle with the
particle trajectory, given by

$\cos\delta=\frac{V_{M}}{V}=\frac{c}{nV}=\frac{1}{\beta n}\leavevmode\nobreak\
.$ (11)

Figure 18:  Detection of high-energy gamma rays by Cherenkov telescopes in air
(left) and in water (right)

Figure 19:  Examples of gamma-ray experiments: Cherenkov telescope H.E.S.S.
(left) and water pool Milagro (right)

The minimal energy of a charged particle is

$\gamma_{min}=\frac{E_{min}}{M}=\frac{n}{\sqrt{n^{2}-1}}\leavevmode\nobreak\
.$ (12)

Particles with higher energy will produce a cone of Cherenkov light. This
effect is used by Cherenkov telescopes for air (H.E.S.S., MAGIC, Veritas, CTA)
and by ground experiments in water (Milagro, HAWK). Detection of the shower in
air and in water is illustrated in Fig. 18.

We present examples of such experiments in Fig. 19. On the left panel we show
a view of the H.E.S.S. experiment. This experiment made the most significant
contribution to the development of TeV gamma-ray astrophysics in recent years.
On the right panel we show the Milagro experiment, a pioneering experiment in
water Cherenkov techniques.

###  0.2.2 Point sources of TeV gamma rays

Figure 20:  Sky in the TeV gamma rays with 3 sources in 1995 (top left), 32
sources in 2005 (top right), and 80 sources in 2009 (bottom)

TeV gamma-ray astrophysics is developing very quickly. One can see the number
of detected sources in the sky as a function of time in Fig. 20. From 3
sources in 1995 one has 32 sources in 2005 and 80 sources in 2008. In addition
not only does the number of observed sources grow, but also the number of
different populations of sources. This is a very important fact for future
experiments with better sensitivity like the Cherenkov Telescope Array (CTA).
They would have a very large potential for detecting many different classes of
sources.

In particular, in Fig. 20 on the bottom panel, red circles show extragalactic
sources which contain BL Lac objects, radio galaxies, and starburst galaxies.
Also in the galactic plane there are many different classes of objects, which
include supernova shells, pulsar wind nebulas, pulsars, binary systems and
dark objects. Dark objects mean they were detected in gamma rays, but there is
no corresponding source in other wavebands.

Figure 21:  Sensitivity of gamma-ray detectors to point sources, from Ref.
[25] Figure 22:  Redshift for gamma rays as a function of energy. Lines show
constant optical depth in two models of IR/O background. Figure 23:  Redshift
for gamma rays as a function of energy. Lines show constant optical depth in
two models of IR/O background.

The sensitivity of gamma-ray detectors to point sources as a function of
energy is shown in Fig. 21. The sensitivity of air telescopes is shown for 50
hours of observation for one source. The sensitivity for ground experiments is
shown for 5 years, but they observe all the sky ($2\pi$sr). At low energies
$E<10$ GeV the sensitivity of the GLAST (Fermi) satellite is the best. One
year of observations are shown. At large energies $E>10$ TeV the ground air-
shower experiments (Tibet) have the best sensitivity. Future CTA projects will
be orders of magnitude better than present-day experiments from 10 GeV to 10
TeV energies.

Another important fact is that gamma rays cannot travel freely in the
intergalactic space. They interact with optical/infrared background photons
and disappear producing pairs of electrons and positrons. In Fig. 22 one can
see the main backgrounds for gamma-ray propagation. They are shown in units of
photon density per cm3. The largest contribution comes from the CMB background
with 400 photons per cm3. However, owing to the small energy of CMB photons,
this background is important only for $E>1000$ TeV. For the experimentally
interesting energy range $E<100$ TeV the main backgrounds are infrared and
optical. Since those backgrounds are created by galaxies and partly by dust
they are strongly model dependent both as a function of energy and as a
function of redshift.

Optical depth can be defined as

$\tau(E)=R\cdot\sigma_{\gamma\gamma}(E)\cdot
n_{back}(z,\epsilon)\leavevmode\nobreak\ ,$ (13)

where $R$ is the distance travelled by photons, $\sigma_{\gamma\gamma}(E)$ is
the pair-production cross section, and $n_{back}(z,\epsilon)$ is the density
of background photons. Distances on the cosmological scale are often expressed
in terms of redshift. One can express it through the Hubble law $R=z\cdot
c/H_{0}$, where $H_{0}=70$ km/s/Mpc is the Hubble constant. In Fig. 23
contours of constant optical depth $\tau(E)$ are shown on the plane redshift
versus energy for $\tau(E)=1,3,10$ in two different models of IR/O background.

Figure 24:  Observation of Mkn 421 as a function of time

There is one important difference between air Cherenkov telescopes and water
Cherenkov detectors. In Fig. 24 we plot world-wide monitoring of the nearby BL
Lac object Mkn 421 as a function of time. One can see that air Cherenkov
telescopes can see a signal only on moonless nights, which restricts their
operation to the corresponding intervals of time. On the contrary, water
Cherenkov telescopes operate all the time they can see a source, which will
allow source activity to be detected all the time. On the other hand, the
problem of water Cherenkov experiments is poor sensitivity, which will prevent
them from detection of relatively low fluxes and very fast variations in time.
Thus both techniques are complementary to each other.

Figure 25:  Central part of the Milky Way galaxy in infrared, optical, and in
TeV gamma rays. The TeV gamma-ray sky from H.E.S.S. observations with a large
number of sources.  Figure 26:  The Milky Way galaxy in TeV gamma rays from
galactic longitude 20∘ to 220∘ and galactic latitude from $-10^{\circ}$ to
$10^{\circ}$. The image is the culmination of a seven-year exposure by the
Milagro instrument.

In Fig. 25 one can see a view of the central part of the Milky Way galaxy in
three energy bands: optical, infrared, and TeV gamma rays. At least three
astronomical source populations: supernova remnants (SNRs), pulsar wind
nebulae (PWNe), and binary systems (BSs) are represented in this figure. In
addition, the H.E.S.S. observations of the central region of our Galaxy
revealed a diffuse TeV $\gamma$-ray emission component which is apparently
dominated by contributions from giant molecular clouds (GMCs). These massive
complexes of gas and dust most likely serve as effective targets for
interactions of relativistic particles from nearby active or recent
accelerators. Thus one may claim that four galactic source populations are
already firmly established as effective TeV $\gamma$-ray emitters. Meanwhile,
many sources discovered by H.E.S.S. in the galactic plane remain unidentified.
Although some of these sources might have direct or indirect links to SNRs,
PWNe, and GMCs, one cannot exclude that a fraction of the H.E.S.S.
unidentified sources are related to other source classes.

The Milagro telescope has made the first measurement of the diffuse TeV gamma-
ray flux from the Galactic Disk. Figure 26 shows the Galaxy (as visible from
the Northern Hemisphere) in TeV gamma rays. In addition to the individual
sources discussed above, the image (compiled from Milagro data) shows the
existence of a diffuse TeV gamma-ray flux between galactic longitudes of 30∘
and 90∘.

###  0.2.3 Extragalactic magnetic fields

Figure 27:  Detection of EGMF through observation of secondary emissions
around a point source [26]

Another very important field which will benefit in the near future from TeV
gamma rays is Extragalactic Magnetic Fields.

Indeed, as discussed above, TeV gamma rays emitted by astrophysical sources
can be measured by detectors on Earth. Practically all TeV gamma rays from
galactic sources come directly to the detectors. However, this is not true for
extragalactic sources. As one can see from Fig. 23, even for nearby sources
like Mkn 501, gamma rays with $E>10$ TeV cannot come freely to the detector.
The pair production on Extragalactic Background Light (EBL) reduces the flux
of $\gamma$-rays from the source by

$F(E_{\gamma_{0}})=F_{0}(E^{\prime}_{\gamma_{0}}(z_{E}))e^{-\tau(E_{\gamma_{0}},z_{E})},$
(14)

where $F(E_{\gamma_{0}})$ is the detected spectrum,
$F_{0}(E^{\prime}_{\gamma_{0}})$ is the initial spectrum of the source, and
$\tau(E_{\gamma_{0}},z_{E})$ is the optical depth Eq. (13). The typical
distance which a primary gamma ray travels is

$D_{\gamma_{0}}=D_{\gamma}(E_{\gamma_{0}}^{\prime},z)=40\frac{\kappa}{(1+z)^{2}}\left[\frac{E_{\gamma_{0}}^{\prime}}{20\mbox{
TeV}}\right]^{-1}\mbox{ Mpc}\leavevmode\nobreak\ ,$ (15)

where a numerical factor $\kappa=\kappa(E_{\gamma_{0}},z)\sim 1$ accounts for
the model uncertainties.

The cascade electrons lose their energy via Inverse Compton (IC) scattering of
the CMB photons within the distance

$D_{e}=\frac{3m_{e}^{2}c^{3}}{4\sigma_{T}U_{\rm
CMB}^{\prime}E_{e}^{\prime}}\simeq
10^{23}(1+z_{\gamma\gamma})^{-4}\left[\frac{E_{e}^{\prime}}{10\mbox{
TeV}}\right]^{-1}\mbox{ cm}$ (16)

The deflection angle of the $e^{+}e^{-}$ pairs, accumulated over the cooling
distance, depends on the correlation length of the magnetic field,
$\lambda_{B}$. Note also that electrons and positrons travel much shorter
distances than primary photons.

The $e^{+}e^{-}$ pairs produced in interactions of multi-TeV $\gamma$-rays
with EBL photons produce secondary $\gamma$-rays via IC scattering of the
Cosmic Microwave Background (CMB) photons. Typical energies of the IC photons
reaching the Earth are

$E_{\gamma}=\frac{4}{3}(1+z_{\gamma\gamma})^{-1}\epsilon_{CMB}^{\prime}\frac{E_{e}^{\prime
2}}{m_{e}^{2}}\simeq 0.32\left[\frac{E^{\prime}_{\gamma_{0}}}{20\mbox{
TeV}}\right]^{2}\mbox{ TeV}$ (17)

where $\epsilon_{CMB}^{\prime}=6\times 10^{-4}(1+z_{\gamma\gamma})$ eV is the
typical energy of CMB photons. In the above equation we have assumed that the
energy of a primary $\gamma$-ray is $E^{\prime}_{\gamma_{0}}\simeq
2E_{e}^{\prime}$ with $E_{\gamma_{0}}^{\prime}$ being the energy of the
primary $\gamma$-rays at the redshift of the pair production. Upscattering of
the infrared/optical background photons gives a sub-dominant contribution to
the IC scattering spectrum because the energy density of CMB is much higher
than the density of the infrared/optical background.

Deflections of $e^{+}e^{-}$ pairs produced by the $\gamma$-rays, which were
initially emitted slightly away from the observer, could lead to ‘redirection’
of the secondary cascade photons toward the observer. This effect leads to the
appearance of two potentially observable effects: extended emission around an
initially point source of $\gamma$-rays [26, 27, 28] and delayed ‘echo’ of
$\gamma$-ray flares of extragalactic sources [29, 30].

Figure 28:  Model predictions and estimates for the EGMF strength. Cyan shaded
region excluded by present day measurements. Black ellipses show measurements
of the field in the Galaxy and galaxy clusters. Left panel: left and right
hatched regions show theoretically allowed range of values of
($\lambda_{B}$,B) for non-helical and helical fields generated at the epoch of
electroweak phase transition during radiation-dominated era. Middle panel:
left and right hatched region show ranges of possible ($\lambda_{B}$,B) for
non-helical and helical magnetic fields produced during the QCD phase
transition. Right panel: hatched region is the range of possible
($\lambda_{B}$,B) for EGMF generated during recombination epoch. Dark grey
shaded region shows the range of ($\lambda_{B}$,B) parameter space accessible
for the $\gamma$-ray measurements via $\gamma$-ray observations [31].

The above processes are illustrated in Fig. 27. Electron deflection $\delta$
depends on the magnetic field in the region of deflection. Note, that, in
principle, EGMF depends on the redshift, $B^{\prime}=B^{\prime}(z)$. In the
simplest case, when the magnetic field strength changes only as a result of
expansion of the Universe, $B^{\prime}(z)\sim B_{0}(1+z)^{2}$, where $B_{0}$
is the present epoch EGMF strength. This gives

$\displaystyle\delta$ $\displaystyle=$ $\displaystyle\frac{D_{e}}{R_{L}}\simeq
3\times 10^{-6}(1+z_{\gamma\gamma})^{-4}\left[\frac{B^{\prime}}{10^{-18}\mbox{
G}}\right]\left[\frac{E_{e}^{\prime}}{10\mbox{ TeV}}\right]^{-2}$ (18)
$\displaystyle\simeq$ $\displaystyle 3\times
10^{-6}(1+z_{\gamma\gamma})^{-2}\left[\frac{B_{0}}{10^{-18}\mbox{
G}}\right]\left[\frac{E_{e}^{\prime}}{10\mbox{ TeV}}\right]^{-2}$

Knowing the deflection angle of electrons, one can readily find the angular
extension of the secondary IC emission from the $e^{+}e^{-}$ pairs

$\Theta_{\rm
ext}\simeq\left\\{\begin{array}[]{ll}0.5^{\circ}(1+z)^{-2}\left[\frac{\tau_{\theta}}{10}\right]^{-1}&\\\
\left[\frac{\displaystyle E_{\gamma}}{\displaystyle 0.1\mbox{
TeV}}\right]^{-1}\left[\displaystyle\frac{B_{0}}{\displaystyle 10^{-14}\mbox{
G}}\right],&\lambda_{B}^{\prime}\gg D_{e}\\\ &\\\
0.07^{\circ}(1+z)^{-1/2}\left[\frac{\tau_{\theta}}{10}\right]^{-1}&\\\
\left[\frac{\displaystyle E_{\gamma}}{\displaystyle 0.1\mbox{
TeV}}\right]^{-3/4}\left[\frac{\displaystyle B_{0}}{\displaystyle
10^{-14}\mbox{ G}}\right]\left[\frac{\displaystyle\lambda_{B0}}{\displaystyle
1\mbox{ kpc}}\right]^{1/2},&\lambda_{B}^{\prime}\ll D_{e}\end{array}\right.$
(19)

This is a key point for detection of the field, since extended emission
depends on energy in a well-defined way and can be reconstructed using
independent measurements at different energies.

The possible ranges of the ($\lambda_{B}$,B) parameter space are shown in Fig.
28 for the cases when magnetogenesis proceeds during electroweak or QCD phase
transitions or at the moment of recombination.

It is interesting to note that predictions for the strength and correlation
length of the primordial magnetic fields fall in a region of ($\lambda_{B}$,B)
parameter space which is not accessible for the existing measurement
techniques, such as Faraday rotation or Zeeman splitting methods. However, it
turns out that this region of ($\lambda_{B}$,B) parameter space is accessible
for the measurement techniques which exploit the potential of the newly opened
field of very-high-energy (VHE) $\gamma$-ray astronomy [31].

###  0.2.4 Summary

Gamma-ray astronomy works, hundreds of sources have been detected in the GeV
energy range and about one hundred in TeV energies.

There are several major questions to be answered in the near future:

  * •

One needs to understand the hadronic component in a variety of astrophysical
sources.

  * •

Extragalactic IR/O backgrounds have already been constrained by observations
of TeV sources to factor two uncertainty. The next step is precision
determination of those backgrounds using measurements of many sources at
different redshifts.

  * •

For the first time one has a possibility to study primordial magnetic fields
through TeV gamma-ray measurements. We can test models of primordial magnetic
fields in the near future.

There are several other important issues which were not discussed in this
Lecture due to lack of time. The corresponding questions are:

  * •

Good measurements of blazar flairs can help to understand gravity near black
holes.

  * •

TeV gamma rays give one more constraint/signature on Dark Matter.

  * •

Constraints on exotic physics (LIV, etc.) will be improved.

##  0.3 High-energy neutrinos

###  0.3.1 Introduction

In this lecture we discuss theoretical predictions and experimental efforts to
detect Ultra-High Energy neutrinos. In Section 0.3.2 we discuss possible ways
to detect UHE neutrinos and their corresponding experiments. In Section 0.3.3
we show theoretical predictions for UHE neutrino fluxes and present the status
of experimental searches for such fluxes. In Section 0.3.4 we discuss another
possibility to detect Galactic neutrino sources at multi-TeV energies. In
Section 0.3.5 we summarize all the results of this lecture.

###  0.3.2 High-energy neutrino experiments

There are three types of ultra-high energy (UHE) neutrino experiments.

First, neutrinos can be detected by UHECR experiments. There are two
possibilities for this. First, one can use the fact that the atmosphere
horizontally has depth 36 times the vertical depth. Relatively young
electromagnetic horizontal showers can be caused by neutrinos only. Hadronic
showers at such a depth consist of muons only. Second, one can look for events
penetrating the Earth in the tau-neutrino channel, i.e., look for upward-going
events. This was used by the Auger experiment (see Fig. 7). The resulting
limit on neutrino flux is shown in Fig. 31. Also less significant limits were
presented by previous UHECR experiments including Fly’s Eye, AGASA, and HiRes
(the HiRes limit is also shown in Fig. 31).

Figure 29:  IceCube detector. Left: Configuration of the IceCube detector.
Eighty strings will be located at a depth of 1.5 km in the Antarctic ice
filling a volume of one cubic kilometre. The present construction stage is
also shown [32]. Right: Simulation of a high-energy neutrino event in the
IceCube detector [33].

Second, one can detect neutrinos in the water or in the ice by detecting
Cherenkov light created by corresponding leptons after neutrino interaction in
the medium. There are two important backgrounds for such measurement. First,
secondary leptons, mostly muons, should not be confused with secondary muons
from extensive air showers in the atmosphere. In order to reduce the
background of atmospheric muons one has to put the detector at a depth greater
than one kilometre from the surface. Second, there are atmospheric neutrinos
created by the same cosmic rays, which would produce isotropy in the space
energy-dependent background. In order to fight this background, one either has
to go to high energies $E>10^{15-16}$ eV, where it is small, or look for point
sources on top of this background.

Experiments that worked with these techniques in the past were Baikal and
ANTARES in water and AMANDA in ice. All those experiments had a volume $0.1$
km3 or less. The new-generation experiment IceCube with a volume of 1 km3 is
in the construction stage at the moment. In Fig. 29 in the left panel one can
see the configuration of this experiment, which consists of 80 strings,
filling a cubic kilometre volume in the Antarctic ice at a depth of 1.5 km
from the surface. Strings already implemented are shaded blue on top of the
picture (see Ref. [32] for more details). Also, as shown in the figure the top
of the detector is covered by an array of ice tanks (ice top). In the right
panel one can see a Monte Carlo simulation of a high-energy neutrino event,
detected by the IceCube experiment. First results of this experiment will be
discussed in Section 0.3.4.

Figure 30:  ANtarctic Impulsive Transient Array (ANITA) radio balloon
experiment. Array of radio antennas flying in the ballon, as shown on the left
panel. It flies in circles over the Antarctic ice at a height of 37 km (see
right panel) and looks for radio signals which UHE neutrinos create in the
ice.

Finally, radio neutrino experiments exploit the Askaryan effect in which
strong coherent radio emission arises from electromagnetic showers in any
dielectric medium. High-energy neutrinos trigger a cascade of electromagnetic
particles in the medium, which has net charge and can emit an analogue of
Cherenkov light in the radio energy range. The main point of this effect is
that the length of the radio wave is macroscopic (tens of centimetres) and is
bigger than the size of the cascade itself. This in turn means that all
electrons in the cascade emit coherently. The effect was first observed in
2000 at SLAC. Recently the Askaryan effect has been clearly confirmed and
characterized for ice as the medium, as part of the pre-flight calibration of
the ANITA-1 payload. The Askaryan effect can be seen only at high energies
$E>10^{17-18}$ eV. Experiments using this effect benefit from the absence of
atmospheric neutrino flux at such high energies, but they also have to look
over a huge effective volume in order to see tiny neutrino fluxes at highest
energies.

Experiments that used this effect to search for UHE neutrinos are FORTE [34],
RICE [35], and ANITA [36, 37]. FORTE is a satellite experiment, which, in
particular, looked over the Greenland ice. Unfortunately, the threshold of
this experiment was very high, $E_{\nu}>10^{22}$ eV, so it could test only
exotic top-down models. RICE was an array of radio antennas located in the ice
at the South Pole at the same place as the AMANDA experiment. This experiment
presented its final results in 2006. Finally, the most advanced for the moment
of this kind of experiment is the ANtarctic Impulsive Transient Array (ANITA)
radio balloon experiment, see Fig. 30. In the left panel one can see an array
of radio antennas in the balloon. In the right panel one can see a schematic
map of flight over the Antarctic at a height of 37 km.

###  0.3.3 Search for cosmogenic neutrinos

Figure 31:  Predictions of cosmogenic neutrino fluxes and theoretical bounds
on them [39, 40]

As discussed in Section 0.1.3 UHECR protons lose their energy in interactions
with CMB photons and produce pions at energies above threshold $E>6\cdot
10^{19}$ eV. This GZK threshold was found in 1966 [10]. As long ago as 1969
Berezinsky and Zatsepin suggested that one can try to observe secondary
neutrinos from pion decays and called them cosmogenic neutrinos [38]. Recently
the ANITA Collaboration proposed to call such neutrinos Berezinsky–Zatsepin
neutrinos, or BZ neutrinos [37]. Below we follow this suggestion.

One can calculate the flux of BZ neutrinos theoretically, after fitting the
corresponding proton spectrum to the experimental flux above some energy. The
absolute limit for neutrino flux comes from the fact that gamma rays
unavoidably produced from $\pi^{0}$ decays and from electrons $\pi^{\pm}$
decays cascade down to GeV energies and the maximum flux of such gamma rays
cannot overshoot the EGRET measuremen shown in Fig. 16. This bound on the BZ
neutrino flux is called “gamma-ray bound” in Fig. 31. Note that there are many
additional ways to create photons in the EGRET energy range, including
electron–positron pair production discussed in the previous section, so the
real BZ neutrino flux is always lower than this region.

Figure 32:  Experimental limits on cosmogenic neutrino flux. Best up-to-date
ANITA-1 limits based on no surviving candidates for 18 days of live time shown
as ANITA-2008 [37]. Also limits from Auger [41], HiRes [42], FORTE [34], Anita
prototype ANITAlite [36], RICE [35], and AMANDA II [43] are shown.

Also in Fig. 31 we plot two theoretical limits derived under a set of
theoretical assumptions. One is called the Waxman–Bahcall (WB) bound and the
other the MPR bound. On the same figure we show several examples of
theoretical neutrino fluxes which violate both WB and MPR bounds, but all of
them are consistent with the experimental gamma-ray bound.

In Fig. 32 we show present-day experimental bounds confronting theoretical
predictions for BZ neutrinos from Ref. [37]. One can see that the best up-to-
date experimental bounds come from the ANITA experiment. ANITA-1 was able to
view a volume of ice of $\sim 1.6$ Mkm3 during 17.3 days, however, volumetric
acceptance to a diffuse neutrino flux, accounting for the small solid angle of
acceptance for any given volume element, is several hundred km3 water-
equivalent steradians at $E_{\nu}=10^{19}$ eV. This allowed them for the first
time a tough theoretically interesting region, excluding part of the parameter
space with highest neutrino fluxes.

On the same figure one can see existing limits on diffuse neutrino flux from
the Auger [41], HiRes [42], FORTE [34], Anita prototype ANITAlite [36], RICE
[35], and AMANDA II [43] experiments.

Let us note also that in Fig. 32 the composition is assumed to be proton-
dominated. If recent Auger results presented in Fig. 9 are confirmed,
theoretical expectations for neutrino flux in Fig. 32 will be strongly
reduced. This will make observations of the diffused flux of UHE neutrinos an
even more complicated issue. However, at lower energies one still can have a
hope of seeing point sources with neutrinos, as will be discussed in the next
section.

###  0.3.4 Point sources of UHE neutrinos

Figure 33:  Neutrino–nucleon cross-section as a function of the neutrino
energy. Charge-current and neutral-current contributions to the cross-section
are shown with thin solid and dashed lines. The total cross-section is
presented by a thick solid line. See Ref. [44] for details.

At highest energies the neutrino flux is too low to detect one single source
of neutrinos, but at lower energies $E<1000$ TeV the flux from a single source
can be high enough to detect it. Indeed, in Fig. 33 the neutrino–nucleon
cross-section is shown as a function of energy. This cross-section is
proportional to $E$ at low energies $E<1$ TeV and to $E^{0.4}$ at high
energies $E>10^{6}$ GeV. Good candidates for neutrino sources in the Galaxy
are objects emitting TeV gamma rays. They can produce neutrinos in the
proton–proton collisions in objects in the case of binary systems and in the
interaction with molecular clouds in the Galaxy. In the 10 TeV energy range

$\sigma_{p\nu}(10\textrm{ TeV})=10^{-34}\leavevmode\nobreak\
\mbox{cm}^{2}\leavevmode\nobreak\ .$ (20)

In the IceCube detector only a small fraction of neutrinos will produce a
signal:

$\tau_{\nu}=\sigma_{p\nu}n_{ICE}R\sim\leavevmode\nobreak\
10^{-5}\leavevmode\nobreak\ ,$ (21)

where $n_{ICE}\sim 10^{24}/\mbox{cm}^{3}$ is the density of the ice and $R=1$
km is the height of the IceCube detector.

The expected flux of neutrinos produced in the proton–proton collisions in the
Galactic sources is

$F_{\nu}\sim F_{\gamma}=10^{-12}\frac{1}{\mbox{cm}^{2}\mbox{s}}\approx 3\cdot
10^{5}\frac{1}{\mbox{km}^{2}\mbox{yr}}\leavevmode\nobreak\ .$ (22)

Thus in the IceCube detector one can expect three events per year for a $10$
TeV neutrino flux.

Figure 34:  Left: Simulated detection of Milagro TeV galactic sources by
IceCube. Right: Significance of Milagro hotspots after five years of
observation of IceCube.

In Fig. 34 one can see a simulation of Milagro sources from Fig. 26 after five
years of working of the IceCube detector.

Figure 35:  Equatorial sky-map of events (points) and pre-trial significances
(p-value) of the all-sky point source search in the 22-string IceCube detector
[45]. The solid curve is the galactic plane. The most significant spot arrives
in a random sky with probability $P\sim 1\%$.

We now present recent results for point-source searches using data recorded
during 2007–08 with 22 strings of IceCube (1/4 of the detector). An all-sky
search within the declination range $-5^{\circ}$ to $+85^{\circ}$ found the
most significant deviation from the background at $153.4^{\circ}$ r.a.,
$11.4^{\circ}$ dec. Accounting for all trials in the point-source search, the
final p-value for this result is 1.34%, consistent with the null hypothesis of
background-only events at the 2.2$\sigma$ level. No obvious source candidates
are near this location, and an analysis of the timing of the events did not
find any evidence of a burst in time. The location can be added to the a
priori source candidate list for analysis using future IceCube data, in which
case a similar excess would be identified with much higher significance [45].

###  0.3.5 Summary

IceCube is half-complete. If it observes first sources, a new field of
astroparticle physics will be started: neutrino astrophysics. If not, much
bigger detectors are needed with a size of at least 10 km3. Secondary neutrino
flux from UHECR protons can be detected by future radio experiments, like
ANITA. Neutrinos from some bright galactic sources can be detected by IceCube.
Extragalactic sources can be observed during bright flair activity. In order
to detect continuous flux from sources like Cen A one needs detectors much
larger than 1 km3. Galactic SN can be detected with neutrinos at low and high
energies. Cubic-kilometre water detectors will be constructed if IceCube gives
positive results.

### Acknowledgements

I would like to thank the Organizing Committee of the 5th CERN Latin American
School for giving me the opportunity to present lectures there and for the
excellent organization of the School.

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