# High-energy cosmic particles

Silvia Mollerach

###### Abstract

A review of the status of the knowledge in the field of High-energy cosmic
particles is presented. The spectrum, arrival direction distribution and
composition measurements are summarized, to- gether with some implications for
the understanding of the cosmic ray origin and their propagation. Special
emphasis is put in the ultra-high energy range, corresponding to particles of
extragalactic origin.

##  1 Introduction

High energy cosmic rays (CR) are particles that arrive from space with a wide
range of energies from $10^{9}$ eV to $10^{20}$ eV. The overall spectrum falls
approximately as $E^{-3}$, as shown in Figure 1. The main spectral features
are a steepening at few PeV, called the knee, and a softening at few EeV (1
EeV $=10^{18}$ eV), called the ankle. There is also a strong steepening close
to $10^{20}$ eV. Up to $\sim$ TeV energies it is possible to detect directly
the particles from space using satellites, balloons and detectors in the
International Space Station, and precise determinations of the particle mass
and charge are possible. At higher energies, the flux of particles is very low
and CRs can only be detected indirectly through the air showers of secondary
particles that they develop by interactions in the atmosphere.

Figure 1: Energy flux ($E^{2}d\Phi/dE$) of cosmic particles as measured by
different experiments. The total spectrum, as well as those of different
components, are included (courtesy of C. Evoli [1]).

The lower energy particles come from sources within our Galaxy, while at the
highest energies they are of extragalactic origin. It is still not known at
which energy happens the transition from Galactic to extragalactic CR origin.

The main open questions that we would like to answer are where and how these
cosmic particles have been accelerated and how they propagated to the Earth.
We have to take into account that during their propagation the particles can
interact with the radiation and matter present along their way and be
deflected by the magnetic fields. Thus, the energy, arrival direction, and
sometimes even the mass of the particles can be changed.

##  2 Galactic Cosmic Rays

The standard scenario for Galactic CRs is that they are accelerated in shock
waves in Supernova explosions and then propagate diffusively in the
interstellar medium. Evidence for this comes from the diffuse $\gamma$-ray
emission at GeV energies from the Galactic disk observed by Fermi LAT. This
can be explained as the result of the decay of neutral pions produced in CR
interactions with gas in the disk,
$p+gas\rightarrow\pi^{0}\rightarrow\gamma\gamma$. Moreover, several supernova
remnants, such as IC433 and W44, show $\gamma$-ray emission from their
surroundings with the characteristic spectral shape of the $\pi^{0}$ decay,
that is evidence of hadrons being accelerated to CR energies in the supernova
remnant shocks [2].

Galactic supernova remnants can provide enough energy to account for the
observed CRs if $10\%$ of the kinetic energy of the explosion goes into
accelerating CRs. Moreover, the diffusive shock acceleration mechanism
predicts a spectrum for the accelerated particles close to a power-law,
$\propto E^{-\alpha}$ with $\alpha\simeq 2$–2.4, that after taking into
account the effects of a diffusive propagation in the Galactic magnetic field,
is close to the observed one.

The particles being accelerated are taken from the interstellar medium (ISM),
so it is expected that CRs have a similar abundance of elements as the ISM.
This is actually the case except for few nuclei: Li, Be, B, F and the Sc-Mn
group, that are secondary particles produced by spallation of primary
particles colliding with matter in the Galactic disk. By studying the
abundances of these secondary particles relative to the primary ones, as for
example the B/C ratio, it is possible to study how was the propagation of the
particles inside the Galaxy. It is found that particles spend a long time
wandering around the Galaxy, propagating diffusively. Moreover, by studying
the B/C ratio dependence with the rigidity of the particles ($\sim E/Z$ in the
relativistic limit, with $Z$ the charge), it can be seen that the magnetic
field turbulence is compatible with the Kolmogorov one [3].

We have seen in this conference many detailed measurements by the AMS
Collaboration of the spectrum of individual elements (and even isotopes),
$e^{+}$ and $e^{-}$, that gave an impressive input to the field of Galactic
CRs. Explaining the observed spectral features led to a lively interplay
between experiments and theories, from detailed modelling of the diffusion
processes, investigating the need of new astrophysical sources and possible
signals of dark matter [4]. These direct measurements of the spectrum of
individual nuclei are possible only up to 100 MeV - 1 TeV, depending on the
nucleus. At higher energies, to study for example the end of the Galactic CR
spectrum and the extragalactic CRs, we have to resort to indirect measurements
that cannot make this individual measurements of the identity of the
particles, and nuclei can only be grouped in broad ranges of masses. The
results of KASCADE-Grande [5] show that the light component of the CRs has a
steepening in its spectrum at energies close to the knee, while the heavy
component has a steepening at around $10^{17}$ eV, where there is another
feature of the spectrum that is called the second knee. These measurements can
be interpreted as related to the end of the Galactic CR spectrum: the light
component starts fading at the knee energy, while the heavy component starts
fading at the second knee one, suggesting that the underlying cause for this
steepening is related to the CR rigidities.

##  3 Indirect Cosmic Ray measurements

Cosmic rays of higher energy are detected through the air showers that they
produce in the atmosphere. They can be measured using an array of detectors
that sample the particles reaching the ground. The largest observatory in
operation is the Pierre Auger Observatory located in the Province of Mendoza
(Argentina). The array is composed of 1660 water-Cherenkov detectors in a 1.5
km triangular grid, covering $3000$ km2. It is overlooked by 27 fluorescence
detectors in four sites around the perimeter of the array. The largest
observatory in the Northern hemisphere is the Telescope Array in Utah, USA,
composed of 507 scintillators in a 1.2 km square grid, covering 700 km2 and
overlooked by 36 fluorescence detectors. The fluorescence detectors measure
the UV fluorescence light from nitrogen molecules excited by particles in the
extensive air shower, leading to a glow along their path in the atmosphere.
Hybrid detectors work in the following way: in moonless nights, when the
fluorescence detectors can be operated (with a duty cycle of $\sim 15\%$) the
amount of deposited energy is measured as a function of the atmospheric depth,
and by integrating it a calorimetric determination of the total energy
deposited by the shower is obtained, from which the energy of the original
particle can be estimated. The telescopes also measure the atmospheric depth
at which the shower reaches its maximum development, which is a useful
indicator of the mass composition of the incident particle. On the other hand,
the array of surface detectors sample with nearly 100$\%$ duty cycle the
particles reaching the ground at different distances from the shower core.
This allows one to reconstruct the CR arrival direction and to estimate the
signal expected at a reference distance, that for the Pierre Auger Observatory
is chosen as 1000 m from the shower core. This provides a good estimator for
the energy of the incident particle, which can be calibrated with that
measured by the fluorescence detectors for the fraction of the events measured
by both detectors.

##  4 Spectrum and composition of ultra-high energy cosmic rays

The measured spectrum by the Pierre auger Observatory is shown in Figure 2.
The second knee at 0.15 EeV, presumably due to the fading of the heavy mass
galactic component, is clearly seen. At higher energies, the ankle hardening
appears at 6.2 EeV, followed by a recently measured steeping at 12 EeV, before
the very strong steepening observed at 50 EeV.

Figure 2: Spectrum of cosmic rays measured by the Pierre Auger Observatory,
combining the results from the different detectors and analyses [6]

The most widely used mass composition indicator for extensive air showers is
the amount of atmosphere traversed up to the shower maximum, $X_{\rm max}$.
Showers initiated by heavy nuclei develop higher in the atmosphere, and have
smaller fluctuations than proton initiated ones. This can be understood by the
superposition of smaller showers initiated by the nucleons. Figure 3 shows the
expectations for p and Fe primaries for different hadronic interaction models
together with the measurements by the Pierre Auger Observatory for the mean
value of $X_{\rm max}$ (left panel) and its dispersion (right panel). The data
indicate that the composition becomes lighter for increasing energies up to 2
EeV, and then becomes heavier above this energy.

Figure 3: Measurements of the mean atmospheric depth of the shower maximum
$X_{\rm max}$ and its dispersion from the Pierre auger Observatory [7]. The
expectations for p and Fe primaries for different hadronic interactions models
are also displayed.

When we want to make contact between the spectrum and the composition of
cosmic rays measured at the Earth and those of the accelerated particles at
the sources, we have to take into account that CRs interact with the radiation
backgrounds in their way, what makes them lose energy and even change
composition. The main relevant processes are pair production,
photodisintegration of nuclei and photo-pion production. For example, at
$10^{20}$ eV a proton or an Fe nucleus needs to come from distances closer
than $\sim 75$ Mpc, and nuclei with intermediate masses from even closer
distances.

If we try to interpret the observed spectrum and composition with a simple
model of uniformly distributed sources in which different elements are
accelerated with a spectrum dependent on the rigidity of the particles, the
Pierre Auger Observatory results favour a scenario with mixed composition at
the sources, with a very hard spectrum and a rather low rigidity cutoff
$R_{cut}=E_{cut}/Z\simeq 5$ EeV. As shown in Figure 4, increasingly heavier
elements dominate the spectrum with increasing energies [8, 9]. In this kind
of scenario, the final steepening of the spectrum results from a combination
of propagation effects and the maximum rigidity of the acceleration at the
sources.

Figure 4: Fit to the cosmic ray spectrum and composition measurements above
the ankle (solid brown lines) by the Pierre Auger Collaboration. In the left
panel the contribution of the different mass groups (with the color code of
the right panels) are displayed [9]

Let us notice that in the scenario described above to explain the spectrum and
composition at the highest energies, this high energy component cannot give
the dominant contribution to the spectrum at energies slightly below the
ankle. Recalling that the Galactic component was fading above $10^{17}$ eV,
there is a gap between the two contributions, so that there is probably the
need for a new extragalactic component in the middle. Thus, it appears that
two different extragalactic source populations would be required to be able to
explain the full CR spectrum.

##  5 Hadronic interactions in air showers

We have already mentioned the electromagnetic part of the air showers, that is
manly produced by the decays of neutral pions and that is the one measured by
the fluorescence detectors, and also contributes to the signals measured in
the surface detectors. There is also a muonic part of the air showers, that
comes mainly from the decays of charged pions. The muonic component contains a
subdominant fraction of the shower energy, but it can give useful information
about the primary particle mass composition [12]. Higher mass primaries
produce showers with more muons than lighter ones. A good theoretical model
for the development of air showers should be able to describe consistently
both the electromagnetic and the muonic parts of the showers. Muons are
measured at the Pierre Auger Observatory by an array of underground
scinitillator detectors covering a small part of the surface array, that work
in the energy range around $10^{18}$ eV. They can also be studied with the
water-Cherenkov detectors by looking at the very inclined showers in which the
electromagnetic part has been absorbed in the atmosphere, best suited in the
energy range around $10^{19}$ eV.

Figure 5: The upper panels show the muon density estimators for the
underground muon detectors (left) [10] and for the inclined showers from the
water-Cherenkov measurements as a function of the energy (right) [11]. Lines
corresponds to expectations for two different hadronic interaction models and
points are the data. The lower panels show, for two different energies, the
expected muon density estimator and mean $X_{max}$ for different composition
and hadronic models (lines) and the measurements from the Pierre Auger
Observatory.

The upper panels of Figure 5 show the expectations for the muon number
estimators in the underground muon detectors (left) and for the inclined
showers (right) [11], for proton and Fe showers and for different hadronic
interaction models. Also shown are the data points, that turn out to be
slightly above the expectations even for Fe composition. Moreover, when we
combine the $X_{\rm max}$ measurement with the muon measurements for the same
energy bin, as shown in the lower panels for two energies, it is clear that
none of the hadronic interactions models can consistently explain the
observations for any composition [12].

Monte Carlo simulations of extensive air showers, considering the mass
composition inferred from the $X_{\rm max}$ measurements, predict a muon
density at ground smaller than the observed one. There is a 30–50 $\%$ lack of
muons in the simulations. This is an indication that some modification in the
hadronic interaction models would be required .

##  6 Arrival directions distribution

The Pierre Auger Observatory has measured a dipolar anisotropy with an
amplitude of $d=0.066^{+0.012}_{-0.009}$ in the arrival direction of CRs with
energies above 8 EeV, with a significance of 6$\sigma$ [13]. The direction
points to ($\alpha,\delta)=(98^{\circ},-25^{\circ})$, at $135^{\circ}$ from
the direction of the Galactic center, this is evidence of an extragalactic
origin. The left panel of Figure 6 shows the flux smoothed in an angular
window of $45^{\circ}$. The amplitude of the dipole is observed to be
increasing with energy, as can be seen in the right panel of Figure 6. This is
consistent with expectations, since higher energy particles travel more
rectilinearly. Telescope Array in the Northern hemisphere has recently
measured a modulation in right ascension of amplitude $r=0.033\pm 0.019$,
pointing to $\alpha=131^{\circ}\pm 33^{\circ}$ [14]. This amplitude
corresponds to an equatorial dipole component
$d_{\perp}=r/\langle\cos\delta\rangle\simeq 1.3~{}r\simeq 0.043\pm 0.025$,
that is consistent both with the the Pierre Auger Observatory results
($d_{\perp}=0.060\pm 0.010$) and with isotropic expectations within the
statistical uncertainties.

Figure 6: Flux of CRs with energies above 8 EeV smoothed in an angular scale
of $45^{\circ}$ (left panel) and amplitude of the dipolar component as a
function of energy (right panel) [13].

Regarding the large scale anisotropies at lower energies, we show in Figure 7
a compilation of the measurements by IceCube, KASCADE-Grande and the Pierre
Auger Observatory of the equatorial dipole component in the energy range from
1 PeV to 100 EeV. The amplitude increases from few $10^{-3}$ to about 10$\%$
in that energy range, and the phases show a change from being close to the RA
of the Galactic center at low energies to nearly the opposite direction at the
highest energies, suggesting a transition from anisotropies of Galactic origin
below $\sim 1$ EeV to extragalactic origin above few EeV.

Figure 7: Amplitude (left panel) and phase (right panel) of the equatorial
component of the dipole from different experiments [13].

At higher energies and smaller angular scales, a combined analysis of the
Pierre Auger Observatory and the Telescope Array data, allowing a full
coverage of the sky, shows two hot spots, as seen in Figure 8. Different
energy thresholds (40 EeV for Auger and 53.2 EeV for TA) were chosen to match
the measured integral fluxes in the common observed region of the sky, and
after scanning in 7 different angular window scales, the two most
statistically significant excesses appeared at an angular window of
$20^{\circ}$ around ($\alpha,\delta)=(192^{\circ},-50^{\circ})$, with 4.7
$\sigma$ pre-trial (2.2 $\sigma$ post-trial) and at an angular window of
$15^{\circ}$ around ($\alpha,\delta)=(142^{\circ},54^{\circ})$, with 4.2
$\sigma$ pre-trial (1.5 $\sigma$ post-trial), where the post-trial
significance accounts for the scan in angles and directions in the sky.

Figure 8: Significance of the flux excess in a joint analysis of the Pierre
Auger Observatory and Telescope Array data [15].

In summary, the arrival directions distribution of ultra-high energy cosmic
rays shows a significant dipole above 8 EeV, there are some hints of medium
scale anisotropies above 40 EeV and no evidence of small scale anisotropies.
This is probably due to the fact that the deflections in the intergalactic
magnetic field are significant, what is consistent with the transition to a
heavier composition at the highest energies. This fact makes it difficult to
identify the actual sources. There are several proposed source candidates that
meet the minimal conditions for being accelerator sites, like AGNs, starburst
galaxies, GRBs and magnetars, but the identification is difficult since the
arrival directions of CRs do not point to their sources due to the magnetic
deflections.

##  7 Multimessenger astronomy

One possibility to try to identify the sites of CR acceleration is to resort
to other neutral messengers, like neutrinos, photons and neutrons (see e.g.
[16]). Combined efforts in this direction are taking place, like the search
for high energy neutrinos in coincidence with the binary neutron star merger
GW170817 observed by Advanced LIGO and Virgo detectors in coincidence with a
short GRB [17] (detected by Fermi-GBM and INTEGRAL and followed by many
optical observatories around the globe). IceCube, Antares, the Pierre Auger
Observatory [18] and also Baikal [19] have looked for neutrinos in windows of
$\pm 500$ sec and in the subsequent 14 days time and found none, putting upper
limits to the flux of neutrinos from this source.

A very exciting recent result is the measurement of a high energy neutrino of
290 TeV detected by IceCube in coincidence with the direction of a rotating
supermassive black hole, the blazar TXS 0506+056 at a redshift of 0.33, that
was in an active flaring phase at that moment as measured by Fermi-LAT [20].
This is probably the first detection of an extragalactic cosmic ray
accelerator.

##  8 The Future

To end this very quick review let us point out that at this moment there are
improvements taking place in the largest CR observatories. The Pierre Auger
Observatory is implementing an upgrade, AugerPrime, with the installation of
plastic scintillators and radio antennas above all the water-Cherenkov
detectors, with the aim to improve the sensitivity to mass composition by
measuring the muonic and electromagnetic components of every shower [21]. The
Telescope Array is extending the area of the array (TAx4) to cover 3000 km2.
In this conference we also heard about the plans to observe fluorescence light
from space (POEMMA) [22] and to instrument huge surfaces with radio antennas
(GRAND) [23] that will boost the exposure at the highest energies in the next
decade.

In summary, there have been many advances in understanding high energy cosmic
particles. There are still many open questions and new projects being
developed and planned to answer them.

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