###### Abstract

The Cosmic Ray Extremely Distributed Observatory (CREDO) is a newly formed,
global collaboration dedicated to observing and studying cosmic rays (CR) and
cosmic ray ensembles (CRE): groups of a minimum of two CR with a common
primary interaction vertex or the same parent particle. The CREDO program
embraces testing known CR and CRE scenarios, and preparing to observe
unexpected physics, it is also suitable for multi-messenger and multi-mission
applications. Perfectly matched to CREDO capabilities, CRE could be formed
both within classical models (e.g. as products of photon-photon interactions),
and exotic scenarios (e.g. as results of decay of Super Heavy Dark Matter
particles). Their fronts might be significantly extended in space and time,
and they might include cosmic rays of energies spanning the whole cosmic ray
energy spectrum, with a footprint composed of at least two extensive air
showers with correlated arrival directions and arrival times. Since CRE are
mostly expected to be spread over large areas and, because of the expected
wide energy range of the contributing particles, CRE detection might only be
feasible when using available cosmic ray infrastructure collectively, i.e. as
a globally extended network of detectors. Thus, with this review article, the
CREDO Collaboration invites the astroparticle physics community to actively
join or to contribute to the research dedicated to CRE, and in particular to
share any cosmic ray data useful for the specific CRE detection strategies.

###### keywords:

cosmic rays; cosmic ray ensembles; extensive air showers; large scale cosmic
ray correlations; CREDO Collaboration

xx 1 5 Received: date; Accepted: date; Published: date Cosmic Ray Extremely
Distributed Observatory Piotr Homola1*, Dmitriy Beznosko2, Gopal Bhatta3,
Łukasz Bibrzycki4, Michalina Borczyńska5, Łukasz Bratek6, Nikolai Budnev7,
Dariusz Burakowski8, David E. Alvarez-Castillo1,9, Kevin Almeida Cheminant1,
Aleksander Ćwikła10, Punsiri Dam-o11, Niraj Dhital12, Alan R. Duffy13, Piotr
Głownia6, Krzysztof Gorzkiewicz1, Dariusz Góra1, Alok C. Gupta14, Zuzana
Hlávková15, Martin Homola15, Joanna Jałocha6, Robert Kamiński1, Michał
Karbowiak16, Marcin Kasztelan17, Renata Kierepko1, Marek Knap8, Péter
Kovács18, Szymon Kuliński5, Bartosz Łozowski19, Marek Magryś20, Mikhail V.
Medvedev21,22, Justyna Mędrala23, Jerzy W. Mietelski1, Justyna Miszczyk1,
Alona Mozgova24, Antonio Napolitano25, Vahab Nazari1,9, Y. Jack Ng26, Michał
Niedźwiecki10, Cristina Oancea27,28, Bogusław Ogan8, Gabriela Opiła23,
Krzysztof Oziomek20, Maciej Pawlik20,23, Marcin Piekarczyk4, Bożena
Poncyljusz5, Jerzy Pryga29, Matías Rosas30, Krzysztof Rzecki23, Jilberto
Zamora-Saa31, Katarzyna Smelcerz10, Karel Smolek32, Weronika Stanek23,
Jarosław Stasielak1, Sławomir Stuglik1, Jolanta Sulma33, Oleksandr Sushchov1,
Manana Svanidze34, Kyle Tam35, Arman Tursunov36, José M. Vaquero37, Tadeusz
Wibig${}^{16}\orcidY{}$, Krzysztof W. Woźniak1 Piotr Homola, Dmitriy Beznosko,
Gopal Bhatta, Łukasz Bibrzycki, Michalina Borczyńska, Łukasz Bratek, Nikolai
Budnev, Dariusz Burakowski, David E. Alvarez-Castillo, Kevin Almeida
Cheminant, Aleksander Ćwikła, Punsiri Dam-o, Niraj Dhital, Alan R. Duffy,
Piotr Głownia, Krzysztof Gorzkiewicz, Dariusz Góra, Alok C. Gupta, Zuzana
Hlávková, Martin Homola, Joanna Jałocha, Robert Kamiński, Michał Karbowiak,
Marcin Kasztelan, Renata Kierepko, Marek Knap, Péter Kovács, Szymon Kuliński,
Bartosz Łozowski, Marek Magryś, Mikhail V. Medvedev, Justyna Mędrala, Jerzy W.
Mietelski, Justyna Miszczyk, Alona Mozgova, Antonio Napolitano, Vahab Nazari,
Y. Jack Ng, Michał Niedźwiecki, Cristina Oancea, Bogusław Ogan, Gabriela
Opiła, Krzysztof Oziomek, Maciej Pawlik, Marcin Piekarczyk, Bożena Poncyliusz,
Jerzy Pryga, Matías Rosas, Krzysztof Rzecki, Jilberto Zamora-Saa, Katarzyna
Smelcerz, Karel Smolek, Weronika Stanek, Jarosław Stasielak, Sławomir Stuglik,
Jolanta Sulma, Oleksandr Sushchov, Manana Svanidze, Kyle Tam, Arman Tursunov,
José M. Vaquero, Tadeusz Wibig, Krzysztof W. Woźniak Correspondence:
<EMAIL_ADDRESS>Tel.: +48-12-662-8341

## Introduction

While state-of-the-art cosmic ray research to date has been focused on the
detection and analysis of cosmic particles observed through individual
detectors or arrays, the correlated observations of cosmic rays on the global
scale remain insufficiently explored, yet no less promising. This
collaborative perspective could provide a deeper insight into the physical
processes within energy ranges rarely considered, including the highest
energies known. Here we discuss a general approach to research dedicated to
detecting and studying the astroparticle physics phenomena called Cosmic Ray
Ensembles (CRE) defined as groups of a minimum of two correlated, be it
spatially or temporally, cosmic rays with a common primary interaction vertex
or the same parent particle. Such particles, constituents of CRE, are
messengers of the primary physical processes – probes of the physics that
happened even billions of years ago, at energies even millions of times higher
than energies to which we can accelerate particles using man-made
infrastructure.

Figure 1: Cosmic-Ray Ensembles: a novelty in cosmic-ray research and in multi-
messenger astroparticle physics.

Armed with the particle physics background telling us that cosmic ray
particles are expected to interact with radiation and matter on their way
through the Cosmos and give birth to CRE, we ask not whether CRE exist, but
under which circumstances and with which conditions they can reach the Earth
and be detected with the available or possible infrastructure. As illustrated
in Fig. 1, the signatures of CRE might be spread over very large surfaces
which might make them hardly detectable by existing detector systems operating
individually. On the other hand, if these detector systems operate under a
planetary (and beyond) network, as proposed by The Cosmic-Ray Extremely
Distributed Observatory (CREDO) Homola and et al. (2018) (CREDO Collab.); Góra
and et al. (2018) (CREDO Collab.); Homola and et al. (2020) (CREDO Collab.),
the chances for detection of CRE will naturally increase. The components of
CRE might have energies that practically span the whole cosmic-ray energy
spectrum. Thus, all the cosmic ray detectors working in this range, beginning
from smartphones (e.g. DECO Vandenbroucke and et al (2016), CRAYFIS Whiteson
et al. (2016), CREDO Detector cre ; Bibrzycki and et al. (2020) (CREDO
Collab.); Niedzwiecki and et al. (2019) (CREDO Collab.), Cosmic Ray App cos )
and pocket size open-hardware scintillator detectors (e.g. Cosmic Watch Axani
et al. (2018); Schaub et al. (2018) or CosmicPi cos ), through numerous larger
educational detectors and arrays (e.g. HiSPARC Colle et al. (2007); Fokkema
(2012), QuarkNet Bardeen et al. (2018), Showers of Knowledge Bychkov and
Guskov (2012), CZELTA Smolek and et al. (2008)) to the professional
infrastructure that receives or will receive cosmic rays as a signal or as a
background Pierre Auger Observatory Pierre Auger Collaboration (2015),
Telescope Array Kawai and et al. (2008), JEM-EUSO Adams and et al. (2015a)
(JEM-EUSO Collab.); Adams and et al. (2015b) (JEM-EUSO Collab.), HAWC DeYoung
(2012), MAGIC Ferenc (2005), H.E.S.S. Vasileiadis and et al. (2005), VERITAS
Krennrich and et al. (2004); Park and et al. (2015), IceCube Aartsen and et
al. (2017) (IceCube Collab.), Baikal-GVD D and et al. (2016) (Baikal-GVD
Collab.), ANTARES Telescope Ageron and et al. (2011) (ANTARES Collab),
European Southern Observatory Franza and Wilson (1982), other astronomical
observatories, underground observatories, accelerator experiments in the off-
beam mode) could contribute to a common effort towards a hunt for CRE.
Therefore it is not only desirable, but also feasible to put the CRE research
into a routine implementation. So far, the experimental searches for cosmic-
ray correlations have been realized on different scales with arrays of
detectors located at schools and universities. However, all those efforts were
dedicated to very specific scenarios, concerning mostly fragmentation of
nuclei in background electromagnetic radiation fields Gerasimova and Zatsepin
(1960), which limits the number of particles in the group (ensemble) to just a
few. Some of these projects include e.g. CHICOS Carlson et al. (2005) in the
U.S., ALTA Pospıšil et al. (2009) in Canada, GELATICA (Svanidze et al., 2011)
in Georgia, EEE Abbrescia and et al (2016) in Italy, LAAS Ochi and et al
(2003); Matsumoto and et al (2019) in Japan, and the aforementioned CZELTA in
Czech Republic. Time correlation of registered showers was studied at
distances from 100 m to 7000 km, and in some cases evidence for unexpected
coincidences have been found. However, these were without any convincing
follow-up studies and data taking campaigns, which is hard without global
coordination. Only very recently the idea of looking for large scale
correlations in a general and global way took shape with the CREDO
Collaboration, formalized in September 2019 Collaboration . CREDO is meant to
be a multi-technique (different detector types) and doubly open (for both data
upload and offering access) infrastructure enabling global research programs
concerning radiation (both cosmic and terrestrial), with a number of multi-
messenger, multi-mission and transdisciplinary opportunities. With this review
article we invite the community to both benefit from the openness of CREDO and
to contribute to its program with the research dedicated to a general search
for ensembles of cosmic rays, especially photons of different energies. Since
the concept of CREDO assumes the openness for independent data streams, it is
expected that the projects mentioned above, as well as the other cosmic ray
infrastructure including private, widely spread detectors such as smartphones,
will have a direct interest in connecting to the global CREDO system, thus
reinforcing its scientific attractiveness, and chances of individual research
programs.

As this article is meant to serve as a review of the current status and
perspectives of CREDO and the research related to CRE, its structure follows
the scientific and logical roadmap to observing and studying cosmic ray
ensembles. We begin with a general description of the field in Section 1
“Foundations of the CREDO methodology” and 2 “CREDO within the cosmic ray
landscape”, and theoretical modeling of CRE sources in Section 3 “UHECR
sources and cosmic ray ensembles”. Then we present and discuss example CRE
scenarios with an emphasis on the simulations of propagation of the CRE
components through the Cosmos and within the Earth’s atmosphere (Section 4
“CRE simulations”), describe the status of the observational efforts (Sections
5 “CREDO detectors: cloud of clouds”, 6 “Data management and analysis”, and 7
“Building the scale: public engagement as a scientific need”), and conclude
the article with the outlook, summary and conclusion (Sections 8 and 9).

##  1 Foundations of the CREDO methodology

The CREDO experiment by its very idea of making discoveries and approaching
truth in various research areas, touches something one can call the borderline
of the current state of our knowledge. As explained below, there are reasons
to anticipate that the experiment has the potential to falsify some of the
adopted models. In the context of CREDO one can even ask questions about
science itself and its methodology.

As an example one can consider exotic QED processes which are potentially
within the observational scope of CREDO. Namely, pair creation or photon
splitting in strong magnetic fields. These predictions of QED can now be
tested in the context of cosmic rays physics under extreme astrophysical
conditions met in pulsar magnetospheres (with typical magnetic field strengths
of $10^{12}$ Gauss, or even $10^{14}$ Gauss in magnetars). In such conditions
there are several observational signatures of the two processes Usov (2002);
Harding and et al (1996). What is more, the photon splitting phenomenon (in
exotic scenarios) fits very well in the context of cosmic ray ensembles (CRE)
that are potentially within the observational scope of CREDO (as long as the
opening angle of the secondary photons would not be too large). Therefore, the
CREDO experiment opens up new opportunities to test the well-established QED
theory as well as consider more exotic scenarios. The experiment is
potentially capable of changing our view of the basis of science, specifically
by providing a new type of means to falsify generally accepted theories in an
energy range that has not been yet available for to date observatories. In
this way one arrives at the strictly philosophical question to be addressed
and that naturally arises in the context of CREDO – the issue of parsimony of
the scientific method or Occam’s razor.

It has been accepted that the scientific method of explaining and
understanding facts should follow the principle of not multiplying entities
without necessity. Explaining all new phenomena should be based on what one
has already had, namely, based on the theories and models that successfully
worked so far, and only if this attempt is found to have failed one may
consider rejecting these theories and models. Occasionally, the parsimony
principle, when understood in a fundamentalistic manner, would stand in the
way of knowledge. This kind of epistemological attitude might lead to
supplementing old models and theories with new “epicycles”, rather than
encouraging one to humbly admit that some of the assumptions being adopted so
far need to be rejected as inconsistent with reality. A solution to this state
of things is to presume that the parsimony principle, although an invaluable
component of the scientific method, is not something the scientific method
entirely stands on. Sometimes one has to bypass the strict rule (which in
practice is done by the majority of the scientific community). Accordingly, if
the CREDO experiment (or some other experiment) comes up with an anomalous
result, not falling within the framework of accepted models and theories,
first the possibility of an error should be considered, be it in the
measurement or interpretation side. However, one should also not be afraid of
pushing the limits and going beyond the realm of modern knowledge by extending
or redefining the adopted concepts as well as the language with which we
describe reality.

The CREDO initiative inspires one to deliberate on falsifiability, another
important element of the scientific method. It is often said that scientific
statements should be falsifiable – refutable by contradicting evidence. This
is not definitely true. For example, general statements about existence are
most often unfalsifiable, nevertheless they are easy to be verified
empirically, which makes the statements quite scientific. Even though science
is not entirely determined by falsifiability, this attribute is very
advantageous and often characterizes statements formulated by science, either
as models or scientific theories.

Classical electrodynamics provides a good example of a theory that is
falsifiable. For the purpose of illustration imagine that CREDO (or another
experiment of this kind) comes up with some evidence for spontaneous photon
splitting (to be in touch with the experimental scope of CREDO pointed out
earlier) – a phenomenon there is no place for in the linear Maxwell
electrodynamics. There are effective terms that could be incorporated to the
electromagnetic Lagrangian to mimic at the classical level such effects. To be
more specific, some QED vacuum polarization effects such as photon-photon
scattering or photon splitting in external fields can be effectively described
by classical theory (the Euler-Heisenberg Lagrangian is used in this context),
however, these nonlinear phenomena are merely interaction effects arising upon
quantization of linear Maxwell fields in accordance with methods of quantum
field theory, therefore already explainable within the current paradigm. The
real change in the electromagnetic theory required to incorporate new
phenomena such as spontaneous photon splitting that could occur in free space
and observed through cosmic ray ensemble evolution, would be to replace the
Maxwell Lagrangian by an alternative one resulting in nonlinear equations
before quantization, or maybe even to alter the quantization method as such.
Is that to mean that Maxwell’s electrodynamics would just be falsified by an
observation of a spontaneous photon splitting?

Stated clearly, it is not that simple – scientific theories are deeply
founded, routinely withstanding repeated attempts at falsification. In the
first place, one should try to explain a particular observational result
within the current theory. Only if such attempts turn out absolutely
unsuccessful and a growing number of anomalies are observed at the same time,
one would rather conclude that the theory has been falsified – though the old
theory will probably still survive as a good approximation (as this was the
case with Newtonian and relativistic mechanics). Thus, falsifying a theory is
not an easy task, at least not possible based merely on a single observation
or measurement. This being said, experiments such as CREDO appear even more
valuable, since both for the verification or falsification to be feasible, one
needs as many channels as possible through which the universe is looked at.

##  2 CREDO within the cosmic ray landscape

Although CRE detectable on or around the Earth can be initiated by particles
spanning a wide range of energies, and since it is not a priori evident
whether the chances of observing a CRE increase with the energy of the primary
particle, one should stay open-minded about possible focus concerning the
energy regimes of investigation. Here, for clarity, we chose to focus on the
cosmic rays of the highest energies known, $E$ > 1018 eV, hereafter referred
to as ultra-high energy cosmic rays (UHECR), capable of initiating CRE
composed of billions of component particles which can propagate unaffected
large astrophysical distances, as in case of GeV-TeV photons (see e.g. Risse
and Homola (2007)), of which an observable fraction may reach the human
technosphere.

The surprisingly constant, power-law character of the energy spectrum of
cosmic radiation observed by more than ten orders of magnitude with an almost
constant exponent of about (-3) could be, in principle, continued on without
any obstacles. At least until the mid-1960s there was no reason to expect any
definite end. Although the sources and mechanisms of acceleration of single
elementary particles to the energy of a dozen joules both then and now are
unknown (the search is still ongoing). Review of objects in the sky that would
potentially come into question, their spatial sizes ($L$) and magnetic fields
($B$) suggests that their capabilities ($E_{max}<ZeBL$) do not reach far
beyond the limit of 1020 eV. It should be remembered that any acceleration
mechanism by its nature would have to be of a statistical character and
therefore, when analysing the average or typical parameters of primary cosmic
ray particles, it is difficult to exclude the occurrence of large and
extremely large fluctuations Tsallis et al. (2003).

The situation changed substantially after the discovery of the cosmic
microwave background (CMB) radiation. If we assume that the primary particles
of cosmic radiation are protons, as Greisen Greisen (1966), Zatsepin and
Kuzmin Zatsepin and Kuzmin (1966) noticed immediately, a sudden end of the
spectrum must be caused by collisions of them with CMB photons and resonant
production of the $\Delta^{+}$ particle. $\Delta^{+}$ decays instantly again
into a nucleon, and its energy is on average about 20% less than before the
collision. This process occurs as long as the nucleons have enough energy,
which happens at about 5-6$\times 10^{19}$ eV. However, particles of cosmic
radiation do not have to be protons. Observations suggest (e.g. Wibig and
Wolfendale (2005)), that heavier nuclei with a higher charge ($Ze$), thus
easier to be accelerated, may entirely dominate the highest energy cosmic
radiation flux. For nuclei with energies of about 1020 eV, when energies are
calculated separately for each nucleon, the GZK mechanism does not work, but
this does not mean that the Universe for them remains transparent. In the
centre of mass system, when colliding with photons of intergalactic radiation
(infrared mostly) they excite to a giant dipole resonance, and then fragment,
most preferably emitting few neutrons. Although fragments retain the same
energy per nucleon, as a whole they have correspondingly reduced their total
energy.

Searching for the end of the cosmic radiation spectrum, according to what has
been just said, could lead to solving the problem of mass composition of
cosmic radiation of the highest energy, and thus bring us closer to
identifying its sources (and acceleration mechanisms). However, it
unfortunately happens that both the GZK cut-off and the photodisintegration of
the nuclei start to work effectively in a similar range of energy, just where
today’s observations of cosmic radiation end because of the scarce cosmic ray
flux. In addition to the statistics, another circumstance is that two giant
experiments in operation today which statistically dominate the measurements
of giant showers in the highest energy range: the Pierre Auger Observatory in
Argentina and the Telescope Array in Utah, US, while claiming a general
agreement of the energy spectra within experimental uncertainties up to 10
EeV, they admit the need for non-linearity to bring the spectra in agreement
at the higher energies, and within the range of common declinations. However,
the sources of this non-linearity have not been identified, yet Deligny
(2020). It turns out, then, that the current status of the UHECR observations
does not allow definite conclusions about the exact location and nature of the
observed cut-off of the energy spectrum, implying the uncertainty about the
cosmic ray composition at the highest energies known.

Either way, the results of the leading UHECR observatories and their
conclusions from widely quoted publications (Abbasi and et al. (2008) (HiRes
Collaboration); Abbasi and et al (2014); Abraham and et al. (2008) (Pierre
Auger Collaboration); Valino (2016)) indicate that the spectrum of cosmic
radiation is significantly suppressed at the highest energies, although it is
not known at which energy, and whether this energy depends e.g. on the kind of
the sources. Such a picture is widely accepted and despite minor scratches,
small inconsistencies and doubts it seems that we understand it. There
shouldn’t be many particles above the cut-off and in fact this is the case.
However, among the aforementioned minor doubts, there are still recorded in
the last century in several (or actually almost all) large and significant
giant air shower experiments, the cases initiated by particles with estimated
energies exceeding $10^{20}$ eV.

The first, historical, Volcano Ranch event was recorded by Linsley in 1962
with the energy of $10^{20}$ eV, Linsley (1963). In the 1980s the Haverah Park
experiment reported a significant increase in the number of showers with
energies exceeding $\sim 10^{20}$ eV Cunningham et al. (1980); Watson (1991);
Lawrence et al. (1991) . In the Yakutsk array, the record energy was rated at
$1.5\times 10^{20}$ eV Afanasiev and et al (1995). The Japanese AGASA
experiment published the event from December 3, 1993 which had an energy of
$2\times 10^{20}$ eV Teshima and el al (2000). However, a world record was set
in the USA in the Fly’s Eye experiment: $3.2\times 10^{20}$ eV Bird and et al
(1995). These cases have not been discussed recently in literature, but it
seems that they require some explanation. The first, more straightforward
explanation is that the experimenters might have been misled about the energy
reconstruction of their record event by the imperfectness of the tools
available at that time, with particular emphasis on numerical tools.
Thankfully, the Monte-Carlo methods developed in the 21st century are
certainly more precise and they allow today making more adequate corrections
than decades ago, in particular in experimental procedures like localization
of shower axis, or estimation of shower energy, whether by collecting
fluorescent light or determining the charged particle density distribution on
the ground. And this explanation could be enough, provided one does not
discuss in detail the statistics of the “above 1020 eV” cosmic ray detections
of 20th century experiments in contemporary analyses. But, as already
mentioned, the two great experiments, the Pierre Auger Observatory and the
Telescope Array, also reported around 20 UHECR cases of energies above 1020 eV
observed already with the newest tools and methods (see e.g. Ref. Aab and et
al. (2020) (Pierre Auger Collaboration) where 15 events with energies above
1020 eV are mentioned collectively). To list just a few such events in detail
we mention the Pierre Auger Observatory measurements which contain an event
with energy $1.4\times 10^{20}$ eV Abreu and et al. (2010) (Pierre Auger
Collaboration) – or $1.3\times 10^{20}$ eV Aab and et al. (2015) (Pierre Auger
Collaboration), and the Telescope Array announcement concerning an event of
similar energy $1.39\times 10^{20}$ eV Abbasi and et al (2014). It is of
course clear that if the cosmic ray energy spectrum breaks around 5-6$\times
10^{19}$ eV, this is most likely a (gradual) suppression rather than an abrupt
cut-off, so there must be a few events exceeding $10^{20}$ eV. However, the
current statistics of these events does not allow telling whether they are
compatible with the spectrum cut-off or not.

It is a great achievement that today we can tell that the UHECR spectrum has
been quite well measured – see for example two recent Pierre Auger Observatory
papers Aab and et al. (2020) (Pierre Auger Collaboration, Pierre Auger
Collaboration), and that a lot of effort and resources are being currently
invested into explaining the nature of the observed spectrum suppression (GZK-
like versus acceleration limit). Nevertheless the current results are still
inconclusive, and it is therefore advisable to continue research in the
highest energy regime of cosmic rays, and to try alternative methods whenever
possible. In other words, the status of the dispute in the UHECR area
encourages a closer look at the field and being ready for a major revision or
breakthrough in the understanding of physics at the highest energies known.
The CREDO initiative with its objectives dedicated to going beyond studying
individual cosmic rays and taking under investigation also UHECR products –
cosmic ray ensembles, may provide a precious complementary approach to UHECR
studies.

##  3 UHECR sources and cosmic ray ensembles

The Standard Model (SM) of particle physics predicts that if cosmic rays (CR)
are primarily composed by protons, there should exist a limit on the maximum
energy of the CR coming from distances farther than $\sim 100$ Mpc. This bound
is called the GZK limit and was presented in Refs. Greisen (1966); Zatsepin
and Kuzmin (1966); Stecker (1968). Despite this, UHECR with energies above the
GZK limit have been reported, by experimentalist, from directions where there
are no nearby111The current experimental data suggests an extragalactic origin
for UHECRs with energies above the GZK cutoff Aab et al. . sources Zotov et
al. (2017); Verzi et al. (2017). Therefore, it seems that there is a missing
piece in our understanding of the sourcing, nature, and/or propagation of the
CR.

The cosmic ray background has been simulated by means of numerical propagation
codes Kalashev et al. (2001); Aloisio and et al (2012), and the results have
shown that it is very unlikely that CR with energy greater than GZK limit to
be photons Aab and et al. (2017) (Pierre Auger Collaboration).

In general, one can distinguish two qualitatively different approaches in
unveiling the physics of UHECRs: theoretical models assuming interactions of
exotic super-heavy matter (including extra dimensions, Lorentz invariance
violation, cosmic strings, existence of new particles etc Weiler (1982, 1984);
Aloisio and et al (2015); Tyler et al. (2001); Domokos and Kovesi-Domokos
(1999); Coleman and Glashow (1997); Bhattacharjee and Sigl (2000); Bietenholz
(2011); Scully and Stecker (2009); Gorham et al. (2012); Rubtsov et al.
(2014); Tasson (2014); Rubtsov et al. (2017); Mohanmurthy et al. (2016);
Klinkhamer and Schreck (2008); Alcantara et al. (2019); Aloisio and Tortorici
(2008); Supanitsky and Medina-Tanco (2019)) and acceleration scenarios
describing processes, in which the particles are accelerated by a particular
astrophysical object (shocks in relativistic plasma jets, unipolar induction
mechanisms, second-order Fermi acceleration, etc.). Acceleration scenarios
rely on the existence of powerful astrophysical sources with available energy
that is sufficient for the energy transfer from these objects to cosmic ray
particles.

In the age of multi-wavelength and multi messenger astronomy, transient
astronomical objects are of the great interest for UHECRs emission. There are
several classes of astronomical objects which can be prime targets for UHECR
observations e.g. gamma-ray bursts (GRBs); supernovae (SN); fast radio bursts
(FRBs); various classes of active galactic nuclei (AGN) such as Seyfert
galaxies, radio galaxies and blazars; and possible neutrino emitting blazars.
In the recent past there are evidences that these objects emit or can emit
UHECRs. A 5 millisecond bright fast radio burst of extragalactic origin was
detected (Lorimer et al., 2007). It is claimed that the radio galaxies have
emitted UHECRs (Nagar and Matulich, 2008). There is an evidence of hadronic
$\gamma-$ray emission from supernova remnants (Moskalenko et al., 2008).
Blazars are one of the most prominent sources of UHERCs emission. There are
several papers which estimated / predicted neutrino and UHERCs emission from
blazars (e.g., Murase et al., 2012; Rodrigues et al., 2018, and references
therein). About 2 decades ago, it was predicted that there were some very
bright high energy peaked blazars which would be neutrino loud(Neronov and
Semikoz, 2002). And recently, the IceCube Collaboration found the evidence of
neutrino emission from the blazar TXS 0506$+$056 (Collaboration, 2018) which
opened a new window to search for such another blazars too.

###  3.1 Supermassive black holes as UHECR sources

Among the most powerful astrophysical sources, one can highlight supermassive
black holes (SMBHs) located in the centers of most galaxies due to their
compactness and enormous energy available for the extraction. Below we shall
briefly show the capability of SMBHs to power the UHECRs in a given model. It
appears that up to $29\%$ of the total energy ($M_{\rm BH}c^{2}$) of the black
hole is rotational energy and available for extraction (Bekenstein, 1973).
Nowadays, all tests of general relativity indicate that astrophysical black
holes can be fully characterized by their masses and spins, while other
properties of black holes are hidden inside the event horizon and unavailable
to the external observer. For a typical SMBH of $10^{9}$ solar masses the
extractable energy is of the order of $10^{74}$eV, turning SMBHs into the
Universe’s largest and the most compact energy reservoirs. Therefore, it is
important to search for the processes, which tap these enormous energy sources
in the most efficient way.

Attempts to tap the energy of black holes started in 1969 by Roger Penrose
Penrose (1969), followed by many authors (see, e.g. references Blandford and
Znajek (1977); Wagh et al. (1985); Parthasarathy et al. (1986); Dadhich et al.
(2018) and references therein), who used the existence of negative energy
states of particles with respect to a stationary observer at infinity. If a
particle decays into two fragments near a black hole with one of the fragments
attaining negative energy, the other fragment (respecting energy conservation)
may escape from the black hole with greater energy than those of the primary
particle. The remarkable property of the rotating black hole is the existence
of a special region outside the event horizon called the ergosphere, where the
energy of a particle relative to infinity can be negative. However, the
negative energy states may also appear due to purely electromagnetic
interactions between the SMBH and surrounding matter without the need for
ergosphere (Tursunov and Dadhich, 2019; Tursunov et al., 2020).

Black holes, as any astrophysical object, are immersed into magnetic fields.
Rotation of the black hole in an external magnetic field leads to the twisting
of magnetic field lines due to the frame-dragging effect. Similar to a
classical Faraday unipolar inductor, a black hole rotating in a magnetic field
attains non-zero induced electric charge (Wald, 1974). This charge has been
shown to be non-negligible for any astrophysical black hole and is potentially
observationally measurable (Zajacek et al., 2018). Since the induced charge of
the black hole is coupled and proportional to the black hole spin, its
discharge is equivalent to the slowing down of the black hole and decreasing
the black hole’s rotational energy. To demonstrate the process of black hole
energy extraction and resulting acceleration of particles to ultra-high
energy, one can consider the ionization or decay of a neutral particle into
charged fragments in the vicinity of rotating SMBH immersed into an external
magnetic field. If the black hole possesses induced electric charge, the
energy of charged fragments after decay of the neutral particle obtains a
strong Coulombic contribution in addition to the gravitational negative energy
in the ergosphere. Since the induced charge of SMBHs is more likely positive
(Zajacek et al., 2018), these are the protons, which would escape from the
black hole with tremendous energy (Tursunov et al., 2020). This is the ultra-
efficient regime of the so-called magnetic Penrose process that can serve as a
possible mechanism for acceleration of UHECRs when applied to SMBH candidates.
The energy of an escaping UHE particle depends on its charge to mass ratio,
strength of external magnetic field and the mass of the black hole. For
protons accelerated in this mechanism, the maximum energy is predicted to be

$\centering E_{\rm p}=1.3\times 10^{21}{\rm
eV}~{}\frac{Z~{}m_{p}}{m}~{}\frac{B}{10^{4}{\rm
G}}~{}\frac{M}{10^{10}M_{\odot}}.\@add@centering$ (1)

In Figure 2 we demonstrate the acceleration of UHE protons resulting from the
hydrogen ionization in the SMBH vicinity. Similar results are obtained for the
neutron beta decay ($n\rightarrow p^{+}+e^{-}+\bar{\nu}_{\rm e}$). Here we
provide verifiable constraints on the SMBH mass and magnetic field as UHECR
source. As an example we indicate the few famous nearby SMBH candidates, which
are capable of producing UHE protons of certain energies. It is interesting to
note that the black hole located at the centre of our Galaxy can accelerate
particles up to the energies corresponding to the knee of the cosmic ray
spectrum. On the right side of Figure 2 we demonstrate the results of
numerical simulation of the magnetic Penrose process (for details, see
Tursunov et al., 2020; Stuchlík et al., 2020; Tursunov and Dadhich, 2019).
Remarkably, the mechanism operates in viable physical conditions for typical
SMBHs, without the need for a large acceleration zone or exotic assumptions
for black holes.

Figure 2:  Left: constraints on the SMBH mass and magnetic field for UHE
protons and chosen nearby sources (at the distance $<20$ Mpc from the Solar
system) fitting UHECRs of certain energy. Data is taken from (Baczko and et
al, 2016; Eckart et al., 2012; Doeleman et al., 2012; Kino et al., 2015; Daly,
2019; Piotrovich et al., 2020), tSMBH source corresponds to a typical SMBH of
mass $10^{9}M_{\odot}$ and magnetic field $10^{4\pm 0.5}$G. Right: numerical
simulation of a decay (ionization) of a freely falling neutral particle (grey
thick) into two charged fragments in the vicinity of a rotating black hole
immersed in an external magnetic field. Positively charged fragment (blue) is
accelerated by the black hole and escapes to infinity along the symmetry axis.
Negatively charged fragment (red) ultimately falls into the black hole,
extracting its rotational energy (see, details in Tursunov et al., 2020).

###  3.2 Axion-like particles as UHECRs

A different approach to explain the observation of UHECR is avoiding the GZK
cutoff via particles beyond the SM. In such a case UHECR must be composed by
new particles that must fulfill the following conditions: (i) be stable enough
to reach the Earth from cosmological distances; (ii) interact very weakly with
the Cosmic Microwave Background and the extra galactic magnetic fields, in
order they do not lose very much energy; (iii) have a significant flux at
their origin; and (iv) interact strong enough in the near galaxy, with the Sun
or Earth magnetic field.

One of the most popular candidates are axions, which were first proposed by
Peccei and Quinn, by introducing an additional global axial symmetry to the
standard model Lagrangian Peccei and Quinn (1977a, b) allowing to solve the
strong CP problem dynamically. Additionally, axions were proposed as
candidates to avoid GZK cutoff in reference Mirizzi et al. (2008); Csaki et
al. (2003). However, it has been shown that it is extremely unlikely that the
axion production, together with their conversion to photons by the galactic
magnetic field, accounts for UHECR within the present exclusion limits
Gorbunov et al. (2001).

A different scenario comes from the consideration of particles with similar
features of axions, called Axion-Like Particles (ALPs). The general Lagrangian
model involving ALPs read as

$\mathscr{L}_{\textsc{alp}}=\frac{1}{2}\partial_{\mu}A\
\partial^{\mu}A-\frac{1}{2}m_{A}^{2}A^{2}-\frac{g_{\textsc{alp}}}{4}aF_{\mu\nu}\tilde{F}^{\mu\nu},$
(2)

here $A$ is the ALP field, $m_{A}$ is the ALP mass, $g_{\textsc{alp}}$ is a
model-dependent coupling between ALPs and photons, $F_{\mu\nu}$ and
$\tilde{F}_{\mu\nu}$ are the electromagnetic field strength and its dual,
respectively.

The Lagrangian in Eq. (2) provides a decay channel for ALPs to photons
($A\to\gamma\gamma$), which plays a fundamental role in experimental searches.
To leading order, the decay width for the above mentioned decay is given by
Beringer and et al (2012); Cadamuro and Redondo (2012)

$\Gamma_{A}\left(A\to\gamma\gamma\right)=\frac{g_{\textsc{alp}}^{2}m_{A}^{3}}{64\pi}.$
(3)

An important feature of ALPs is that they can be converted into photons (and
vice-versa) by means of the Primakoff effect Halprin et al. (1966); this
effect occurs when a strong external magnetic field exist in the region where
the ALPs are propagating. The Primakoff effect can induce an ALP-photon
oscillation, similar to the neutrinos flavor oscillation Sikivie (1983). This
ALP-Photon oscillation changes the polarization of photons traveling in
external magnetic fields, providing an additional mechanism in order to detect
these pseudoscalar particles Maiani et al. (1986). The ALP-Photon oscillation
could also produce an apparent dimming of distant sources as well, affecting
the luminosity-redshift relation of Ia supernovae, the dispersion of quasar
spectra, and the spectrum of the CMB Mirizzi et al. (2008).

On the other hand, due to the weak interaction between ALPs and the CMB, this
can travel across the Universe essentially without decaying. The decay length
of a particle is given by

$\lambda_{A}=\frac{E_{A}}{\Gamma_{A}m_{A}},$ (4)

where $E_{A}$ is the energy of ALP. If we require that the decay length has to
be at least of the order of magnitude of the observed universe $R_{U}$ as
considered in Ref. Gorbunov et al. (2001), one finds the following condition

$R_{U}\lesssim\lambda_{A}\equiv\frac{E_{A}}{\Gamma_{A}m_{A}}\quad\Rightarrow\quad\Gamma_{A}\lesssim\frac{E_{A}}{R_{U}m_{A}}.$
(5)

The Eq. (5) allows one to establish a restriction on the ALPs coupling, which
allow it to reach the Earth from distances beyond the $R_{\textsc{gzk}}$
radius

$g_{\textsc{alp}}\lesssim\left(\frac{64\pi
E_{a}}{R_{U}m_{a}^{4}}\right)^{1/2}.$ (6)

This scenario has been studied in Refs. Gorbunov et al. (2001); Csaki et al.
(2003); Fairbairn et al. (2011), constraining their parameter space according
to current experimental data.

###  3.3 Dark Matter as a source of UHECR

Two long-standing problems of contemporary astrophysics can be formulated as:
(i) What is the nature of Dark Matter? and (ii) How to explain the existence
of cosmic rays with energies greater than $10^{20}$ eV? A plausible hypothesis
is that these two mysteries of science can be explained with just one
scenario. This is in agreement with “Occam’s razor”, which favors the least
possible set of solutions to a collection of seemingly independent problems.
According to this scenario, Super Heavy Dark Matter (SHDM) may decay or be
destroyed via annihilation (see e.g., (Chung et al., 1999)). This implies a
production of super massive – with rest energies of $E\geq 10^{23}$ eV –
particles in the early Universe, during the inflation phase. Such particles
could annihilate or decay presently, leading to the production of jets
containing copious amounts of less massive secondaries, possibly or even
mainly photons. The energies of these secondaries could easily be of the order
of $10^{20}$ eV, the value that seems to be out of reach in the acceleration
processes in the potential sources.

The key prediction of such scenarios in the SHDM group is that the UHECR flux
observed on Earth should be dominated by photons (see e.g., (Rubtsov and et
al, 2006)). On the other hand, the highest energy events observed by the
leading collaborations: Pierre Auger Observatory and Telescope Array, are not
considered photon candidates if the present state of the art air shower
reconstruction procedures are applied. In fact there are no photon candidates
within the energy range where SHDM model should give a photon flux, i.e., for
energies above above $10^{18}$ eV, and this non-observation result leads to
very stringent upper limits on photon fluxes (Petrera, 2019; Aab and et al.
(2019), Pierre Auger Collaboration; Abu-Zayyad and et al. (2013), Telescope
Array Collaboration).

However, there are two main concerns about such conclusions. First, the
present state of the art analysis does not take into account mechanisms that
could potentially lead to a good mimicking of hadronic air showers with the
showers induced by photons, e.g., a very efficient splitting of the primary
energy into secondary photons/particles and underestimation of photonuclear
interaction cross-sections. Second, the present state-of-the-art analysis does
not take into account mechanisms that could lead to an efficient screening or
cascading of the very-high or ultra-high energy photons on their way to the
Earth, e.g., interactions under special cases of Lorentz invariance violation
(Klinkhamer and Schreck, 2008), so that the products of such screening or
cascading are spread over large areas and thus out of reach of the presently
operating observatories, which is interpreted as non-observation of ultra-high
energy (UHE) photons. If the first possibility occurs, this would mean that
UHE photons might have already been detected and they might be in the data but
not properly identified. If the second possibility – namely that the real
properties of cosmic rays and the relevant propagation mechanisms are not well
understood – takes place, then one has little or no chance to detect most of
the very high energy photons that travel towards us. Both possibilities
obviously question the conclusion about limitations imposed on the SHDM
scenarios by the presently accepted upper limits to photon fluxes.
Furthermore, such a conclusion can be accepted only if both concerns above are
alleviated. A detailed study of this issue is imperative in the forthcoming
years.

An inherent part of the SHDM scenario is the very existence of such DM
particles. It is not an overstatement that science has currently no clue of
what DM particles are, nor what their properties would be.

For a long time, the Weakly Interacting Massive Particles (WIMPs) were the
most favored candidate. There was a reason for that – the “WIMP Miracle”. The
number density of the particles that freeze out in the early universe in a
certain epoch is set by the balance of the two rates: the production-
annihilation rate $n_{X}\langle\sigma v\rangle$ and the Universe’s expansion
rate $H$ (the Hubble constant at that epoch). Note that $H$ characterizes the
temperature of plasma in the universe $T$, so the number density of particles
which are in thermal equilibrium can drop exponentially fast with lowering
temperature if particles are heavy, $m_{X}c^{2}\gg k_{B}T$. On the other hand,
the cross-section depends on the coupling constant (i.e., the type of
interaction) and the particle’s mass. Next, the mass density of DM in the
universe depends on both the density and mass, $\Omega_{X}\propto n_{X}m_{X}$,
where $\Omega_{X}$ is the ratio (at present) of the particle-“X” mass density
to the critical density in the universe. Furthermore, the coupling constant
describing weak interactions – the Fermi constant, $G_{F}\approx 1.1\times
10^{5}$ GeV-2 naturally introduces the new mass scale of about $100$ GeV.
Finally, if the cross-section is the weak cross-section and the particle’s
mass is about $m_{X}\sim 100$ GeV, then the abundance of “$X$” is
$\Omega_{X}\propto\langle\sigma v\rangle^{-1}\sim m^{2}_{X}/g_{X}^{4}$ and
$g_{X}\sim 0.6$, so $\Omega_{X}\sim 0.1$. Thus, “$X$” is Dark Matter. This is
the “WIMP miracle”: particle physics independently predicts particles with the
right mass density to be Dark Matter. In this scenario, $\langle\sigma
v\rangle\simeq 3\times 10^{-26}\textrm{ cm}^{3}\textrm{s}^{-1}$; since $v\leq
c$, the gross-section should be $\sigma\geq 10^{-36}\textrm{ cm}^{2}$.
Numerous ongoing direct-detection DM experiments have reached sensitivity
levels that correspond to $\sigma\sim 10^{-44}-10^{-45}\textrm{ cm}^{2}$ in
the mass range of interest – from tens of GeV to a few TeV, without a
statistically significant and reproducible detection. Thus, the WIMP miracle
is at odds with experiment.

The dismissal of the most favorable WIMP miracle in Dark Matter theory has
ignited great interest in alternative scenarios. At present, all bets
regarding the non-standard DM scenarios are on the table. There is no deficit
of the putative candidates, including the super-heavy dark sector candidates.
Here are some examples, as follows. (1) Magnetic monopoles (’t Hooft, 1974;
Polyakov, 1974) are topological defects that naturally appear in Grand Unified
Theories (GUT) and carry a magnetic charge. The natural mass scale for them is
the GUT scale, $\sim 10^{25}$ eV. However, the actual mass of a monopole is
not constrained and all mass scales above the one that can be probed in an
experiment are considered. Being topological defects, monopoles are copiously
produced in a GUT phase transition, creating a severe over-closing problem
$\Omega_{X}\gg 1$. This problem is remedied by inflation, which reduces the
monopole abundance in the amount enough to not contradict observational and
recent cosmological constraints (Medvedev and Loeb, 2017). (2) Wimpzillas
(Kolb and Long, 2017) are superheavy DM particles, which mass scale is many
orders of magnitude above the conventional WIMP scale, possibly as large as
the GUT scale. The WIMP mass cannot exceed hundreds of TeV. Otherwise, heavier
WIMPs would over-close the universe, $\Omega_{X}>1$. Therefore, Wimpzillas,
like monopoles, are not ‘thermal relics’. They emerge out of thermal
equilibrium right after inflation and their density is not determined by the
balance of the production-annihilation rate and the universe expansion rate.
(3) Planckian-scale particles (Garny et al., 2016, 2018, 2019) is a whole
class of candidates that appears in a minimal scenario of DM, where only
gravitational interactions with the standard model are assumed. There is only
one parameter in the scenario – the particle mass, which ranges from TeV up to
the GUT scale. These particles are assumed to be produced by gravitational
scattering in the thermal plasma of the Standard Model sector after inflation.
For example, the Kaluza-Klein excitation of the graviton in the string theory
is one of the realizations of this scenario. The above discussion does not
present a complete list of SHDM candidates, of course, but just a few popular
examples. There are more theoretically predicted candidates.

The search for signatures of propagation and/or decay of particle primaries
beyond the Standard Model is to be taken seriously and thoroughly. In this
regard, CREDO observatory can serve as an indirect search for one of the non-
standard Dark Matter candidates: super heavy particles with masses equal or
exceeding $10^{23}$ eV. Such particles could be produced in the early Universe
around the inflation phase and decay or annihilate presently leading to
observable products in the UHE range (Bhattacharjee, 2000). The interest in
SHDM scenario is supported by certain difficulties the electromagnetic theory
faces at explaining UHECR acceleration, which is discussed below, in Section
3.4.

###  3.4 Constraint on electromagnetic acceleration of UHECR

Electrically charged UHECR traversing a region of size $R$ filled with
magnetic field $B$ assumed to be uniform, loses its energy due to synchrotron
radiative energy loss (Medvedev, 2003) according to

$\frac{dE}{dx}=F_{rad}=-\frac{2}{3}\left(\frac{Ze}{Am_{p}c^{2}}\right)^{4}B^{2}E^{2},$
(7)

where $A$ and $Z$ are the atomic mass and charge of an accelerated nucleus,
$m_{p}$ is the proton mass. The solution to this equation is trivial:

$E=\left(E_{0}^{-1}+E_{cr}^{-1}\right)^{-1}.$ (8)

Thus, for an arbitrarily large initial energy, $E_{0}\to\infty$, the particle
energy cannot exceed the ‘critical energy’ threshold:

$E_{cr}=\frac{3}{2}\left(\frac{Am_{p}c^{2}}{Ze}\right)^{4}\left({B^{2}R}\right)^{-1}\sim
3\times 10^{16}\frac{(A/Z)^{4}}{B_{G}^{2}R_{kpc}}~{}\textrm{eV},$ (9)

where $B_{G}$ is in Gauss and $R_{kpc}$ is in kiloparsec.

Furthermore, even if one is to continuously accelerate the particle along its
curved path via an inductive electric force $F_{EM}=Ze\,E_{ind}\simeq
Ze(v/c)B\sim Ze\,B$, one has the following energy evolution:

$\frac{dE}{dx}=F_{EM}+F_{rad}=ZeB-\frac{2}{3}\left(\frac{Ze}{Am_{p}c^{2}}\right)^{4}B^{2}E^{2}.$
(10)

It has a beautiful solution (assuming the initial energy is small compared to
the final energy):

$E=\sqrt{E_{acc}E_{cr}}\tanh\sqrt{E_{acc}/E_{cr}},$ (11)

where

$E_{acc}=Ze\,B\,R\sim 9\times 10^{23}Z\,B_{G}\,R_{kpc}$ (12)

is the maximum energy the accelerated particle can reach without losses. This
solution has two obvious asymptotic scalings. If $E_{acc}\ll E_{cr}$, i.e.,
losses are small, one recovers the Hillas constraint (Hillas, 1984) $E\simeq
E_{acc}$, and in the opposite limit one has

$E_{\rm max}\simeq\sqrt{E_{acc}E_{cr}}\sim 10^{20}A^{2}Z^{-3/2}B^{-1/2}\
~{}\textrm{eV}.$ (13)

Figure 3: The $B$-$R$ “diagram of state” for UHECR acceleration (Medvedev,
2003). The long-dashed line is the original Hillas relation, Eqn. (12), for a
proton of energy $3\times 10^{20}$ eV. The short-dashed and dot-dashed lines
represent the radiative cooling constraints given by Eqns. (9) and (13), for
the same proton energy. Above the dot-dashed line, the force of radiative
friction dominates over an electromagnetic force. The solid lines represent
the boundaries of the allowed parameter regions for protons with energies
$3\times 10^{20}$, $10^{22}$, and $3\times 10^{23}$ eV, from the outermost to
the innermost “wedge”, respectively. The dotted lines are the same boundaries
for an iron nuclei with energy $3\times 10^{20}$ eV. Only those astrophysical
objects which fall inside the “wedges” are, in principle, capable of
accelerating the particles to such energies. The grey vertical lines mark two
characteristic spatial scales: the GZK attenuation distance ($\sim 20$ Mpc)
and the Hubble horizon size ($\sim 4$ Gpc). For GRB sources we took into
account that the Lorentz boost changes with radius.

These results are summarized in Figure 3. All the curves, except for two
dotted ones, correspond to protons ($A=Z=1$), and the dotted are for iron
nuclei ($A=56,\,Z=26$). The details are discussed in the figure caption. Here
we make a few important conclusions. First, there is an absolute maximum
energy of UHECR accelerated electromagnetically and subject to radiative
losses (e.g., in dipolar magnetospheres, galactic and extragalactic shocks and
such), which is given by the balance of the acceleration and losses. This puts
the upper limit on the magnetic field strength, given by the dot-dashed
horizontal line and by Eq. (13):

$B\lesssim E_{20}^{-2}A^{4}Z^{-3}\textrm{ Gauss},$ (14)

where $E_{20}=E/(10^{20}\textrm{ eV})$. Second, there is a corresponding limit
on the size of an accelerator. This is the size that corresponds to the “tip
of the wedges”, which can be obtained, for instance, from Equations (13) and
(12), namely

$R\gtrsim 6\times 10^{-2}E_{20}^{3}A^{-4}Z^{2}\textrm{ pc}.$ (15)

This constraint effectively rules out compact accelerators, such as neutron
stars, white dwarfs and such. Large objects, such as galactic halos, radio
lobes, and galaxy clusters become favorable. Third, electromagnetic
acceleration of UHECR beyond $\sim 3\times 10^{22}$ eV is hard because the
size of an accelerator becomes comparable to the GZK distance. Furthermore,
the acceleration beyond $\sim 3\times 10^{23}$ eV would require an accelerator
of the size of the observable universe, which is questionable. Fourth, our
analysis above does not take into account that the source may be moving
relativistically with a large Lorentz factor, as in a gamma-ray burst outflow,
for example. Accounting for this, relaxes the size and field strength
constraints but not very dramatically, as far as UHECR are concerned. Fifth,
our analysis excludes special arrangements such as linear accelerators. If one
can arrange particle acceleration along a straight path, e.g., strictly along
a static straight magnetic field line, then the particle would experience no
synchrotron energy loss, regardless of the field strength (still well below
the QED, ‘Schwinger field’ strength). In this case, our analysis is
inapplicable.

###  3.5 SQM objects

Recently, strange quark matter (SQM) objects (either in the form of stars or
planets) have been shown to efficiently convert mechanical energy into
hadronic energy when they oscillate Kutschera et al. (2020). This is possible
thanks to the property that the mass density at the edge of SQM objects of
$4.7\times 10^{14}\mathrm{g}/\mathrm{cm}^{3}$ is the critical density below
which SQM is unstable with respect to decay into photons, hadrons, and
leptons. Either compression or expansion of the SQM object, such as
oscillation induced deformations, releases energy. Oscillations of SQM objects
could be induced in stellar or planetary systems where tidal interactions are
ubiquitous. The excitation energy is converted into electromagnetic energy in
a short time of $1\,\mathrm{ms}$, during a few oscillations. Higher amplitude
oscillations result in faster energy release that could lead even to
fragmentation or dissolution of SQM objects. In the context of CREDO, it would
be interesting to observe periodic signatures of such events.

SQM stars and planets are very sensitive to radial oscillations. The amplitude
of oscillations is physically determined by the excitation process in close
encounters of SQM objects and another compact star or black hole. Depending on
the closest approach distance, the energy transferred to the oscillations can
reach $10^{53}\,\mathrm{erg}$ when the closest approach distance is 3 times
the star radius. By mode couplings, monopole (that is, spherically symmetric
radial) oscillations also would be excited. For violent encounters, the
induced oscillations of the radius result in excitation energy in the surface
layer of every SQM object, equally for stars of pulsar masses and planetary-
mass SQM objects. Fractional amplitudes of radial oscillations $\chi=10^{-6}$
are quite possible. The corresponding deposited energy to be radiated away for
a star of mass $1.4\mathrm{M}_{\odot}$ is estimated to be $6.6\times
10^{36}\,\mathrm{erg}$. For more violent encounters (such as inspiraling of a
tightly bound binary system), one can expect even amplitudes $\chi={10}^{-3}$
and the corresponding energy orders of magnitudes higher. A tightly bound
binary system could induce periodic distortions of a SQM companion and
associated periodic bursts of intense radiation (associated with gravitational
radiation). In the evolution of binary systems with the SQM objects, the
energy loss due to excitations of SQM stars and planets must be accounted for
and this can change significantly the predictions obtained with unexcited SQM
objects (this would be particularly relevant to binary gravitational wave
sources, its exact template calculation should account for excitations of SQM
objects).

To understand the possible radiation scenarios, one may bring to attention the
following estimations taken from Kutschera et al. (2020). For small SQM
objects called planets, the excited energy is deposited in the whole volume of
the object. The energy then scales quadratically with the fractional amplitude
of radial oscillations $\chi$ – for planets $E=7.4\times
10^{48}\cdot\frac{M}{\mathrm{M}_{\oplus}}\chi^{2}\,\mathrm{erg}$. In
particular, $E=7.4\times 10^{38}\,\mathrm{erg}$ for an Earth mass SQM planet
undergoing radial deformation of amplitude $\chi=10^{-5}$. As the mass of the
considered objects increases, the deposition zone shrinks toward the surface
and the energy law changes. In the intermediate region of masses the energy
scaling law can be obtained only numerically. For masses on the order of solar
mass, the energy deposition zone becomes a thin layer and the total energy to
be eventually radiated away can again be estimated analytically and it scales
cubically with the fractional amplitude of oscillations $\chi$ (the resulting
formula is given in Kutschera et al. (2020)). Furthermore, one also has to
take into account a more complicated mass-radius relation for relativistic SQM
stars implied by the equilibrium state numerical solution. For the
representative star model of $M=1.4\,\mathrm{M}_{\odot}$ the radius is
$R=10.3\,\mathrm{km}$ and the energy to be released behaves as $E=6.6\times
10^{54}\chi^{3}\mathrm{erg}$. For the amplitude $\chi=0.001$ this gives
$E=6.6\times 10^{45}\,\mathrm{erg}$ in a $20$m-wide deposition shell.

The process of excitation of quark matter is an irreversible one. The
excitation energy will be dissipated eventually into heat and radiation. In
the intermediate phase the excitation energy is being converted into
electromagnetic energy. The generation rate of radial oscillations of the SQM
star can be estimated by assuming that the timescale of radial oscillations is
comparable with that already known in the model without the excitation energy,
which is $T=0.37\times 10^{-3}\mathrm{s}$. The period is much larger than the
timescale for electromagnetic interactions of $10^{-16}\mathrm{s}$. Thus the
excitation energy can be assumed to be converted into electromagnetic energy
inside the SQM star instantaneously. The rate of electromagnetic energy
generation within a quarter of the oscillation period is $7.2\times
10^{49}\mathrm{erg}/\mathrm{s}$ for $\chi=10^{-3}$ (and it increases with
$\chi$, eg. $6.7\times 10^{55}\mathrm{erg}/\mathrm{s}$ for $\chi=0.1$).
Further investigations are required to find how much of the energy will be
radiated away and how fast this will proceed. A rough conservative estimation
made in Kutschera et al. (2020) shows that the luminosity for the energy
radiated away by the outermost shell of thickness on the order of the photon
mean free path would amount to $L=1.3\times 10^{34}\mathrm{erg}/\mathrm{s}$
(for $\chi=10^{-3}$) with a corresponding effective temperature of $2.0\times
10^{6}\,\mathrm{K}$. The total energy of $E=6.6\times 10^{45}\,\mathrm{erg}$
released in the star would thus sustain radiation for $1.6\times 10^{4}$
years. However, neutrino cooling will switch on in $10^{-6}\,\mathrm{s}$ and
the star will cool fast. The estimated neutrino cooling time for the volume of
the star $1.4\times 10^{3}\,\mathrm{s}$ is $3.5\times 10^{8}$ times shorter
(respectively, $1.5\times 10^{5}\,\mathrm{s}$ for the volume of the initial
deposition shell is $3.4\times 10^{6}$ times shorter) than the electromagnetic
radiation time. With the considered excitation mechanism accounted for, the
extreme, e.g. $\chi=0.1$ large oscillations, are rather excluded in nature,
since the energy of such oscillations would be less than the value of
excitation energy generated during the time of a single oscillation, therefore
oscillations would be damped during the first cycle). For lower amplitudes the
energy generation time is longer. More accurate calculations would require
taking into account the evolution of the temperature of the SQM star. The
damping effect on radial oscillations by weak quark processes, although
efficient, is not expected to determine the discussed strong interaction
phase, although it might dominate the thermalization of excited SQM.

###  3.6 Neutron star collapse to third family

Massive neutron stars may support in their cores exotic states of matter
different from hadronic, like deconfined quark matter. These stars are denoted
hybrid stars. In the case of a strong first order phase transition inside
compact stars, their mass-radius relation presents a gap of unstable
configurations between pure hadronic and hybrid stars. The latter ones will
populate the so-called “third branch”, following the hadronic neutron stars
and white dwarfs branches. The transition scenarios may correspond to a
neutron star configuration lying at the top end of the hadronic branch whose
central density is right below the critical value for deconfinement. There are
possible ways for the increase of central density of such a neutron star, thus
triggering the transition to a third branch configuration. For instance, a
fast rotating neutron star may lose energy by dipole emission resulting in a
spin down, or a neutron star in a binary system may undergo an accretion-
induced spin-up by matter from a companion. The latter case has been recently
proposed as an explanation for eccentric orbits of binary systems where the
neutron star is able to accrete matter from a circumbinary disk created after
a low-mass X-ray episode. Consequently, the neutrino burst which accompanies
the deconfinement phase transition in the neutron star interior may trigger a
pulsar kick producing the observed eccentric orbit Alvarez-Castillo and et al
(2019). A pair of compact stars of about the same mass, each one of them lying
in different branches of their mass-radius relation are usually called “twin
stars”, see Benic et al. (2015); Alvarez-Castillo and Blaschke (2017);
Blaschke et al. (2020). The aforementioned dynamical scenarios, where one of
the neutron stars collapses into its twin star, may conserve the total baryon
number resulting in a mass defect of less than a tenth of the solar mass for
state-of-the-art equations of state, which corresponds to an energy of a few
$10^{51}$ ergs Alvarez-Castillo et al. (2015).

It is therefore feasible that the possible deconfinement phase transition in
compact stars produce energetic emissions, for instance acting as an engine
for Gamma Ray Bursts, with an accompanied characteristic neutrino signal as
well as high energy cosmic rays. An analogous situation can be discussed in
the framework of neutron star mergers, where both electromagnetic and
gravitational radiation are emitted, together with cosmic rays. For the
GW170817 event , it has been estimated that the cosmic rays flux is able to
support the population of cosmic rays detected at Earth below the “ankle”
Rodrigues et al. (2019).

###  3.7 UHECR as the spacetime structure probe?

The CRE hypothesis can be considered a candidate scenario for a number of
unexplained cosmic-ray measurements. The examples include Smith et al. 1983
Smith et al. (1983) (32 TeV EAS within 5 minutes while only one such event
would have been expected) and Fegan et al. 1983 Fegan et al. (1983)
(simultaneous increase in the cosmic-ray shower rate at two recording stations
250 km apart). On one hand the mentioned measurements were single
observations, not seen by other groups, but on the other, nobody checked
further on a global scale. We are going to do so within this project – using
the CREDO meta-structure composed of the detectors operated by numerous
research groups in all the available energy ranges. This will offer a chance
to confirm or question the aforementioned historical reports, potentially
leading to the observation of New Physics effects, including probing the
spacetime structure. Although the expectations concerning the potential
observations of spacetime structure manifestations through effects accumulated
over large astrophysical distances are highly uncertain due to missing physics
formalism below the Planck scale, as stated e.g. in Ng, Y Jack (2003); Carlip
(2015), the cumulation of time delays of high energy photons travelling
astrophysical distances is thinkable, especially if one considers photons of
different energies emitted simultaneously. The cumulative time delay of higher
energy photons with respect to the lower energy ones might or might not depend
on photon energies – it is hard to tell due to the missing formalism regarding
the proper averaging of spacetime foam fluctuations Ng, Y Jack (2003). (Due to
quantum fluctuations, spacetime, when probed at very small scales, will appear
very complicated – something akin in complexity to a chaotic turbulent froth,
which physicist John Wheeler dubbed quantum foam, also known as spacetime
foam.) If the cumulative effects of spacetime foam fluctuations are
independent of photon energies, then they might be too small to be observed.
On the other hand, if they depend on energy, one cannot exclude time delays
even as large as of the order of minutes – comparable to the observations
mentioned above. Therefore if, as hoped in CREDO, we can observe CRE composed
of high energy photons of different energies, possibly spanning the whole
cosmic ray energy spectrum, i.e. from GeV to ZeV, then in any case we will
have a new “spacetime probe” at hand – to bring a new input for tuning the
existing, or even building the new spacetime models, be it delay evidence or
null results that further constrain the available theories. Thus, in any case,
we are entitled to expect that within this proposal we will contribute in a
novel way to getting closer to understanding the cumulative effects in
spacetime foam fluctuations, which would mean a contribution to the
foundations of science. While proper averaging methods of cumulative spacetime
foam fluctuations are yet to be developed (as stated in Ng, Y Jack (2003)),
and despite the uncertainty concerning energy dependence of such effects, not
exploring the new research opportunity offered by CREDO would be a
methodological mistake. The research in the proposed direction should begin
with a wide review of spacetime structure models which predict differences in
time delays between the arrival times of high energy photons of different
energies. With such a review the experimental efforts dedicated to CRE could
be prioritized accordingly so that appropriate detection and monitoring
algorithms could be developed, including the alerting mechanisms on a
subthreshold level to be analysed in accordance with the multi-messenger
astrophysics strategies. The latter direction gives promising perspectives for
new advances in astrophysics, reflected also in the new attention of
theorists, also those addressing the questions related to space time structure
(see e.g. Carlip (2019); Wang and Unruh (2019); Ng, Y Jack (2019)) and private
interest in discussions222P. Homola’s private communication with S. Carlip, Y.
J. Ng, and Q. Wang..

##  4 CRE simulations

High energy particles that propagate through the Universe unavoidably interact
with background radiation, magnetic fields, and matter, initiating cascades of
secondary particles which might be observed with available techniques – like
in artificial particle colliders but on a much larger scale. While an
interaction of a particle during its propagation through the Cosmos is
commonly approximated with extinction, one has to admit that the logically
correct question about chances for observing CRE is not if they exist, but
when and how we could observe them. This argument is illustrated with Fig. 4.
Let us consider a CRE initiated near the Earth, taking as an example the
preshower effect Erber (1966); McBreen and Lambert (1981); Homola and et al
(2005); Dhital and et al. (2018) (CREDO Collab.), i.e. an interaction of an
UHE photon and subsequent secondary electrons with the geomagnetic field above
the Earth’s atmosphere. The word “preshower” is meant to describe the result
of the initial interaction: “pre” emphasizes the location of the interaction
vertex above the atmosphere, i.e. before the extensive air showers (EAS) are
initiated; “shower” addresses the number of particles that emerge instead of
one primary UHE photon. Since the distribution of preshower particles (mostly
photons) above the atmosphere is confined to a very small region (a fraction
of cm2) the resultant extensive air shower will have properties very similar
to air showers initiated by single primary particles of the energies
corresponding to the photon which initiated this preshower. Thus the
observation of a preshower-like CRE will require nothing else but a standard
infrastructure dedicated to the detection of UHECR, and in Fig. 4 (left panel)
we name this scenario an “obvious detection” example. On the other hand, if a
CRE particle distribution is so sparse that only one particle can reach the
ideal detector system at a time, there is no technical chance to interpret
this individual particle as a component of a CRE. Thus we consider this
scenario an obvious technical limitation for CRE observation, in Fig. 4 named
“obvious extinction” (right panel). Consequently, the focus of any research
dedicated to CRE is limited to the scenarios that can result in particle
distributions less sparse than the “obvious extinction” limit, as also
illustrated in Fig. 4 with the “obvious between” CRE case (middle panel), so
far unexplored with a globally coordinated observational effort.

Figure 4: Obviously in experimental reach, although not yet probed, detection
of Cosmic Ray Ensembles, using ultra-high energy photons as example primary
particles.

As far as CRE scenarios are concerned, the ongoing simulation studies include
synchrotron radiation of high energy electrons in the presence of planetary,
stellar and galactic magnetic fields.

As shown e.g. in Ref. Risse and Homola (2007), in case of the preshower effect
occurring due to UHE photon interactions with the geomagnetic field the
resultant EAS can hardly be distinguished from those initiated by individual
particles based on standard air shower observables like the atmospheric depth
of shower maximum development or muon content in the particle distribution on
the ground – unless a large statistics of events is available. Given the
stringent UHE photon limits one does not expect many photon- or preshower-
induced events to be observed even with the largest air shower detector arrays
like the Pierre Auger Observatory or Telescope Array. Instead, one might
consider alternative observables and alternative infrastructures, more
sensitive to electromagnetic multi-primary EAS origins, e.g. those connected
with Cherenkov emission induced by air shower particles and being observed by
gamma-ray telescopes. A study in this direction was presented in Ref. Almeida
Cheminant and et al. (2020) (CREDO Collab.), where the authors analyze the
feasibility of detecting preshower-induced EAS using Monte-Carlo simulations
of nearly horizontal air showers for the example of the La Palma site of the
Cherenkov Telescope Array (CTA), as illustrated in Fig. 5.

Figure 5: An ultra-high energy photon interacting with the transverse
component of the geomagnetic field produces an $e^{+}/e^{-}$ pair ${\sim}$1000
km above sea level which emits bremsstrahlung photons. As such a process can
repeat itself for some of these photons, a collection of particles (mainly
photons and a few $e^{+}$ and $e^{-}$) reaches the top of the atmosphere.
Consequently, atmospheric air showers are produced and in the case of nearly
horizontal showers, only the muonic component reaches the Imaging Atmospheric
Cherenkov Telescopes (IACTs) on the ground, which detect the Cherenkov
emission of this component. Almeida Cheminant and et al. (2020) (CREDO
Collab.)

It was demonstrated that there is a realistic chance for identification of
preshowers induced by 40 EeV photons coming from an astrophysical point source
during 30 hours of observation. This result confirms the Imaging Atmospheric
Cherenkov Telescope (IACT) technique could be used to probe physical phenomena
not only in the TeV domain, but also in the EeV regime, with a particular
connection to the CRE-related physics. Although, as inferred from the upper
limits to UHE photons, the rate of expected preshower events for the studied
configuration of the observatory is quite low, the gamma/hadron separation
obtained by adopting the nearly-horizontal observation mode allows for strong
filters to be applied in order to identify such events with a high degree of
confidence. Searches for particles with low expected flux using IACTs have
been previously performed, as it is the case for the tau neutrino Ahnen et al.
(2018) or UHE cosmic rays, as demonstrated in Neronov et al. (2016). Moreover,
multimessenger alerts obtained from other operating observatories may allow
fast pointing of the telescopes towards sources suspected to be capable of
producing UHE photons, e.g. via interactions between UHE cosmic rays possibly
produced by AGNs and the cosmic microwave background, or during gamma-ray
bursts, which would significantly increase the chance probability to observe
UHE photons and preshower-like CRE. Such potential is well illustrated by the
correlation of the arrival direction of a 290 TeV neutrino observed by IceCube
with gamma emissions from blazar TXS 0506+056 observed by MAGIC and FERMI-LAT
IceCube Collaboration et al. (2018). Moreover, a program of observation could
be run on catalogs of high energy sources, with an observation time
significantly higher than the 30h presented in Ref. Almeida Cheminant and et
al. (2020) (CREDO Collab.).

Figure 6: An example energy spectrum of a cosmic ray ensemble generated by an
ultra-high energy photon in the vicinity of the Sun, after the interaction
with the solar magnetic field (primary photon energy: 1020 eV, the
heliocentric latitude of “the closest approach point”: 0o, and the impact
parameter: 3 R⊙). Dhital and et al. (2018) (CREDO Collab.)

To generalize the notion “preshower”, the term “super-preshower” was
introduced (see e.g. Dhital and et al. (2018) (CREDO Collab.)). Super-
preshowers (SPS) are cascades of electromagnetic particles, thus a subset of
potentially wider CRE family, originated above the Earth’s atmosphere, no
matter the initiating process and distance to the Earth. Super-preshowers can
be classified with respect to their potentially principal observable
properties: spread in space and arrival times. For an example, a cascade
initiated due to the preshower effect in the geomagnetic field (even at
altitudes as high as 10000 km a.s.l.) is expected to have the lateral spread
above the atmosphere (100 km a.s.l.) in the order of millimeters, and
negligible spread of arrival times Homola and et al (2005); Homola et al.
(2013). If the preshower effect was to occur in the vicinity of the Sun, one
would expect still negligible spread of arrival times, but the lateral spread
then might reach the size of the Earth Dhital and et al. (2018) (CREDO
Collab.) or even larger. The resultant SPS signature is then expected to be
composed of even hundreds of thousands of extensive air showers, forming a
characteristic, very thin (order of centimeters) and elongated (up to millions
of kilometers) pattern. This example shows that by analyzing the properties of
CRE/SPS one might approach attributing a non-trivial physical scenario to the
observable event category, provided the underlying uncertainties are properly
understood and quantified – as planned by CREDO. The few calculations
performed so far in this direction can still serve only as qualitative
indications concerning potential CRE/SPS observables. For instance, in
Ref.Bednarek (1999) the lateral spread of an SPS originated nearby the Sun is
simulated using a private code and assuming that the SPS is composed only of
photons of energies larger than E=1017 eV, while from the more detailed
calculation done in Ref. Dhital and et al. (2018) (CREDO Collab.), obtained
with an open source public code PRESHOWER Homola and et al (2005); Homola et
al. (2013), one learns that the energy spectrum of SPS particles might be
extended over a wide range, down to TeV and lower, as illutrated in Fig. 6.
TeV photons would certainly induce air showers that would contain particles,
mostly muons, observable on the Earth’s surface. While in large cosmic-ray
observatories these muons are treated as background, the complete CRE/SPS-
oriented research we propose here has to include a proper handling of this
“unwanted muon background” which can be processed to extract a signal induced
by ensembles of low energy air showers arriving simultaneously at the detector
– very clear, unique, and so far untested signature. We make one step further
and propose a global analysis of the data from the available detectors to
search for extremely spread CRE/SPS events, inaccessible by the largest
observatories taken individually. The experimental question which can be
addressed in this regard is: “which CRE/SPS fronts, and in which
circumstances, can be detected by a network of devices located on Earth or
around it?”. It is the question about the SPS/CRE particle density on the top
of the atmosphere (or speaking more general: on top and within the
technosphere) and the particle density, or any other observable information,
like e.g. Cherenkov light, related to the resultant air shower ensembles.

Another type of a CRE scenario, where electromagnetic particles play a role,
is the propagation of very high energy electrons through intergalactic and
galactic magnetic fields. One of the analysis in this direction currently
being carried out within the CREDO Collaboration concerns the propagation of
electrons of energies between 1017 eV and 1019 eV within the Galaxy, using
CRPropa Batista et al. (2016) – a Monte Carlo simulation of cosmic ray
propagation and the state-of-the art modeling of the galactic magnetic fields
to quantify the chances of observing a CRE on Earth. The intermediate results
indicate qualitatively that one might have a chance of observing a CRE
originating from synchrotron radiation occurring within the Galaxy or maybe
event at some other extragalactic sources. Quantification of the observational
chances is still on the way, but already the qualitative study conveys a very
important message: even “conventional” and abundant electromagnetic processes
like synchrotron radiation in galactic magnetic fields are expected to
generate CRE reaching the Earth.

At the end of this section it is worth emphasizing that the experimental
strategies dedicated to CRE do not need to rely on specific theoretical
scenarios – one might also “fish” for clearly non-random cosmic-ray global
footprints. This approach is justified by the ultra-high energy physics
uncertainties we are aware of – large enough to admit that we might not be
able to imagine all the possible physics scenarios predicting a CRE signal
that would be observable on Earth. It is therefore sensible “just” to explore
fully the potential of the infrastructure we have at hand and go fishing for
signatures we are not able to predict, but which we can distinguish from the
diffuse (random) cosmic-ray background.

##  5 CREDO detectors: cloud of clouds

As explained above, any experimental strategy oriented on observation and
investigation on large scale cosmic ray correlations in the form of widely
defined CRE require a global approach to cosmic-ray research. Since both
extensive air showers and incoherent cosmic rays might originate from a CRE,
one realizes that in fact any detectors capable of detecting cosmic ray
signals, both on the ground or on satellites, can potentially serve as
valuable components of a global data acquisition system. In other words, the
chances for CRE observation increase with any single detector or observatory
joining the collective observational effort. Within this general concept,
schematically depicted in Fig. 7 the role of CREDO can be understood as an
umbrella research program that enables a collaborative effort dedicated to CRE
with the use of existing infrastructure and expertise, and with openness for
designing and building complementary detectors or arrays – if required and
justified by specific CRE models and research plans.

Figure 7: The concept of the Cosmic Ray Extremely Distributed Observatory
(CREDO): open on two ends (data upload and access), using both professional,
dedicated cosmic ray infrastructure and off-the-shelf detection solutions,
including smartphones.

Widening the participation in the CREDO program increases its scientific
potential. The CREDO program benefits all participants by being as open as
possible through the following: removing or reducing as many non-scientific
barriers that block findability, availability and interoperability of
contributing data sets as possible, and facilitating the usage of the systems,
taking into account different needs and levels of expertise of the individual
participants and institutional stakeholders. To illustrate technological
diversity behind the general CREDO concept in this section, we briefly sketch
a landscape of detection techniques used in the state-of-the-art cosmic ray
research with particular emphasis on the current situation, needs and
interests of the CREDO Collaboration.

###  5.1 Cosmic ray detection techniques

The current CREDO collaboration with existing experiments and all the future
planned detector installations allows for the extension of the widely used EAS
(Extensive Air Shower) detection and analysis techniques. EAS detector systems
are typically designed as a grid of individual detectors that spreads over a
large area. This is due to two reasons: the disk of the EAS at the observation
level can be up to a few kilometers in diameter for ultra-high energy events,
and the frequency of such events per km2 is low so higher grid area means
higher event rate.

The most common technique that is applied as part of data analysis uses the
particle density distribution within the EAS disk. The average distribution of
the particle density in the disk varies with the distance from the shower axis
in a known way; it additionally depends on the energy of the primary – E0.
Figure 8 Beisembaev et al. (2019) illustrates the distribution of the particle
densities in simulated EAS disks at the different distance from the axis of
simulated showers. This is shown for several values of the E0 of the primary
protons. The simulations were done using CORSIKA Heck et al. (1998) software
package. Note that the particle density distribution is non-linear (approx.
inverse quadratic far from the axis). Additionally, each individual detector
within the grid provides the time of the hit, e.g. some timing information
when the signal in this detector went over a preset threshold. This
information is used to determine the EAS arrival direction.

Figure 8: Particle density distribution in simulated EAS disk vs. distance
from axis for different E0 Beisembaev et al. (2019).

However, there is an unused piece of information here. As the EAS disk passes
the detection level, the detectors can measure not only the integral number of
detected particles but their distribution over time as well, getting an
effective width of the disk Beznosko et al. (2020). This technique was first
developed and used at the Horizon-T Beisembaev et al. (2020) experiment that
holds close ties with the CREDO collaboration. This approach uses the width of
the EAS disk as measured by different detectors during the event. Figure 9
Beisembaev et al. (2019) illustrates the widths of the same simulated EAS from
Figure 8. The grey lines of the plot show approximated widths at the distances
from the axis where particle density is low for reliable determination. The
width behaves in a more linear way when compared to particle density,
specifically closer to the axis, and is weakly dependent on the primary
particle energy E0. Using all available information from arrival time ,
particle density distribution and disk width, one gains advantages such as the
ability to do some analysis on the events with axis outside of the detector
active area. This ability is due to the fact that the approximate position of
the axis position can be reasonably estimated from the disk width information.
However, such detectors and specifically electronics are more costly as fast
Flash ADC and fast PMT with matching detection medium are required Beznosko et
al. (2017).

Figure 9: Simulated EAS disk width vs. distance from axis for different E0
Beisembaev et al. (2019).

###  5.2 Overview of the different EAS detection techniques – scintillator,
water Cherenkov, CMOS/CCD, air fluorescence, radio

Numerous methods are used by existing experiments to detect charged particles
from the EAS disk. As we cannot see the particles themselves, the principle is
to convert the passage of the particle through the detector into a signal that
is easy to process, or observe the result of the particle interaction with the
detection medium.

### CMOS/CCD

The most direct method involves using a silicon-based pixelated strip. The
most commonly found detectors of this type are in everyone’s cell phones and
photo cameras – they are the CMOS/CCD photosensors (more information is
available in Fossum and Hondongwa (2014)). On passage through the pixel,
charged particles as well as gamma and x-rays affect CMOS/CCD sensors in a
similar way as light does. If the camera cap is closed (or cell phone lens is
well covered) so that the sensor is in the dark, the pixels affected, or hit,
by a particle passage will produce a response as if they were exposed to
light. If more than a single pixel is hit, a part of the particle track may be
detected as well as shown in Figure 10. This method is currently used by the
CREDO Collaboration using the cell phone cameras and a special app Bibrzycki
and et al. (2020) (CREDO Collab.); Niedzwiecki and et al. (2019) (CREDO
Collab.) extendable or portable to a browser application.

Figure 10: A sample event of a cosmic ray leaving a track on a CCD sensor
Niedzwiecki and et al. (2019) (CREDO Collab.).

### Water-based Cherenkov detector

Another detection method that is based on observing the results of particle-
matter interaction relies on the detection of the Cherenkov light – an
electromagnetic shock wave from the charged particle passing the transparent
medium (water, air, glass, plastic) faster than the speed of light inside that
medium (read more on Cherenkov radiation in Watson (2011)). The shock wave
consists of thousands of photons per 1 cm of particle path in the medium that
can be detected using fast photodetectors with internal signal amplification,
such as PMT (Photo Multiplier Tube).

The design of the water-based Cherenkov detector is very simple – an insulated
volume of water and at least one PMT that is optically connected with this
volume. A charged particle creates a cone of Cherenkov light that is detected
by a PMT. If the volume is very large and many PMTs are used, the Cherenkov
light cone can be imaged and used for measuring particle momentum and
direction: this technique is used, for example, by Super-Kamiokande detector
(more information please see Walter (2008)).

The advantages of water-based detectors are the detection speed (on the order
of one nanosecond Beznosko et al. (2017)) and relatively lower cost since the
detection medium is water (typically, ultra-pure). However, the Cherenkov
signal is relatively weak. Other disadvantages are low to no mobility and the
insulation of high voltage electric components like PMT from the water.

### Scintillator-based particle detectors

The scintillators are the materials that produce a so-called scintillation
light in response to a charged particle passage in addition to Cherenkov
light. The main advantages of scintillators over water or glass as detection
medium is that there is about 10-15 times more scintillation light photons
than from Cherenkov radiation. Also, most scintillators are solid and the
detector is easily movable in most cases and does not require a lot of
additional external support, but there are liquid and even water-based
scintillators Bignell et al. (2015). Specifically, plastic scintillators are
lightweight and inert solids that can be used for production of detectors that
are suitable for installation at schools. In such cases, PMT cannot be used
due to high voltage being a hazard, but there are silicon versions of PMT that
work at the safe voltage such as SiPM, MPPC, MRS etc. Duspayev et al. (2016)
Beznosko (2009). Thus, scintillator-based detectors are most suited for CREDO
long-term outreach and educational goals. The main disadvantages are the cost
and a slower response when compared to Cherenkov light Beznosko et al. (2017)
– on the order of 10 ns for plastic and liquid scintillators, on the order of
100 ns for inorganic.

### Air fluorescence detectors

As the EAS disk travels through the air, the charged particles that comprise
it ionize the air molecules along the entire EAS path. As the electrons return
to their ground state, the energy is released as light. This light can be
collected by typically the collection of mirrors with multiple PMTs as light
detectors (there are various designs and detectors are used). The main
advantage for this method is that with some luck when viewed at the right
angle, an actual development of EAS can be captured and accurate estimates of
the properties of the parent particle can be made. The main con is that the
observations can be done only during Moonless and clear nights. Fluorescent
detectors are often combined with scintillator or water-Cherenkov detectors.
More information can be found in Tkachev and et al (2013).

### Radio signal detectors

As the EAS disk moves in the Earth magnetic field, the positive and negative
charges within it experience Lorentz force in opposite directions and radiate
in a radio frequency range around 30-80 MHz or so Aab and et al. (2016)
(Pierre Auger Collab.). This effect is highest for the EAS closer to the
horizon and moving perpendicular to the magnetic lines of Earth. While many
experiments are actively trying to use this method, it is a supplement to all
other detection methods listed.

###  5.3 The CREDO extension proposals

The involvement of non-scientists and outreach is one of the pillars for CREDO
collaboration. There are currently proposals to design and produce portable,
most likely scintillator-based EAS detectors that could be used at education
establishments (schools, universities) as both demonstrators and part of the
education process. The designs are all being proposed with the flash ADC
capabilities to utilize this expanded set of analysis techniques that involve
using advanced EAS timing information and possibly extend the searches for new
phenomena within EAS such as ‘unusual’ events described in Beisembaev et al.
(2019) Beisembaev and et al (2019).

One of such designs is CREDO-Maze, a project that will create a global, unique
physical apparatus, which will consist of a network of local (school)
measuring stations. The concept of the CREDO-Maze array was developed based on
the 20 years old Roland Maze Project Gawin et al. (2002); Feder et al. (2005).
The technology today has developed greatly and the local shower array idea of
Linsley Linsley (1985) can now be implemented much more easily and,
critically, much more cheaply. Eventually it is planned to equip high-schools
with sets of at least four professional portable cosmic ray detectors
connected locally and forming the small school EAS array. Feasibility of EAS
detection with such a mini-network was demonstrated in Ref. Karbowiak et al.
(2020) where pocket-size (sensitive surface of $\sim$ ($25cm^{2}$) affordable
(cost $\sim$ 100 $ / piece) scintillator detectors Axani et al. (2018) were
used. The CREDO-Maze project uses technologically sophisticated measuring
equipment in extracurricular activities: detectors of charged relativistic
elementary particles will be made of small ($0.02m^{2}$) plastic
scintillators. The light pulses will be collected by optical fibers shifting
the wavelength from ultraviolet to green and then light will be converted into
electrical signals by Silicon Photomultipliers. Further electronics will be
based on high speed digital circuits and microcontrollers to connect to
higher-level servers via the Internet and WiFi links. Prototypes of individual
components of the apparatus have been largely developed independently by
several institutions.

One of the important parameters of proposed equipment is the cost. It is easy
to build expensive and complicated, 100$\%$ effective professional arrays. We
are on the way of building the prototype which cost (including scintillators,
SiPMs, trigger electronics, storage and data transmission micro-computer) is
below 200 $ (compared to 3000 € per detector for $\mu$Cosmics detector in
Petropoulos et al. (2020). Prototypes of individual elements of the apparatus
have been largely developed independently in several partner academic centres:
University of Lodz, National Centre for Nuclear Studies and Institute of
Nuclear Physics in Poland, Institute of Experimental and Applied Physics, in
Czech Republic, Swinburne University of Technology in Australia. Completion of
the whole and its technical adaptation for replication will be one of the
interesting tasks of the project. It is an interesting concept to deliver to
some of the end-users (schools) kits, which are adapted for this purpose,
assembled only in basic, skill-intensive parts. This would allow students in
their local project groups to build and assemble from them a fully operational
and efficient whole, under the supervision, of course, of the staff of the
institutes managing the local project networks. The independent construction
of the operating scientific equipment is an additional motivating element and
undoubtedly increases the involvement of young people and the general interest
of those not participating in the project. These effects were observed in
previous attempts to implement similar activities on a smaller scale.

On the other side it should be mentioned that proposed devices are designed
and implemented in such a way that, while maintaining high standards, they are
as inexpensive as possible. Technologies will be developed to ensure that the
measurement kits can be duplicated and distributed to end users as “self-
assembly kits” with different degrees of sophistication of the finished
components. As potential business projects they will be able, together with
educational material pledges and software, to provide a ready-made market
product. With positive recommendations based on our research results, the
potential market, the demand of educational institutions, seems to be quite
considerable. The creation of local structures comprising young people
involved and organised in research groups (led by teachers/educators) using
network communication and based on science centres, as, e.g., higher education
institutions, universities, is an important step in the development and
institutional activities research performing organisations, including , as
well as research funding organisations. The proposed actions open up new areas
of innovation in non-formal non-school education. Creating a model system of
social communication networks and demonstrating its effectiveness in the
proposed field being an element of STEM will allow to plan and create similar
networks realized in other areas of education. There are no contraindications
for such networks to cover various groups of young people and research
centres.

Another concept of building a large scale cosmic-ray network is based on
engaging the wide community, thanks to the attractive properties and
portability of devices such as pixel cameras. A benchmark standard here is
Minipix Timepix-EDU, a hybrid semiconductor pixel detector, with a silicone
sensor of various thicknesses (e.g. 300, 500 $\mu m$) provided by ADVACAM adv
, using the technology developed within the Medipix Collaboration at CERN med
. This detector provides specific characteristics: fast-data acquisition,
portable, lightweight, easy to use and easy to place in difficult-to-access
environments, and can be operated remotely. Minipix Timepix EDU is a
simplified and price effective version of the Minipix Timepix detector. It was
designed and created with the purpose to make science accessible to the public
(schools, scientific research centers, non-commercial institutions). The
simplified version of the software Pixet, with predefined settings, makes it
possible to operate the detector without advanced training in data acquisition
just by connecting the device to the USB port of the PC.

Figure 11: Illustration of the Minipix Timepix EDU detector dedicated for
educational purposes, www.advacam.com, accessed on 22.09.2020.

The ASIC read–out chip contains a matrix of 256 by 256 pixels (total 65,536
independent channels) and an active sensor area of 14 mm by 14 mm, where one
pixel corresponds to 55 $\mu m$, see Fig. 11. The dark noise signal enables
measurements of low–Linear Energy Transfer (LET) particles with high
precision. Given to the per–pixel calibration, an adjustable threshold is made
in each pixel. This allows a detection efficiency close to 100% for heavy
charged particles, making these detectors unique and suitable for the
detection of cosmic rays.

### Online track visualization and processing software

The software package Pixet Pro (D. Turecek, J. Jakubek, 2020, Advacam s.r.o.,
Prague, Czech Republic) is used to operate the detector and to control the
readout, data acquisition and recording. The detectors can be connected to a
standard notebook using a USB 2.0 port. The PC connectivity and cross-platform
operating system compatibility includes Windows, Linux and Mac OS.

Figure 12: An example of per-pixel energy deposited by various particles in a
mixed radiation field measured using a Minipix Timepix detector with Silicone
sensor. The detector was operated in ToT-frame mode with an acquisition time
of 10 ms. Low-energy, narrow, curly tracks are typical for electrons, high-
energy, wide, straight tracks for energetic heavy charged particles such as
protons.

An example of a mixed field frame can be seen in Figure 12. Large roundish
blobs are created by alpha particles, long strikes by cosmic muons, curving
tracks by electrons or small dots by gamma or X-rays. Moreover, rare and
exotic events can be observed: Delta electrons, recoiled nuclei, cascade of
two or more nuclear transitions, proton tracks. According to the frame
occupancy the acquisition time can be set. Other parameters such as threshold
are already predefined. Further, the data can be processed as dose rates,
absorbed dose, fluence maps, energy deposited, LET spectra Granja and et al
(2016).

A notable role in the implementation of the CRE-oriented detection strategies
is also going to be played by professional, medium size detectors giving a
high quality signal.

Since 2018, low-background, digital gamma gamma-ray spectrometer with active
shield has been operating in a ground level laboratory in the Department of
Nuclear Physical Chemistry, Institute of Nuclear Physics Polish Academy of
Sciences (IFJ PAN), Krakow, Poland. The spectrometer is equipped with Broad
Energy Germanium detector BE5030 (Canberra, USA), multi-layer passive shield
and five large, plastic scintillators (Scionix, Netherlands), playing a role
of additional active shield (veto system). Areas of scintillation detectors
range from ca. 0.14 up to 0.49 m2. Data acquisition as well as signal
processing are performed by means of digital analyzer (so called digitizer)
DT5725 (CAEN, Italy) Gorzkiewicz et al. (2019).

The main role of both passive and active shielding is reduction of the
radiation background of the germanium detector. However, thanks to digital
data acquisition it has become possible to expand the research potential of
the constructed spectrometer. Registering and storing data generated by all
spectrometer’s detectors and using manifold, off-line data exploration
techniques allowed one to initiate continuous monitoring of the cosmic-ray
muon flux.

From the CREDO Project point of view, such device may be used as a reference
detector because scintillators register several dozen of muons per second and
thanks to their non-collinear orientation (Fig. 1 in Gorzkiewicz et al.
(2019)) it is possible to detect at least 3 muons correlated both
geometrically and in time. Preliminary research showed that during single
gamma-ray spectrometry measurement, that lasts 426721 s (about 5 days),
scintillators registered 329 events of 5-fold detection coincidences of muons
(Fig. 13) that could originate from air showers.

Figure 13: Distribution of maximum time intervals of 329 events of five-fold
coincidences registered by spectrometer’s active shield during single gamma-
ray spectrometry measurement (time of measurement 426721 s).

Additional advantage of continuous monitoring of cosmic-ray muons flux is the
possibility to investigate correlation of changes in its intensity and
Earthquakes that modulate the local geomagnetic field Kovalyov and Kovalyov
(2014).

###  5.4 Inter-detector communication

An important aspect of R$\&$D concerning the CRE detection feasibility is
communication between detectors constituting an array. It requires attention
especially in deployment areas with limited access to internet and/or
electricity, where data received by an individual detector cannot be
transferred directly to the central acquisition system. Communication might
also be critically important in situations which require some preprocessing of
the data collected by a subset of the array, before sending a trigger message
to the central system. The communication issues concerning the CRE-related
applications were addressed in Ref. Smelcerz and et al. (2020) (CREDO
Collab.). They are the subject of further ongoing investigations and
engineering works, below we briefly summarize the current status of these
efforts.

We focus on a scenario, when designing the network, which assumes that the
detectors are mobile devices that can be located in hard-to-reach areas, such
as deserts or forests, as in highly urbanized areas, i.e. cities, and even
inside blocks (Fig. 14). Such assumptions force the network to have the
following features:

  * •

scalability – it is easy to connect new devices to the network, the network
should be self-configuring

  * •

low energy consumption during data transmission – an indispensable parameter
to ensure support for mobile devices (without access to power from the
network)

  * •

universality – the network must operate both in dense urban buildings and in
desert or forest areas

  * •

wireless – provides the ability to collect data without the need for expensive
infrastructure in the form of cables and the need to use human force (manual
data collection from SD cards), in other words, significantly reduces the cost
of maintaining the project

  * •

as long range as possible – guarantees stable transmission without the need to
use re-transmitters or uneconomical use of too many gates

Figure 14: Symbolic diagram for the CREDO network scenario.

####  5.4.1 Solutions available on the market in wireless networks

In order to choose the right solution for wireless transmission in the CREDO
network, the solutions already existing on the market were compared in terms
of parameters important for the CREDO project. The results are presented in
Table 1. The table completely omits Bluetooth technology due to the very small
range (10-50m) blu , which does not meet the long range criterion.

Feature | ZigBeeZig  | LoRaLoR  | SigFoxSig  | WiFiWiF  | GPRSGPR
---|---|---|---|---|---
Frequency |  868/915 MHz and 2.4 GHz |  100 MHz to 1.67 GHz |  868/915 MHz |  2.4 GHz |  900–1800 MHz
Power consumption tx |  37 mW |  100 mW |  122 mW |  835 mW |  560 mW
Range |  100 m |  5 km |  10 km |  100 m |  1–10 km
Cons |  Requires infrastructure |  Available Gateways on the market are only for 438 and 868MHz |  Requires infrastructure similar to GSM (masts and receiving stations) |  No Internet connection in non-urbanized areas; high power consumption |  No access in non-urbanized areas; high power consumption
Suitable for battery devices? |  Yes |  Yes |  Yes |  No, too much power consumption |  No, too much power consumption
Table 1: Comparison of wireless communication solutions available on the
market.

Based on the table above, ZigBee, LoRa and SigFox were selected for testing
and deeper analysis. It is worth noting that the ranges given in the table are
the best result, often achievable only in an open area, not in built-up areas.
It was decided that all tests will be carried out in built-up areas,
considering city centers as the most problematic environment for establishing
long-range wireless communication. No retransmitters were used in the tests.
The first tests were conducted for the ZigBee network. We managed to achieve a
range of about 30m, similar to that presented by Kuzminykh et al. (2017).
Then, tests were carried out for the sigFox network Dis (a). Due to the
necessity to use ready-made SigFox infrastructure and the still incomplete
coverage of the area with this infrastructure, further development work using
this standard was abandoned. Finally, tests were carried out on LoRa modules
Dis (a, b). We did not manage to achieve satisfactory results (100-300 m).
Experiments carried out by Centenaro et al. (2016) in built-up areas in cities
that used the actual LoRa network and its ready infrastructure also did not
reach the maximum range of 5 km.

After the tests, it became clear to us that in order to obtain good coverage
both in the city without the use of repeaters, and in open areas, where there
is no network infrastructure. We need to develop our own system. We
immediately decided to work at lower frequencies (169 MHz) so as to minimize
the attenuation of waves by obstacles Saunders and Aragón-Zavala (2007).

####  5.4.2 Definition of CREDO Wireless Sensor Detector Network

The CREDO Wireless Sensor Detector Network (CREDO WSDN) is a fusion of the
well-known Wireless Sensor Network (WSN) currently used most frequently in
solutions for the Internet of Things (IoT).

CREDO WSDN is a wireless network, organized in a star topology, based on radio
waves at the frequency of 169MHz, used to transmit information to the Sink
collective station, from dedicated mobile cosmic ray detectors. Sink has a COM
connection to the PC station, which in turn is connected to the Internet. The
internet provides the end user (e.g. a scientist) with access to the collected
data. Additionally, additional sensors, such as humidity or temperature
sensors, can be connected to the CREDO WSDN to investigate the correlation
between events detected by the detectors and other parameters in the area.
Fig.15 presents the CREDO WSDN topology.

Figure 15: CREDO WSDN topology.

Due to the fact that the network is to be specially adapted to communication
on mobile devices (mobile detectors), in the current version of the system
communication is only one-way, i.e. the data from the detector is sent to
Sink. The radio transmitter will be integrated with the detector itself, not a
separate device as it was in the first version of the system. These measures
are primarily intended to reduce the power consumption of the detector itself,
which is to operate on battery power.
The CREDO network consists of several main elements, such as radio
communication on 169 MHz, a Sink station, a microcontroller or a power source.
The features and role of the most important elements of the entire system are
discussed below.

### Radio communication

Radio communication takes place at 169 MHz, unidirectional in a star topology.
These features ensure not only excellent coverage in built-up areas or in
buildings, but also the optimization of energy consumption – only the Sink
station must remain listening all the time. At the moment, the best result
that we have achieved is a range of 8 km in built-up areas.

### Transmitter

We plan to introduce a new version of the transmitter. This year, a new
STM32WL chip is to appear on the market – it is a microcontroller integrated
with the radio STM . It has excellent sensitivity and transmitter power. At
the same time the energy consumption is half less of the previous solution,
thanks to the use of a built-in impulse converter. Usually, such a solution
significantly worsens the sensitivity of the receiver, but this time it does
not have this effect. Additional feature will be that the same system will
count pulses caused by particle impacts.

### Receiving station (Sink)

The receiving station in current version already has very good sensitivity
Smelcerz and et al. (2020) (CREDO Collab.) however, as we plan to upgrade the
transmitters, there’s a prototype of a new receiving station as well,
currently during testing. The new version with a new LNA (Low Noise
Amplifiers) amplifier with lower noise and much lower distortion for now
increased the range by 4km compared to the previous version (from 4km to 8km).
A new version will be tested as well with several antennas to increase the
sensitivity.

### Mobile Detectors

The reason why the network was created was the need to handle the transmission
between battery-powered devices, and more specifically mobile cosmic ray
detectors. At the moment, the first prototype of the scintillation detector
has been developed, the tests are showing promising results, and the device is
already adapted to battery power.

### Microcontroller

The microcontroller acts as the brain of the entire system, makes decisions
about how to configure the network, when to transmit the collected data, and
informs Sink about the transmitter battery status. It is found both in Sink,
transmitting stations and in the detector.

####  5.4.3 CREDO network tests in the field

During the tests on the first version, it was possible to achieve a
satisfactory range of 4 km in built-up areas Smelcerz and et al. (2020) (CREDO
Collab.). Currently, after changes to the design of the transmitter and the
collection station (Sink), the range has increased to 8 km. Also there was
significant improvement in range in Elevated Areas (mountains). In the new
version of the receiving station, we managed to establish communication on a
cloudy day, in the area where the mountain was located. An interesting
phenomenon that we were able to observe was the reflection of the wave from
the stratosphere on a cloudy day (Fig. 16) Saunders and Aragón-Zavala (2007).

Figure 16: Reflection of the radio wave. Saunders and Aragón-Zavala (2007)

####  5.4.4 Future work and conclusion

The CREDO communication system, thanks to its scalability and universality,
can be used in many areas of IoT and can be an alternative to existing
solutions, where due to the lack of infrastructure or too high costs of their
implementation, they cannot be launched. There are still many challenges ahead
of us, we are constantly working on increasing the range. Maintaining security
in the network and possibly encrypting data is also a challenge. The
phenomenon that we want to study better is the reflection of waves from the
stratosphere. We will also be conducting tests with new mobile scintillation
detectors in the near future, which will be immediately integrated with
transmitting stations.

###  5.5 Detection efficiency

Independently of the available cosmic ray infrastructures and expertise that
is or might be contributing to the implementation of the CREDO strategies, the
novel hardware extensions of the global network of detectors require new
studies and tools providing information of detection efficiency on different
identification and reconstruction levels: a) individual particles and the
corresponding detection rates, b) extensive air showers and the corresponding
cosmic-ray fluxes, and finally c) Cosmic Ray Ensembles. The level a) is being
addressed elsewhere within this Special Issue Bibrzycki and et al. (2020)
(CREDO Collab.), considerations of level c) were initiated with Ref. Verbetsky
and Svanidze (2020), and a study dedicated to arrays of portable detectors
like CREDO-Maze described above is under preparation.

##  6 Data management and analysis

###  6.1 CREDO IT Infrastructure

From its very beginning the CREDO initiative assumed a necessity for a
scalable data acquisition and processing infrastructure. While most of the
infrastructure is supplied by volunteers, in the form of smartphones and other
detectors, there still exists a need to create a central repository of
detection events. Information about each individual detection event is
recorded first by the end device, then it is transferred to the central
repository. This repository allows for managing and sharing information among
interested parties, it serves as a base for CREDO data analysis. It also
fulfills the role of the system’s central point, providing APIs (Application
Programming Interface) and information about stored data itself. The CREDO it
ecosystem, with some of the implementation details, is depicted in Figure 17.

Figure 17: Diagram representing the architecture of storage application.

The CREDO data repository uses a dedicated API, tailored for the project’s
needs. The object structure used in the API closely models the information
about physical detection events and additionally contains metadata, e.g. what
detector was used or what was the operating time of the detector. Data storage
in CREDO project is provided with respect to the FAIR principles Wilkinson et
al. (2016), namely we provide means to Find the data, Access it, enable
Interoperability and Reuse of the data. One of the means to achieve this goal
is the API, which was implemented as a set of REST services adhering to the
OpenAPI standard ope . OpenAPI is a widely accepted service standard, which
includes community-developed guidelines for developing interfaces exposing
data and metadata. This standard focuses on data openness, technical
accessibility and discoverability, which allow for effortless integration. The
stored data is publicly accessible, and so it will be in the future, which
should enable the reuse of information and verification of experiments based
on the given data.

Central processing for CREDO data storage was implemented as an extensible
database, a storage system running in a containerized environment with aim to
enhance reliability, portability and security. The main component, responsible
for gathering and managing data, was implemented as a Django dja  web
application. User devices communicate with the API exposed by the main
application, the data is subjected to basic filtering and then placed in the
storage back end. The storage is supplied through the usage of MariaDB mar
relational database cluster. Redis red , a key-value in memory object store is
used as a temporary cache, implemented in order to speed up queries and data
presentation. The external service providing S3 compatible access is used for
backups and exporting, prepared beforehand, larger chunks of data.

Due to the nature of observed physics phenomena and the community factor, data
stream characteristics are often difficult to predict. Additionally, data
analysis is done mainly in an exploratory manner, so the underlying hardware
infrastructure needs to be flexible enough to adapt to requirements of the
moment. The presented system has been deployed in a production environment (in
this case, virtual machines are hosted in the cloud provided by ACC Cyfronet
AGH) and is continuously gathering information about detection events from the
CREDO detector network. There are several performance metrics, i. e. CPU usage
and request latency, which are constantly monitored thus allowing us to
determine if the current hardware configuration delivers required performance.
In the case of inadequate resources, the cloud management system is able to
autonomously and proactively spawn additional service instances which will
allow for load distribution and handling of the data influx.

It is important to emphasize that the adopted solutions and protocols enable
two-end open access: data collected by various detectors can be transmitted to
the central system if only their format is kept compatible with the CREDO API
structure, and also the access to the data being stored centrally is being
granted to everybody upon request including a sensible motivation. The web-
based monitor of the CREDO data acquisition system including basic user and
detection statistics is available publicly api  and the technical information
regarding the full data access is being provided upon approving of individual
requests.

###  6.2 The current data set

Regardless of the ongoing efforts concerning the FAIR principles, the CREDO
data set is continuously available on request for individual users if a
sensible motivation for the usage is presented. In addition, all the currently
available scripts and tools facilitating data access, selection, and further
processing are made freely available in the public CREDO Collaboration
repository cre  as a project that can be imported into the PyCharm integrated
development environment Pyc .

The CREDO data set is divided into three basic categories:

  1. 1.

Detections – a set of detections containing detailed information about
individual events on all devices;

  2. 2.

Pings – activity logs of devices, including the information about their
connections to the database and time of work in the detecting mode;

  3. 3.

Mappings – three collections containing information about users, devices and
teams.

Most of the data collected by CREDO to date comes from smartphones with the
CREDO Detector app, operating on the Android system. The data statistics since
the premiere of the app until September 1, 2020 includes:

  * •

11,150 users (unique accounts) have registered

  * •

15,739 devices were used for particle detection

  * •

4,941,133 candidate detections registered

  * •

the total operating time of the devices is over 379,629 days (over 1039 years)

The raw data files currently occupy 44 GB (detections: 39.3 GB; pings: 1.6 GB;
mappings: 3.1 GB). Assuming the single CMOS camera sensor has a diagonal in
size of $1/3^{\prime\prime}$ (on average), the total area of all the presently
registered devices is 0.56 m2. The daily average value of detections per
device calculated from the number of candidate detections registered and the
number of total operating time of the devices is about 13 candidate detections
registered daily. Currently standard data filtering and clusterization are
being performed continuously, and very early results show a perspective for
more advanced image processing and classification using machine learning or
deep learning techniques to perform more efficient classification of candidate
detections.

A single detection record is stored in JavaScript Object Notation (JSON) open
standard data format and it contains the following information:

  1. 1.

user – detection user information: “team_id”, “user_id”;

  2. 2.

location – geographical coordinates: “latitude”, “longitude”;

  3. 3.

time – detection time information: “timestamp” (detection unix time in
milliseconds), “time_received”: reception time in the database;

  4. 4.

picture – detection image information: “id” (unique detection identification),
“frame_content”: image (a fragment of the snapshot, typically containing a
margin of 30 pixels around the brightest pixel position – see below) code in
base64, “height”: resolution “vertical” dimension, “width”: resolution
“horizontal” dimension;

  5. 5.

server side visibility – “visible” (tells whether a detection pass through the
server side filters, sensitive e.g. to repeatedly flashing pixels or
incompatible versions of the applications sending the data);

  6. 6.

brightest pixel position – “x”, “y” (row and column number of the brightest
pixel).

It often happens that a single picture taken by a smartphone in the detection
mode contains more than one pixel that fulfill trigger conditions and can be
classified as detections. If these pixels are located sufficiently far one
from another, i.e. more than the extraction margin explained in p. 4 above,
then they are considered separate detections and each of them is assigned an
individual detection record. In this way clearly distinguishable particle hits
collected in one shot are easily identifiable as detections with the same
“timestamp”. An example set of particle track candidates collected by CREDO
Detector is presented in Fig. 18.

Figure 18: Example particle candidate tracks recorded with a smartphone using
the CREDO Detector mobile application. [source: the CREDO Collaboration
materials and measurements]

The nature of the penetrating radiation measurements made by CMOS sensors
assumes identification of pixels that are significantly brighter than the
background. The currently used algorithms allow such identification only when
the visible light does not reach the sensor, i.e. with the smartphone camera
covered tightly. Intentional or unintentional uncovering of the smartphone
camera might result in collecting images generated by visible light, sometimes
hardly distinguishable from signal excesses induced by penetrating particles
(see Fig. 19 for some examples).

Figure 19: Example artifact tracks recorded with a smartphone using the CREDO
Detector mobile application. [source: the CREDO Collaboration materials and
measurements]

One might apply a specific software filter to remove such a contamination from
the data sample being analysed. The internally available preliminary studies
in this direction show that the number of bright pixels that compose the image
might be a sufficient data quality measure. The rule of thumb currently used
within the CREDO Collaboration is based on the data collected by a number of
“trustable” devices (operated by non-anonymous team members engaged in the
application development) and it shows that one does not expect detections of
penetrating particles that generate tracks composed of more than 70 pixels
with brightness above 70, in the 0-255 scale.

Another type of contamination is the electronic noise which typically gives
images composed of individual (or very few) bright pixels only that are being
recorded very frequently compared to the expected detection frequency of the
cosmic and local radiation. These electronic artifacts can be “detected” e.g.
if the pixel brightness threshold is improperly set, and such a situation can
be identified by monitoring the detection frequency and comparing it to the
expected 100$\%$ sensor efficiency for the sensor in use. For an example, a
typical CMOS sensor in a smartphone with a surface of 0.2 cm2 can see at most
one cosmic background muon in 5 minutes (the expected integrated background
muon flux is 1/cm2/minute). Assuming that the local radioactive sources might
induce a signal at most $\sim$10 times more often, one does not expect
detection rates larger than 2/minute, and this is in fact the case when
looking at the statistics collected from the reference (“trustable”) devices.
An example of the corresponding filter being used with the CREDO Collaboration
requires that detection frequency is less than 10 detections with different
timestamps per minute.

Despite the fact that with full access to the raw data sets users are able and
welcome to apply their own filters and perform their own analyses, the CREDO
Collaboration will periodically release its official data sets and
recommendations concerning the data quality which will be based on the
appropriate and publically available studies. If it comes to scientific
results, the researchers will be expected either to refer to the official data
sets, or to describe and justify their own selections.

The examples of the already ongoing analyses concerning the CREDO data set
include image classification based on the shapes of particle track candidates
Niedzwiecki and et al. (2019) (CREDO Collab.), monitoring detections collected
by individual devices in search for temporal event clustering in 5 minute
intervals Eur  and muon identification and zenith angle reconstruction based
on the lengths of the rectilinear particle tracks Karbowiak and et al. (2020)
(CREDO Collaboariton).

One of the examples of novel and promising directions of analyses related to
the CREDO data is exploitation of the techniques of cyclostationary signal
processing and its generalizations Napolitano (2012), Napolitano (2019).
Cyclostationarity is a statistical property of science data generated by the
combination/interaction of periodic and random phenomena. That is, these data
have second- or higher-order statistical functions that are periodic functions
of time. More general models can account for the presence of multiple,
possibly incommensurate, and irregular periodicities (Napolitano, 2019,
Chapters 1,2). The observed signals are not periodic, but the hidden
periodicity can be restored by estimating statistical functions from the data.
These statistical functions contain information of the generating mechanism of
the data that cannot be extracted starting from the classical stationary
modeling of the observed signals.

The extensions of cyclostationarity can be of interest if time dilation
effects have to be accounted for (Napolitano, 2012, Chapter 7). In particular,
the effects of constant relative radial speed and/or constant relative radial
acceleration between cosmic source and receiver can be suitably modeled by
exploiting the generalizations of cyclostationarity. General time-warping of
the source signal can be modeled by new and recently proposed signal models
(Napolitano, 2012, Chapter 6), (Napolitano, 2019, Chapters 12-14).

Source location and parameter estimation problems based on measurements taken
at sensors very far apart separated are very interference tolerant if the