2021

[7,8]M. Bertaina [7,8,53]F. Fenu Deceased. This paper is dedicated to Yoshiya
Kawasaki who contributed significantly to the ESAF developments during the
JEM-EUSO mission.[8,16,21,38]Z. Plebaniak

1]Nihon University Chiyoda, Tokyo, Japan 2]University of Alabama in
Huntsville, Huntsville, AL, USA 3]Université de Paris, CNRS, AstroParticule et
Cosmologie, F-75013 Paris, France4]Lehman College, City University of New York
(CUNY), NY, USA5]INAF - Istituto di Astrofisica Spaziale e Fisica Cosmica di
Palermo, Italy 6]Istituto Nazionale di Fisica Nucleare - Sezione di Catania,
Italy 7]Istituto Nazionale di Fisica Nucleare - Sezione di Torino, Italy
8]Dipartimento di Fisica, Università degli Studi di Torino, Via Pietro Giuria
1, Torino, 10125, Italy 9]Institut universitaire de France (IUF) 10]Institute
for Astronomy and Astrophysics, Kepler Center, University of Tübingen,
Germany11]Istituto Nazionale di Fisica Nucleare - Sezione di Bari,
Italy12]Università degli Studi di Bari Aldo Moro, Italy13]Skobeltsyn Institute
of Nuclear Physics, Lomonosov Moscow State University, Russia14]NASA Marshall
Space Flight Center, Huntsville, AL, USA15]Karlsruhe Institute of Technology
(KIT), Germany16]Istituto Nazionale di Fisica Nucleare - Sezione di Roma Tor
Vergata, Italy17]RIKEN, Wako, Japan18]Slovak Academy of Science, Institute of
Experimental Physics, Kosice, Slovakia19]KTH Royal Institute of Technology,
Stockholm, Sweden20]University of Chicago, IL, USA21]Università di Roma Tor
Vergata - Dipartimento di Fisica, Roma, Italy22]Istituto Nazionale di Fisica
Nucleare - Sezione di Napoli, Italy23]Max Planck Institute for Physics,
Munich, Germany24]Dipartimento di Fisica e Astronomia “Ettore Majorana”,
Università di Catania, Italy25]Osservatorio Astrofisico di Torino, Istituto
Nazionale di Astrofisica, Pino Torinese, Italy 26]Joint Laboratory of Optics,
Faculty of Science, Palacký University, Olomouc, Czech Republic27]Università
di Napoli Federico II - Dipartimento di Fisica “Ettore Pancini”,
Italy28]Uninettuno University, Rome, Italy29]Space Science Laboratory,
University of California, Berkeley, CA, USA30]Omega, Ecole Polytechnique,
CNRS/IN2P3, Palaiseau, France31]Colorado School of Mines, Golden, CO,
USA32]Institute for Cosmic Ray Research, University of Tokyo, Kashiwa,
Japan33]Universidad de Alcalá (UAH), Madrid, Spain34]Konan University, Kobe,
Japan35]ECAP, University of Erlangen-Nuremberg, Germany36]NASA Goddard Space
Flight Center, Greenbelt, MD, USA37]Institute of Physics of the Czech Academy
of Sciences, Prague, Czech Republic38]National Centre for Nuclear Research,
Otwock, Poland39]University of Utah, Salt Lake City, UT, USA40]Lab. of Math.
and Sub-Atomic Phys. (LPMPS), Univ. Constantine I, Constantine,
Algeria41]National Astronomical Observatory, Mitaka, Japan42]University of
Iowa, Iowa City, IA, USA43]Joint Institute for Nuclear Research, Dubna,
Russia44]Sungkyunkwan University, Seoul, Republic of Korea45]Faculty of
Physics, University of Warsaw, Poland46]Istituto Nazionale di Fisica Nucleare
- Laboratori Nazionali di Frascati, Italy47]Space Regatta Consortium, Korolev,
Russia48]Hokkaido University, Sapporo, Japan49]Shinshu University, Nagano,
Japan50]ISDC Data Centre for Astrophysics, Versoix, Switzerland51]Centre for
Development of Advanced Technologies (CDTA), Algiers, Algeria52]Fairfield
University, Fairfield, CT, USA53]Agenzia Spaziale Italiana, Via del
Politecnico, 00133, Roma, Italy 54]IRAP, Université de Toulouse, CNRS,
Toulouse, France 55]Center for Pulsed Lasers (CLPU), Spain 56]Pennsylvania
State University, PA, USA 57]Department of Physics and Astronomy, University
of California, Irvine, USA

# Developments and results in the context of the JEM-EUSO program obtained
with the ESAF Simulation and Analysis Framework

S. Abe  J.H. Adams Jr  D. Allard  P. Alldredge  L. Anchordoqui  A. Anzalone
E. Arnone  B. Baret  D. Barghini  M. Battisti  J. Bayer  R. Bellotti
A.A. Belov<EMAIL_ADDRESS>P.F. Bertone  M. Bianciotto  P.L. Biermann
F. Bisconti  C. Blaksley  S. Blin-Bondil  P. Bobik  K. Bolmgren
S. Briz  J. Burton  F. Cafagna  G. Cambié  D. Campana${}^{\textmd{22}}$
F. Capel  R. Caruso  M. Casolino  C. Cassardo  A. Castellina
K. Černý  M.J. Christl  R. Colalillo  L. Conti  G. Cotto  H.J. Crawford
R. Cremonini  A. Creusot  A. Cummings  A. de Castro Gónzalez
C. de la Taille  L. del Peral${}^{\textmd{33}}$ R. Diesing  P. Dinaucourt  A.
Di Nola
A. Ebersoldt  T. Ebisuzaki  J. Eser<EMAIL_ADDRESS>S. Ferrarese
G. Filippatos  W.W. Finch  F. Flaminio  C. Fornaro  D. Fuehne
C. Fuglesang  M. Fukushima  D. Gardiol  G.K. Garipov  A. Golzio
P. Gorodetzky  F. Guarino  C. Guépin  A. Guzmán  A. Haungs  T. Heibges
J. Hernández Carretero${}^{\textmd{33}}$ F. Isgrò  E.G. Judd  F. Kajino  I.
Kaneko
Y. Kawasaki  M. Kleifges  P.A. Klimov  I. Kreykenbohm  J.F. Krizmanic
V. Kungel  E. Kuznetsov  F. López Martínez  S. Mackovjak  D. Mandát
M. Manfrin  A. Marcelli  L. Marcelli  W. Marszał  J.N. Matthews  A. Menshikov
T. Mernik  M. Mese  S.S. Meyer  J. Mimouni  H. Miyamoto  Y. Mizumoto
A. Monaco  J.A. Morales de los Ríos${}^{\textmd{33}}$ S. Nagataki  J. M.
Nachtman  D. Naumov
A. Neronov  T. Nonaka  T. Ogawa  S. Ogio  H. Ohmori  A.V. Olinto  Y. Onel
G. Osteria${}^{\textmd{22}}$ A. Pagliaro  B. Panico${}^{\textmd{27, 22}}$ E.
Parizot  I.H. Park${}^{\textmd{44}}$ B. Pastircak
T. Paul  M. Pech  F. Perfetto${}^{\textmd{22}}$ P. Picozza  L.W. Piotrowski
<EMAIL_ADDRESS>
J. Posligua  R. Prevete  G. Prévôt  H. Prieto${}^{\textmd{33}}$ M. Przybylak
M. Putis
E. Reali  P. Reardon  M.H. Reno  M. Ricci  M.D. Rodríguez
Frías${}^{\textmd{33,55}}$ G. Romoli
G. Sáez Cano${}^{\textmd{33}}$ H. Sagawa  N. Sakaki  A. Santangelo  O.A.
Saprykin  F. Sarazin
M. Sato  H. Schieler  P. Schovánek  V. Scotti  S. Selmane  S.A. Sharakin
K. Shinozaki  J.F. Soriano  J. Szabelski  N. Tajima  T. Tajima  Y. Takahashi
M. Takeda  Y. Takizawa  C. Tenzer  S.B. Thomas  L.G. Tkachev  T. Tomida
S. Toscano  M. Traïche  D. Trofimov  K. Tsuno  P. Vallania  L. Valore
T. M. Venters  C. Vigorito  P. von Ballmoos  M. Vrabel  S. Wada  J. Watts Jr
A. Weindl  L. Wiencke  J. Wilms  D. Winn  H. Wistrand  I.V. Yashin  R. Young
M.Yu. Zotov  [  [  [  [  [  [  [  [  [  [  [  [  [  [  [  [  [  [  [  [  [  [
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###### keywords:

JEM–EUSO, Monte Carlo Simulations, ESAF

##  1 Introduction

The study of Ultra-High Energy Cosmic Rays (UHECRs) and the understanding of
particle acceleration in the cosmos is of utmost importance for astro-particle
physics as well as for fundamental physics. The current main goals are to
identify sources of UHECRs and their composition. UHECRs above $5\times
10^{19}$ eV have a flux lower than 1 event per century per square kilometer
auger , therefore, huge sensitive volumes are necessary to collect enough
statistics.

A space-based detector for UHECR research has the advantage of a very large
exposure and a uniform coverage of the celestial sphere. The idea of space-
based observation of UHECRs was first proposed by John Linsley in the late 70s
with the SOCRAS concept linsley . The principle of observation is based on the
detection of UV light emitted by isotropic fluorescence of atmospheric
nitrogen excited by Extensive Air Showers (EAS) in the Earth’s atmosphere and
forward-beamed Cherenkov radiation diffusely reflected from the Earth’s
surface or dense cloud tops. In 1995 Linsley’s original idea was re-adapted by
Yoshiyuki Takahashi into the MASS concept takahashi  which evolved in 1996, in
the US, into the OWL mission owl . In parallel the MASS, or Airwatch concept
as it was later on renamed, evolved in Europe into EUSO, the Extreme Universe
Space Observatory. Livio Scarsi first proposed EUSO as a free-flyer to the
European Space Agency’s (ESA) F2/F3 f2f3Esa  call in 2000. ESA selected the
mission but recast it as a payload for the Columbus module of the
International Space Station (ISS) euso . The phase-A study for the feasibility
of EUSO, started in 2001 and was successfully completed in March 2004.
Although EUSO was found technically ready to proceed into phase B, ESA did not
continue the program.

In 2006, the Japanese and US teams, under the leadership of Yoshiyuki
Takahashi, redefined the mission as an observatory attached to KIBO, the
Japanese Experiment Module (JEM) of the ISS. They renamed the mission JEM–EUSO
and started a new phase-A study targeting launch in 2013 in the framework of
the second utilization phase of the JEM/EF (Exposure Facility) yoshi-jemeuso .
The Phase A/B1 study of JEM–EUSO led by Japan Aerospace Exploration Agency
(JAXA) continued with extensive simulations, design, and prototype
developments that significantly improved the JEM–EUSO mission profile (see
Fig. 1), targeting a launch in 2016 jemeuso .

Figure 1: Panel a): Conceptual view of the whole JEM–EUSO system. Panel b):
Conceptual design of the JEM–EUSO system: three Fresnel lenses focus the light
on the focal surface. Panel c): Conceptual design of the JEM–EUSO Focal
Surface with its elements and sub-elements parts. The focal surface of the
detector is formed by 137 Photo Detector Modules (PDMs) comprising of $\sim
5000$ Multi-Anode Photo-Multiplier Tubes (MAPMTs) in total (36 MAPMTs per PDM,
64 pixels each). Each PDM is composed by 9 Elementary Cells (ECs). See the
text for details. Figure adapted from ea-instrument .

As a result of this study, the main telescope was designed with a wide Field-
of-View (FoV; $\sim 0.85$ sr) optics composed of three Fresnel lenses.
Different configurations have been studied: the “side-cut” version of the
instrument with a 2.65 m major axis and 1.9 m minor axis (4.5 m2 optical
aperture) to fit in the cargo of the JAXA HTV rocket as described in exposure
and the SpaceX Dragon option with 2.5 m diameter circular optics ea-instrument
. The difference between the two configurations is shown in Fig. 2. The use of
Fresnel lenses realized in Poly(Methil MethAcrylate) - PMMA - allows building
a refractor telescope capable of meeting the requirements of a large optical
system with wide FoV with the constraints of a spaceborne experiment.
Furthermore, the reduced thickness of the lenses allows to reduce the mass of
the optics resulting in a light system capable of withstanding launch
vibration and thermal expansion.

Figure 2: A diagram of the position of the MAPMTs of the Dragon configuration
(blue) of JEM–EUSO superimposed on the same diagram for the HTV configuration
(red). Image taken from guzman-icrc2015 .

The telescope records the EAS-induced tracks with a time resolution of
$2.5~{}\mu$s, known as a Gate Time Unit (GTU). The Focal Surface (FS) detector
is formed by 137 Photo Detector Modules (PDMs) comprising of $\sim 5000$
Multi-Anode Photo-Multiplier Tubes (MAPMTs) in total (36 MAPMTs per PDM, 64
pixels each). Each PDM is composed by 9 Elementary Cells (ECs). One EC is
composed by 4 MAPMTs, 64 pixels each. The FS detector is highly pixelated in
$\sim 3\times 10^{5}$ channels providing a pixel FoV of $\sim 0.074^{\circ}$,
equivalent to $\sim 0.5$ km at ground seen from an altitude of $\sim 400$ km.
An optical filter is placed in front of the MAPMTs to select photons mainly in
the fluorescence bandwidth (290–430 nm).

In 2013 it became clear that JEM–EUSO could not proceed further within the
JAXA leasdership. The mission was put on hold status and JEM–EUSO was
reoriented as an extensive pathfinder program, with the acronym redefined as
the Joint Experiment Missions for Extreme Universe Space Observatory EUSO-
program . The program includes several missions from ground (EUSO–TA eusota ),
on board of stratospheric balloons (EUSO–Balloon eusobal , EUSO–SPB1 spb1 ,
and EUSO–SPB2 spb2 ), and from space (TUS tus  and Mini–EUSO minieuso ). Each
employs fluorescence detectors to test the observational technique, and to
validate the technology. The final goal of the program is the realization of a
large space-based mission following the concepts developed in the past
decades, namely the medium-size K–EUSO keuso  and the large-size POEMMA poemma
missions.

All these detectors demand extensive simulation work to estimate their
performance and to support the analysis of the collected data. It was clear at
the time of the JEM–EUSO mission that the most efficient way was to re-adapt
the existing software instead of developing totally new code. For this reason,
the two official software packages adopted by JEM–EUSO are the Euso Simulation
and Analysis Framework (ESAF) berat , originally developed within the EUSO
project, and the $\overline{\mbox{Off}}\underline{\mbox{Line}}$ package
offline  designed for the Pierre Auger Observatory auger-nim . A comparison
between the two frameworks and their designs is reported in spb2  while
examples of cross-checks carried out in the past on their relative performance
is summarized in Appendix C. The main motivations to adopt both packages are:
a) it is straightforward to re-adapt the EUSO code to the JEM–EUSO
configuration; b) $\overline{\mbox{Off}}\underline{\mbox{Line}}$ output is
extensively tested within the Auger project and thus with experimental data;
c) the possibility to adopt both packages gives opportunities for cross-
checks. A synthetic description of the developments performed with the
$\overline{\mbox{Off}}\underline{\mbox{Line}}$ software to accommodate the
different configurations of the telescopes of the JEM–EUSO program can be
found in tom-offline . In this paper we summarize developments and performance
results obtained with ESAF, including some of those already discussed in
earlier publications.

The main objective of this paper is to demonstrate the potential and
flexibility of the ESAF software and its applications in the context of the
JEM–EUSO program. A comparison with experimental data is provided to show the
utility of the ESAF software in the interpretation of the data. The paper is
structured in the following way. Section 2 outlines the detector
characteristics of the different projects of the JEM–EUSO program which have
been implemented in ESAF. Section 3 summarizes the main features of the ESAF
framework while Section 4 reports the new ESAF developments performed within
the JEM–EUSO program. Section 5 provides the key results obtained with
simulations for the different detector configurations implemented in the
software, namely JEM–EUSO, POEMMA, K–EUSO, Mini–EUSO, TUS, EUSO–SPB1 and
EUSO–TA as well as comparisons with data. The conclusions and perspectives are
the subject of Section 6.

##  2 The missions of the JEM-EUSO program

In this section we summarize the different configurations implemented in ESAF
to simulate the performance of the various projects of the JEM-EUSO program
which have been defined since the original JEM-EUSO mission was put on hold. A
comparison of the main parameters of the different configurations is presented
in table 1.

K–EUSO is the result of the joint efforts to improve the performance of the
Russian KLYPVE mission klypve  by employing the technologies developed for the
JEM–EUSO mission, such as the focal surface detectors and the readout
electronics. The KLYPVE mission, named after Russian words “ultra-high energy
cosmic rays” has undergone pre-phase A study, including launch and
accommodation on the ISS. Since its first conception as KLYPVE, the K–EUSO
project has passed various modifications aimed to increase the FoV and UHECR
statistics keuso1 ; keuso2 , compatibly with shipping possibilities using the
Soyuz spacecraft and to decrease the number of external vehicle activities by
the astronauts. All the different improved solutions have been implemented in
ESAF. We report in Section 5 on the expected performance of the latest version
of the instrument under study fenu-keuso2021 ; keuso  (see Fig. 3a)).

In this configuration, the detector consists of a refractive optical system of
$1400~{}\text{mm}\times 2400~{}\text{mm}$ size. The optics is based on two
Fresnel lenses that focus the light onto a focal surface of
$1300~{}\text{mm}\times 1000~{}\text{mm}$ size. The FS consists of 44 PDMs.
Each pixel has a field of view of 0.1∘ which corresponds to $\sim$700 m on the
ground. The time resolution is in the process of being optimized and ranges
from 1 $\mu$s to 2.5 $\mu$s. The exact value will be based on a trade-off
between the limited hardware and telemetry budgets and the need of a good time
resolution. In the following, the 2.5 $\mu$s GTU has been adopted for
simulations.

The Probe Of Extreme Multi-Messenger Astrophysics (POEMMA) design poemma
combines the concept developed for the OWL mission and the experience of
designing the JEM–EUSO fluorescence detection camera. POEMMA is composed of
two identical satellites flying in formation at an altitude of 525 km with the
ability to observe overlapping regions during moonless nights at angles
ranging from nadir to just above the limb of the Earth, but also with
independent pointing strategies to exploit at maximum the scientific program
of the mission.

Figure 3: Scheme of the simulated K–EUSO detector (panel a) and of the POEMMA
telescope (panel b). Figure adapted from keuso  and poemma .

Each telescope (see Fig. 3b)) is composed of a wide (45∘) FoV Schmidt optical
system with an optical collecting area of over 6 m2. The focal surface of
POEMMA is composed of a hybrid of two types of cameras: about 90% of the FS is
dedicated to the POEMMA fluorescence camera (PFC), while the POEMMA Cherenkov
camera (PCC) occupies the crescent moon shaped edge of the FS which images the
limb of the Earth. The PFC is composed of 55 JEM–EUSO PDMs based on MAPMTs for
a total of $\sim$130,000 channels. The GTU for the PFC is 1 $\mu$s. The much
faster POEMMA Cherenkov camera (PCC) is composed of Silicon Photo-Multipliers
(SiPMs) which is tested with EUSO–SPB2.

The world’s first orbital detector aiming at detecting UHECRs was the Tracking
Ultraviolet Setup (TUS) UV telescope, launched on April 28, 2016 as a part of
the scientific payload of the Lomonosov satellite tus , see Fig. 4.

Figure 4: Artist’s view of the TUS detector on board the Lomonosov satellite
(left) and preflight preparations at the Vostochny cosmodrome (right).

TUS provides the first opportunity to compare ESAF simulations to real data
taken from space. Some examples can be found in tus-jcap  and are reported
here. The instrument recorded data until the end of November 2017. Different
scientific modes were tested: cosmic ray, lightning and meteor modes. The
satellite had a sun-synchronous orbit (i.e. passing over any given point of
the earth surface at the same local mean solar time) with an inclination of
97.3∘, a period of $\sim 94$ min, and a height of 470–500 km. The TUS
telescope consisted of two main parts: a modular Fresnel mirror-concentrator
with an area of $\sim 2~{}\text{m}^{2}$ and 256 PMTs arranged in a $16\times
16$ photo-receiver matrix located in the focal plane of the mirror. The FoV of
one pixel was 10 mrad, which corresponds to a spatial spot of $\sim
5~{}\text{km}\times 5~{}\text{km}$ at sea level. Thus, the full area observed
by TUS at any moment was $\sim 80~{}\text{km}\times 80~{}\text{km}$. TUS was
sensitive to the near-UV band and had a time resolution of 0.8 $\mu$s in the
cosmic ray mode, with a full temporal window of 256 time steps. TUS data offer
the opportunity to develop strategies in the analysis and reconstruction of
events which will be essential for future space-based missions.

Mini–EUSO minieuso  is an UV telescope launched in August 2019 and installed
periodically inside the ISS, with installations occurring every couple of
weeks since October 2019. Mini-EUSO is installed looking down on the Earth
from a nadir-facing window in the Russian Zvezda module (see Fig. 5). So far
$\sim$80 sessions of about 12 hours of data taking have been performed.

Figure 5: Mini–EUSO attached to the Zvezda module on the ISS (left) and
schematic view of the different parts of the Mini–EUSO detector (right).

Mini–EUSO maps the Earth in the UV range (290 - 430 nm) with a spatial
resolutions of $\sim$6 km (similar to TUS) and three different temporal
resolutions of 2.5 $\mu$s, 320 $\mu$s, and 41 ms operating simultaneously.
While the 41 ms time range allows continuous video-taking, the other two modes
allow acquisitions of 4 packets of 128 GTUs each every 5.24 s when the trigger
condition is satisfied, to catch fast luminous transients (flashes, lightning,
etc.). The optical system consists of 2 Fresnel lenses of 25 cm diameter each
with a large FoV of $\sim$44∘. Data carried down to Earth from the ISS allowed
for the first analyses showing that Mini–EUSO observes different Earth
emissions depending on the surface visible, e.g., ground, sea, or clouds as
well as slow transients such as meteors. Tens of thousands of meteor events
have been identified in the data with absolute magnitude lower than +5 (the
events last typically in the order of 1 second). At shorter times scales
(typically hundreds of $\mu$s), several hundreds of lightning associated
signals (among them 26 elves) have been detected. In addition, many
anthropogenic flashes presumably related to airport lights or other flashing
tower lights have been acquired. A summary of the most recent results of
Mini–EUSO can be found in minieuso-uv .

While TUS was conceived mainly to prove the observation of UHECRs from space
with a FS-instrumentation similar to ground-based detectors, Mini–EUSO has
been developed in order to test the same FS-instrumentation foreseen for
K–EUSO and POEMMA. Moreover, it is important to recall that Mini–EUSO was
designed to detect similar photoelectron counts per pixel as JEM–EUSO in the
case of diffused light sources. This is done by compensating the
$\sim$$10^{-2}$ times optics aperture with $\sim$$10^{2}$ times wider pixel
FoV. Therefore, these results on diffuse light sources are representative of
observations of the future large missions K–EUSO and POEMMA, which have
similar apertures and instantaneous FoV. As a consequence, Mini–EUSO energy
threshold for UHECRs is well above $10^{21}$ eV as explained in Section 5.

The JEM–EUSO program includes stratospheric balloon missions with increasing
level of performance and upgraded designs (see Fig. 6). In addition to
demonstrating the capabilities of the JEM–EUSO instruments to detect and
reconstruct EASs from the edge of space, they also give access to direct
measurement of the UV nightglow emission and artificial UV contributions above
ground and oceans, which are important information to optimize the design of
the space-based missions. Three balloon flights have been performed so far:
EUSO–Balloon (Canada, 1 night), EUSO–SPB1 (Pacific Ocean, 12 nights), and
EUSO–SPB2 (Pacific Ocean, 37 hours).

Figure 6: Stratospheric balloon missions EUSO–Balloon, EUSO–SPB1, and
EUSO–SPB2, and ground mission EUSO–TA of the JEM–EUSO program. Image adapted
from EUSO-program .

The telescope configuration of EUSO–Balloon and EUSO–SPB1 is similar: two
Fresnel lenses of $\sim 1$ m2 each and one PDM as FS with 2.5 $\mu$s time
resolution.

EUSO–Balloon eusobal  was launched by National Centre for Space Studies in
France (CNES) from the Timmins base in Ontario (Canada) on the moonless night
of August 25, 2014. After reaching the floating altitude of $\sim$38 km,
EUSO–Balloon imaged the UV intensity with a spatial and temporal resolutions
of 130 m and 2.5 $\mu$s, respectively, in the wavelength range 290 - 430 nm
for more than 5 hours before descending to ground. The full FoV in nadir mode
was $\sim 11^{\circ}$. During 2.5 hours of EUSO–Balloon flight, a helicopter
circled under the balloon operating UV flashers and a UV laser to simulate the
optical signals from UHECRs, to calibrate the apparatus, and to characterise
the optical atmospheric conditions. Data collected by EUSO–Balloon have been
analyzed to infer different information among which the response of the
detector to the UV flasher and laser events, and the UV radiance from the
Earth atmosphere and ground in different conditions: clear and cloudy
atmosphere, forests, lakes, as well as city lights kenji-uv . The helicopter
events proved to be extremely useful to understand the system’s performance
and to test the capability of EUSO–Balloon to detect and reconstruct signals
similar to EASs eser-jinst . A summary of the results of the EUSO–Balloon
mission is reported in balloon-results .

EUSO–SPB1 spb1  was launched on April 25, 2017 from Wanaka (New Zealand) as a
mission of opportunity on a NASA SPB test flight planned to circle the
southern hemisphere. The telescope was an upgraded version of that used in the
EUSO–Balloon mission. The JEM–EUSO first level trigger was implemented with
adaptations for a balloon observation nim-trigger . Prior to flight, in
October 2016, the fully assembled EUSO–SPB1 detector was tested for a week at
the EUSO–TA site to measure its response and for calibrations by means of a
portable Ground Laser System (GLS). Observations of the Central Laser Facility
(CLF), stars and meteors were performed. Unfortunately, although the
instrument was showing nominal behaviour and performance, the flight was
terminated prematurely in the Pacific Ocean about 300 km SE of Easter Island
after only 12 days aloft of the $\sim$100 scheduled, due to a leak in the
balloon, and the payload was lost. During flight, $\sim$30 hours of data were
collected SCOTTI201994 .

EUSO–SPB2 spb2  was launched on May 13, 2023 from Wanaka on a NASA SPB test
flight. It was equipped with 2 telescopes. One telescope was devoted to UHECR
measurements using the fluorescence technique. EUSO–SPB2 employed a Schmidt
camera with 3 PDMs, a 1 $\mu$s GTU, and a more efficient balloon-oriented
trigger logic to improve the sensitivity of the instrument george-asr . The FS
of the second telescope was based on SiPM sensors and a dedicated electronics
to detect the Cherenkov emission in air by UHECR EASs. Unfortunately, the
balloon developed a leak and was terminated over the Pacific Ocean after only
about 37 hours of flight. Despite the very short flight, all instruments
performed very well. Analysis of the flight data is ongoing. Preliminary
results were presented in johannes_icrc2023 .

Table 1: The main parameters of different configurations of JEM-EUSO experiments Experiment | JEM-EUSO | K-EUSO | POEMMA | Mini-EUSO | TUS | EUSO-Balloon | EUSO-SPB1 | EUSO-SPB2 | EUSO-TA
---|---|---|---|---|---|---|---|---|---
Optics type | lenses | lenses | mirror | lenses | mirror | lenses | lenses | mirror | lenses
Optics |  |  |  |  |  |  |  |  |
aperture (m2) |  $\sim$4.5 |  $\sim$3 |  $\sim$6 |  $\sim$0.05 |  $\sim$2 |  $\sim$1 |  $\sim$1 |  $\sim$1 |  $\sim$1
Height (km) | 400 | 400 | 525 | 400 |  $\sim$500 |  $\sim$38 |  $\sim$33 |  $\sim$33 |  $\sim$0
FoV (∘) |  $\sim$64$\times$45 |  $\sim$20$\times$15 |  $\sim$45 |  $\sim$44 |  $\sim$9 |  $\sim$11 |  $\sim$11 |  12$\times$36 |  $\sim$11
Area at ground |  |  |  |  |  |  |  |  |
(km2) |  1.4$\times$105 |  4.8$\times$104 |  1.5$\times$105 |  $\sim$8$\times$104 |  $\sim$6.4$\times$103 |  $\sim$54 |  $\sim$40 |  $\sim$150 | —
PDMs | 137 | 44 | 55 | 1 | 1 | 1 | 1 | 3 | 1
Pixels |  3.2$\times$105 |  1$\times$105 |  1.3$\times$105 | 2304 | 256 | 2304 | 2304 | 6912 | 2304
Spatial ang. |  |  |  |  |  |  |  |  |
resolution (∘) |  $\sim$0.074 |  $\sim$0.1 |  $\sim$0.084 |  $\sim$0.9 |  $\sim$0.7 |  $\sim$0.2 |  $\sim$0.2 |  $\sim$0.25 |  $\sim$0.2
Pixel size |  |  |  |  |  |  |  |  |
at ground (km) |  $\sim$0.5 - 0.6 |  $\sim$0.6 - 0.7 |  $\sim$0.8 |  $\sim$6.3 |  $\sim$5.0 |  $\sim$0.13 |  $\sim$0.12 |  $\sim$0.14 | —
GTU ($\mu$s) | 2.5 | 2.5 | 1.0 | 2.5 | 0.8 | 2.5 | 2.5 | 1.0 | 2.5
Bckg level |  |  |  |  |  |  |  |  |
(cts/pix/GTU) | 1.1 | 0.6 | 1.5 |  $\sim$1.0 |  $\sim$18.0 |  $\sim$0.5 - 1.0 | 1 - 2 |  $\sim$1 | 1 - 2
Reference | exposure ; ea-instrument  | keuso  | poemma ; poemma-prd  | minieuso ; mini-trigger  | tus ; tus-jcap  | eusobal ; balloon-results  | spb1  | spb2 ; johannes_icrc2023  | eusota
|  |  |  |  |  |  |  |  |

EUSO–TA eusota  is a ground-based telescope, installed at the Telescope Array
ta  (TA) site in Black Rock Mesa, Utah, USA (see Fig. 6). This is the first
detector to successfully use a Fresnel lens based optical system and one PDM
foreseen for JEM–EUSO with a 2.5 $\mu$s GTU. The FoV is $10.6^{\circ}\times
10.6^{\circ}$. The telescope is located in front of one of the fluorescence
detector stations of the TA experiment. Between 2015 and 2016, a few campaigns
of joint observations with TA allowed EUSO–TA to detect 9 UHECR events in
$\sim$140 hours of data taking, all lasting 1 or 2 GTUs at maximum, as well as
a few meteors. The limiting magnitude of +5.5 on summed frames ($\sim$3 ms)
was established. These observations provided important data to optimize the
detector technology in view of subsequent balloon and space missions. The
current upgrade of the detector includes a new acquisition system based on the
Zynq board, like in Mini–EUSO, and the implementation of a self-triggering
system which has become operational in June 2022.

##  3 An overview of the Euso Simulation and Analysis Framework

The Euso Simulation and Analysis Framework (ESAF) is a simulation and analysis
software specifically designed for the performance assessment of space-based
cosmic ray observatories. It has been developed in the framework of the EUSO
project berat . The software consists of $\sim 2\cdot 10^{5}$ lines of code
written in C++ following an object oriented approach and makes use of the ROOT
data analysis framework developed at European Organization for Nuclear
Research (CERN) root-official .

In this section, we briefly summarize the key aspects of the ESAF software
while in the following one we report on the new developments to support the
JEM–EUSO program. A short technical description of the ESAF design is reported
in Appendix A. See reference berat  for a detailed and comprehensive
description of the ESAF software.

The ESAF software performs the simulation of an UHECR event, its detection and
the shower parameter reconstruction. In more detail, the ESAF code includes:
a) EAS simulation both by means of internally developed algorithms (e.g., the
SLAST shower generator, which includes the Greisen–Ilina–Linsley (GIL)
parameterization gil ) and interfaces to existing widely-used codes (e.g.,
CORSIKA corsika  or CONEX conex ); b) a complete description of the
atmosphere, including aerosols, ozone and Rayleigh scattering and clouds; c)
fluorescence and Cherenkov light production; d) a complete simulation of
photon propagation, from the production point up to the telescope, including
diffuse reflection interactions with ground and atmosphere, and a Monte-Carlo
code dealing with multiple scattering; e) simulation of optics, geometry and a
photodetector of a telescope; f) simulation of the electronics, trigger, and
background; g) pattern recognition and shower signal identification above
background; h) reconstruction of direction, energy, and slant depth of the
shower maximum ($X_{\max}$), i.e., the atmospheric depth of the shower maximum
from the top of the atmosphere.

The ESAF software produces two distinct executable files called Simu and Reco
respectively. The first one performs the simulation of the entire physical
process, the second one activates the entire reconstruction chain. The two
codes work independently.

##  4 Development of the ESAF simulation and reconstruction frameworks for
JEM-EUSO

Since 2007, when ESAF was adopted also for the JEM–EUSO mission, new
functionality was developed to include specific characteristics of the
JEM–EUSO telescope. More recently, the configurations of almost all the
projects conceived within the JEM–EUSO program have been developed as well.
These new implementations include: a) detector configurations and the new
trigger algorithms; b) two new track recognition algorithms named Linear Track
Trigger (LTT) and Peak and WIndow SEarching (PWISE); c) new reconstruction
algorithms for the energy and $X_{\max}$ EAS parameters; d) light transients
emitted by other classes of events such as ground flashers, space debris,
Transient Luminous Events (TLEs) tles , meteors and nuclearites derujula .

In what follows, the ESAF software is described in more details and a few
examples of its functionality are provided with specific emphasis on the new
implementations.

###  4.1 The EAS simulation framework

The Simu framework of ESAF performs the simulation of the entire physical
process from shower to telemetry. Both an extensive air shower and the photon
propagation are simulated. CONEX conex  and CORSIKA corsika  interfaces have
been implemented in the framework in addition to the ESAF EAS generators such
as SLAST slast . All these generators are currently adopted in ESAF, depending
on the objective of the simulation. CORSIKA and CONEX guarantee more carefully
tuned to experimental results, however, the computation time is usually
considerable. On the other hand, SLAST is a very fast simulator which can
provide a sufficiently good approximation of the EAS development when the user
is interested in an overall performance result. This is the simulator which
has been adopted in the results presented in this paper, unless differently
mentioned.

An atmosphere model according to the 1976 Standard US Atmosphere US_Atmosphere
is implemented, as well as the fluorescence yield parameterization nagano  and
the standard Cherenkov production theory. The LOWTRAN 7 package lowtran7  is
embedded into ESAF to simulate the atmospheric transmission. Both Rayleigh and
Mie scattering as well as the ozone absorption are taken into account. The
presence of clouds is simulated in a parametric way as a uniform layer with
predefined optical depth, altitude and thickness. Photon spectral
distribution, timing and direction are produced for each step of the shower
development (10g/cm2). According to such distributions we generate the single
photons that are propagated to the instrument depending on the solid angle
covered by the telescope pupil. Each of such photons is followed individually
and the transmittance is calculated accordingly. No weighting is applied since
photons are few and therefore we can afford to perform the calculation of each
of them. The optics simulation is performed through a ray trace code developed
at RIKEN naoto . Fig. 7 shows an example of typical sizes of the optical Point
Spread Function (PSF). The images refer to one of the different K–EUSO
configurations that have been designed along the years.

Figure 7: PSF diagrams of one version of the K–EUSO optics. Panels correspond
to light at 357 nm with incident angles from the optical axis 0∘, 4∘, 8∘ and
12∘ respectively. The size of each frame is $20~{}\text{mm}\times
20~{}\text{mm}$. The number of arrived photons increases as the color changes
from blue to red. An arbitrary point-like source has been used to test the
proper implementation of the optics response in ESAF code.

For the RIKEN Monte-Carlo simulator and the GEANT4 optics interface svetlana ,
the real Fresnel structure is implemented, so photons can be reflected or
refracted on the surface of grooves. A cross section drawing of the Mini-EUSO
optics with grooves implemented in the “RIKEN simulator” is reported in
minieuso . In the latter case, the position of the spot on the focal surface
is parameterized in an analytical way as a function of the entrance direction.
An additional random component of Gaussian shape is added to parameterize the
point spread function. An efficiency factor takes into account the
transmittance of lenses. In particular, this is the procedure that has been
adopted to estimate the performance of POEMMA poemma-prd  (see Fig. 3) but it
could be applied to any detector.

The Focal Surface (FS) structure (see Fig. 8) is read as a parameter file,
where the position and orientation of each single MAPMT is defined. The
overall detector efficiency is parameterized at the single pixel level as
product of quantum and collection efficiency. The MAPMTs have an average gain
set by a parameter and the front-end electronics is treated in a simplified
way with a threshold on the current pulse delivered by the MAPMT. The current
pulse associated to each photoelectron is varied according to a gaussian
distribution.

Figure 8: Simulation of a $10^{20}$ eV, $60^{\circ}$ zenith angle proton event
performed for one of the proposed and studied configurations of the K-EUSO
detector. On the left, a photoelectron profile at the focal surface is shown.
The photoelectron image of the same event on the FS is shown in the right
panel.

The background can be added at either the signal from the front-end
electronics or to the pixel counts. The electronics simulation is then
concluded by the trigger. Several algorithms, specific for each detector, have
been implemented in ESAF and can be used in combination. JEM–EUSO, K–EUSO and
POEMMA adopt the same trigger scheme on two levels operated on a PDM basis.
The first level trigger looks for concentrations of the signal localized in
space and time. The second level trigger is activated each time the first
level trigger conditions are satisfied and integrates the signal intensity in
a sequence of test directions.

Directions close to the one of the simulated EAS are expected to have the
larger signal over noise ratio (SNR), overcoming, therefore, the preset
trigger threshold.

Whenever such condition is met, the second level trigger is issued. The
activation of the second level trigger starts the transmission and data
storage procedure.

Thresholds are set to have a rate of spurious triggers from background
fluctuations at the order of a trigger every few seconds of background
simulations at most, to make the rate consistent with the telemetry
requirements.

Details of the logic can be found in nim-trigger  and in joerg-trigger  for
the first and second levels trigger, respectively. The trigger logic for
balloon missions matteo-spb1  is a modified version of the first level trigger
of JEM–EUSO while Mini–EUSO mini-trigger  and TUS tus  missions adopt totally
different approaches described in Sec. 5.4 and Sec. 5.5.

###  4.2 The EAS reconstruction framework

The first task to accomplish in the reconstruction phase (see Fig. 9) is to
identify the signal from the shower in the recorded data.

Figure 9: The general scheme of the reconstruction framework.

A number of track recognition algorithms has been implemented in the code. The
PWISE algorithm guzman  searches for high concentrations of the signal on
single pixels. The algorithm selects pixels and GTUs in which the signal is
above a certain threshold and checks whether this signal excess is persistent
over time. The LTTPatternRecognition mario-asr  is modeled following the
second level trigger philosophy of the JEM–EUSO project. The integration of
the signal is performed in a set of predefined test directions and the one
which maximizes the integral is chosen to reconstruct the event. Both
algorithms exploit the morphology of the signal, which can be seen as a spot
of light moving on the focal surface at the projected speed of light.

The next step is the reconstruction of the shower geometry which is an
essential step, as it allows the search for anisotropy and provides input
required for good energy and Xmax reconstruction.

The TrackDirection2 is the angular reconstruction module mernik-ea . Several
algorithms are implemented in it but two main families of algorithms are in
use; analytical and numerical. In the first group, a fit to the speed of the
shower is performed to determine its inclination after the Track Detector
Plane (TDP) has been identified.

The inclination of the shower in this plane with respect to the horizontal is
inferred from the projected speed of the signal on the focal surface. The
algorithms can be used in an iterative way to improve the knowledge of the
arrival direction of the shower.

In the numerical approach, a series of test geometries are chosen and the
deviations with respect to the timing and arrival direction of the measured
event are calculated. The test direction that best describes the measured
event properties is taken to be the arrival direction. The so-called Numerical
Exact Method 1 has proven to have the best performance and is currently used
as default. Such method minimizes the deviation of the arrival times of the
signal from the test shower w.r.t. the data.

The energy reconstruction is performed in the PmtToShowerReco module fenu . In
this algorithm, the shower profile is reconstructed starting from the signal
after correcting for detector effects, atmospheric absorption and fluorescence
yield. The shower profile is then fit with a parameterization to obtain the
primary particle parameters.

The count profile of the shower is reconstructed by selecting a collection
area that follows the cluster of pixels selected by the PWISE or the
LTTPatternRecognition. The size of this selection area is a trade-off between
the need to collect the highest possible fraction of the signal and the need
to limit the background. A stricter selection is indeed more appropriate for
the direction reconstruction. For this reason, the PWISE algorithm is more
suited for the angular reconstruction, given the typically narrower track
selected. On the other hand, the LTTPatternRecognition, with its very wide
selection of pixels, is more appropriated for the shower profile
reconstruction. The detector modeling allows to take into account the detector
efficiency and to retrieve a photon curve at the entrance pupil. The modeling
is performed through a series of lookup tables, produced with an extensive
Monte-Carlo simulation of the detector response. The arrival direction
associated to each pixel is extracted from the very large number of photons
simulated. The efficiency of the detector as a function of the arrival
direction and on the wavelength can be retrieved then depending on the arrival
direction of photons.

The reconstruction currently implemented is designed for the JEM–EUSO mission,
which was meant to operate in monocular mode. As such, the method is
particularly challenging and has to rely on some iterative procedures. Two
methods are described in fenu-ea , one with and the other without a Cherenkov
reflection peak. The presence of a peak gives a good constraint on the
position of $X_{\rm max}$. The absence of the reflection peak requires using
an iterative procedure starting from the reconstructed arrival direction and
the parameterized maximum slant depth of a standard shower. Such assumptions
are used as starting conditions of an iterative process which minimizes the
biases caused by these first choices. Parameters like arrival direction,
altitude of the shower maximum and slant depth of the maximum can be varied
and the region of the parameter space which best describes the data can be
identified. The atmospheric absorption is then modeled according to the
LOWTRAN7 package lowtran7  and, after estimating the shower position, the
luminosity of the shower can be calculated.

As a final step, a parameterization of the energy distribution of the
secondary particles is used to calculate the fluorescence nagano  and
Cherenkov yields. At the end of the procedure, it is possible to reconstruct
the secondary particles profile of the shower.

The reconstruction of energy and $\mathrm{X}_{\max}$ is then performed through
a fit with a shower profile function to the reconstructed shower profile fenu-
ea . A fit with the so called GIL function gil  is adopted. The GIL is a
simplified parameterization based on older hadronic interaction models. The
difference between GIL and other common descriptions e.g. Gaisser-Hillas is
negligible for our application.

###  4.3 Implementation of other classes of events

The science versatility of experiments like Mini–EUSO and TUS requires the
simulation of many different light transients originating from different
physical phenomena. For this reason, different types of signals have been
included in the capabilities of the ESAF software along the years. In these
cases the time profile, the intensity of light emission and the track
extension of the event have been included without simulating the physical
process responsible for such light emission.

The first class of events implemented in ESAF are Transient Luminous Events
(TLEs) such as blue jets, sprites and elves which have been discovered
relatively recently and are still not well understood pasko . They have
typical durations of ms or tens of ms. Mini–EUSO has a dedicated trigger
algorithm to capture TLEs and other millisecond scale phenomena at high
resolution mini-trigger . These data could help improve the understanding of
the formation mechanisms of filamentary plasma structures, complementing
atmospheric science experiments. The TLE simulator in ESAF is composed of the
TLEGenerator, TLELightSource, TLEBunchRadiativeTransfer classes which are
subroutines of the EventGenerator, LightSource and RadiativeTransfer
interfaces respectively. The TLESpectrumHisto class is responsible for the
spectral distributions of the phenomena.

The left side of Fig. 10 shows a graphical representation of the configurable
parameters of the four different classes of events that can be generated in
ESAF: a) a Toy Model; b) Blue Jet; c) Sprite; d) Elves.

Figure 10: Left: Graphical representation of the configurable parameters of
the four different classes of events that can be generated in ESAF: a) a Toy
Model; b) Blue Jet; c) Sprite; d) Elves. Right: Expected light track of a
typical diffused elve (top) and 3 localized blue jet events (bottom) generated
by ESAF and detectable by Mini–EUSO. Background emission of 1 count/pixel/GTU
is also included. Right plot adapted from CAPEL20182954 .

The right side of Fig. 10 shows examples of typical TLEs as they are simulated
for Mini–EUSO. The simulations employ toy models which in a simplified way
reproduce the size, shape and wavelength spectra of the different physical
phenomena. Details of the implementation of these phenomena in ESAF can be
found in perdichizzi .

Among the scientific objectives of the JEM–EUSO program is the study of slower
events such as meteors and fireballs. The simulation of meteor-induced light
tracks is described in nardelli , which inherits the approach described in ea-
meteors . Similarly to the TLE case, a new class has been developed for
meteors called MeteorLightSource. Meteors produce tracks which are very slow
moving compared to UHECR events, resulting in more than 1000 times more data
produced than for UHECR events. The solution that has been adopted is to fully
track only a fraction of the produced photons and to re-weight them at the
detector level. Regarding the simulation of the light signal of the meteor,
the starting position, direction, speed, duration and magnitude can be chosen
randomly or set as input parameters. The variation of the brightness of the
meteor as a function of time, or the meteor lightcurve, is also chosen
randomly, or provided as an input. Since the shape of the lightcurve can be
highly variable in the real world, the model adopts a very flexible approach,
representing it with a 9th degree polynomial. In most practical applications
performed so far, simulated lightcurves look reasonably realistic, taking into
account the large intrinsic variability of the phenomenon, as shown, for
instance, in the analysis by pecina . Moreover, since it is known that real
meteors can exhibit one or more secondary bursts, the model includes the
possibility to simulate one secondary burst, occurring at some instant before
the end of the event, and having a morphology which is also represented by a
9th degree polynomial (again, fixed or randomly chosen). Moreover, ESAF now
also includes the implementation of a formula by Jacchia jacchia  which links
the magnitude, mass and the velocity of the meteoroid. Given the meteor’s
velocity and magnitude, that are free parameters in the simulations, one can
derive the corresponding mass of the meteoroid. By assuming a value of the
density $\rho$ (so far a fixed value $\rho$ = 3.55 g/cm3 has been assumed in
preliminary tests) it is possible to compute the corresponding size of the
meteoroid. More details about the simulation of meteors for JEM–EUSO,
Mini–EUSO and EUSO–TA can be found in meteoroids2016 , while an example of a
simulated meteor with ESAF is reported in Sec 5.5.

##  5 Simulation of various missions of the JEM–EUSO program and derived
performance

The complexity of the JEM–EUSO program requires an extensive effort to study
the performance of all different detectors of the program. The detectors are
either space-based, like JEM–EUSO, Mini–EUSO, TUS, K–EUSO, and POEMMA or
balloon based, like EUSO–Balloon, EUSO–SPB1 and EUSO–SPB2. EUSO–TA is the only
one located on ground. EUSO–SPB2 is not implemented yet in ESAF in the final
configuration and can be simulated only using the
$\overline{\mbox{Off}}\underline{\mbox{Line}}$ package. For this reason it
will not be discussed in detail in this paper.

All the detectors point normally in nadir mode or with slightly tilted
configurations, except for EUSO–TA which points northwest with an elevation
typically of 15–25∘. All the detectors have different focal surfaces:
Mini–EUSO, EUSO–TA, EUSO–Balloon and EUSO–SPB1 are single-PDMs detectors while
JEM–EUSO, POEMMA and K–EUSO have a multi-PDM layout. TUS on the other hand,
consists of an array of 256 PMTs on a square of $16\times 16$ PMTs. The time
frame adopted in the simulations is $2.5~{}\mu$s with the exception of TUS,
which has a frame of 0.8 $\mu$s and a totally different electronics
configuration. In the following subsections, the main simulation results for
each configuration are summarized starting from the JEM–EUSO case, which has
been studied more extensively than other configurations. The description of
the standard parameters adopted in the simulations is reported in Appendix B.
This section includes information which has already been the subject of
previous publications.

###  5.1 The JEM–EUSO configuration

JEM–EUSO has been conceived as a mission to be installed on the ISS orbiting
at $\sim$400 km height. The main characteristics of the telescope are
summarized in Section 1. Fig. 11 shows the spatial and temporal profile of an
EAS generated by a 1020 eV proton with zenith angle 60∘ simulated with ESAF.
The contribution of the fluorescence and Cherenkov components at the pupil
level are indicated on the right in different colors.

Figure 11: Left: Spatial profile of photon counts from an EAS caused by a 1020
eV proton with zenith angle 60∘. Each square (dark and light brown) represents
a MAPMT. A parts of 6 PDMs are shown. The small coloured squares show the
number of photon counts detected by each channel of the MAPMT. This event is
crossing two PDMs, with the shower starting to develop in the bottom central
PDM and continuing in the top central PDM. Right: Time profile of photons,
obtained adding all photons of the previous picture detected on each GTU of
2.5 $\mu$s ($\sim$80 GTUs for a total signal duration of $\sim$200 $\mu$s). It
is possible to see the contribution to the signal from the three components:
the UV fluorescence light (blue), scattered Cherenkov (green) and Cherenkov
diffusely reflected peak (red).

The optics and detector response are then simulated and Fig. 12 shows the
photons arriving at the detector (blue), the photons arriving at the focal
surface (FS, red) and the photons detected at pixel level (Detected, green).

Figure 12: Photons coming to the detector, photons intersecting the focal
surface (FS) and photons detected as a function of time (in GTU). Due to the
covering factor and quantum efficiency taken into account, the fraction of
photons creating a signal (‘Detected’) is about 0.3. In this example: 1020eV
proton event with 60∘ zenith angle.

By applying the trigger algorithm after introducing the nightglow background,
the geometrical aperture is determined in nadir mode. A tilted configuration
of the telescope is available in ESAF as well. In the tilt mode, the
observation area is scaled by $\propto\sec^{3}(\xi)$ as a function of tilting
angle $\xi$ of the optical axis from the nadir. This increases the sample of
events at the highest energies, however, showers will be seen at larger
distances, therefore they will appear dimmer compared to nadir mode.

In order to estimate the aperture, a specific nightglow emission has to be
assumed. A background level ($I_{\mathrm{BG}}$) of 500
photons/(m${}^{2}\cdot$sr$\cdot$ns) is considered. This is a typically
measured value according to literature garipov ; barbier ; catalano , and it
represents also the value assumed in earlier JEM-EUSO simulations. This
corresponds to an average count level of $\sim$1.1 counts/GTU/pixel. The
assumption of a constant background over the entire FoV, most likely, is an
overly simplistic assumption since the background radiance depends on the
tilting angle under which the atmosphere is observed. However, at a first-
order approximation and especially for low tilting angles we can consider the
shower-to-detector distance to be the leading factor affecting the threshold
in energy. Fig. 13 shows the exposure as a function of energy for nadir and
different tilting angles. As expected by tilting the telescope, both the
threshold energy and exposure increase at the highest energies.

The quasi-nadir configuration of $\xi$ = 20∘ allows keeping at the lowest
energies an almost similar exposure to the nadir configuration, while
increasing it moderately at $\sim 10\%-20\%$ level in the $E\gtrsim 10^{20}$
eV.

Compared to nadir mode, the tilted mode is suitable to increase the exposure
at energies $E\gtrsim 2\times 10^{20}$ eV, where the flux is particularly low.
The exposure calculation is based on a Monte Carlo simulation of proton EASs
of variable energy and direction. To avoid border effects, cosmic rays are
injected in an area $A_{simu}$ larger than the FoV. The ratio of the triggered
$N_{trigg}$ over simulated $N_{simu}$ events is then calculated for each
energy bin. The effects of day-night cycle and Moon phases are taken into
account in $\eta$, the astronomical duty cycle. Effects of clouds and
artificial lights are also taken into account by $\eta_{clouds}$ (see later on
in this section) and $\eta_{city}$, respectively. In this formula, we assumed
$\eta$ = 0.2, $\eta_{clouds}$ = 0.72 and $\eta_{city}$ = 0.9 (which includes
also lightning and aurorae contributions) as estimated in exposure . The
exposure $\mathcal{E}(E)$ is then calculated over time $t$, which is assumed
to be 1 year in the following:

$\mathcal{E}(E)=\frac{N_{trigg}}{N_{simu}}(E)\times
A_{simu}\times\Omega\times\eta\times\eta_{clouds}\times\eta_{city}\times t$
(1)

An overall conversion factor between geometrical aperture and exposure of
$\sim$13% is obtained as a product of
$\eta\times\eta_{clouds}\times\eta_{city}$.

Figure 13: JEM–EUSO, K–EUSO and POEMMA exposures as a function of energy for
nadir (left) and different tilting angles (right). In case of K–EUSO only the
nadir configuration has been simulated as the tilt option is not considered in
the present mission design.

As ESAF provides the opportunity to simulate the presence of clouds, extensive
simulations have been conducted to understand their impact on the aperture
reduction and reconstruction capabilities. Fig. 14 shows the light curves of
EAS with different atmospheric conditions for the case of proton EASs with
$E=10^{20}$ eV and $\theta$ = 60∘. The solid line represents the case for
clear atmosphere. Dashed and dotted lines show the cases for clouds optical
depth $\tau_{C}$ = 1 at height $H_{C}$ = 3 km and $\tau_{C}$ = 0.5 at
$H_{C}=10$ km, respectively. The horizontal axis is the absolute time in GTUs.
The axis on the top indicates the altitude where photons originate for the
given arrival time. In the clear atmosphere condition, the light curve
indicates the EAS development followed by the Cherenkov footprint reflectively
diffused by the Earth’s surface at GTU number 100. For $\theta$ = 60∘ as in
this example, the apparent shower development lasts $\sim$60 GTUs (=150
$\mu$s). Using these data, the EAS parameters are reconstructed.

Figure 14: Arrival time distribution of photons from a proton induced EAS of
$E_{0}$ = 1020 eV and $\theta$ = 60∘ for different atmospheric conditions. The
solid line represents the case for the clear atmosphere. Dashed and dotted
lines denote the cloudy cases for optical depth $\tau_{C}$ = 1 at cloud height
HC = 3 km and $\tau_{C}$ = 0.5 at HC = 10 km, respectively. The axis on the
top indicates the altitude where photons originate for the given arrival time.
The photon number is indicated per m2. In order to compare to the Figure 12
the reader has to multiply by the optics size ($\sim$4.5 m2). Also the
starting time of the event is different because it depends on the first photon
reaching the optics, however, the duration of the event in both cases is 55-60
GTU in clear sky atmosphere. Image adapted from ea-clouds .

In presence of clouds, EAS light curves are affected. If the optical depth of
the cloud is large enough, the shower track is truncated. Upward photons
scattered or emitted below the cloud are extinguished and do not contribute to
the signals at the telescope. For this example, with a cloud at 3 km, the
apparent signals last 40 GTUs. It is still feasible to apply the
reconstruction techniques used in the case of the clear atmosphere by using
only the measurements taken above the cloud. As seen in the figure for the
case of a small optical depth, photon signals originating below the cloud are
attenuated. This likely lowers the estimated energy of the EAS if the same
techniques for the clear atmosphere are applied. Alternatively, the Cherenkov
footprint is still observable and the orientation and apparent velocity are
not affected, thus the consequence on arrival direction determination is
limited. As described in ea-clouds  using of ESAF simulations of EASs in
variable cloudy conditions together with the analyses of satellite
measurements of the cloud distribution indicate that more than 60% of the
cases allow for conventional EAS observation, while an additional $\sim$20%
can be observed with reduced quality. The combination of the relevant factors
results in an effective trigger aperture of $\sim$72% of the aperture in clear
atmosphere condition.

The scientific outputs of such a mission rely on the quality of the
reconstructed EAS parameters. Therefore, the performance on angular, energy
and $X_{\max}$ reconstruction have been extensively studied for the JEM–EUSO
telescope using different configurations, namely the HTV and Dragon layouts,
nadir and tilt options. The study presented in the following adopts either the
SLAST-GIL shower generator or CONEX with EPOS-LHC epos-lhc  hadronic
interaction model. While SLAST-GIL has the advantage of considerably reducing
the simulation time, it adopts a simplified approach based on a parameterized
shower simulation in which shower-to-shower fluctuations are not completely
taken into account. This is not an issue in specific studies such as the
aperture curve determination, however, it might have a more significant impact
in case of reconstruction of EAS parameters. Another advantage of using the
CONEX simulation program is that it is possible to study the behavior of the
detector response to different primary particles. In the following we report
on proton, iron and photon studies.

In Fig. 15 we present the angular resolution in nadir mode for proton, iron
and photon-generated EAS obtained with the Dragon configuration and adopting
the CONEX generator. For proton and iron we have simulated events with
energies of 5$\times$1019 eV and 1020 eV with zenith angles of $\theta$ = 30∘,
45∘, 60∘, and 75∘. For each angle and energy combination, 1000 events are
simulated. Additionally, similar simulations have been performed for photons
at the energy 1020 eV. Due to possible interactions with the geomagnetic
field, special care has to be taken when performing the photon simulations.
The pair production process depends strongly on the magnetic component
transverse to the photon’s direction of motion, and, therefore, the event
simulation is sensitive to the value and direction of the local geomagnetic
field homola . We characterize the error in the reconstructed arrival
direction as the angle between the simulated arrival direction vector
$\hat{\Omega}_{\rm Simu}$ and its reconstructed counterpart $\hat{\Omega}_{\rm
Reco}$. We define $\gamma=\arccos{(\hat{\Omega}_{\rm
Simu}\cdot\hat{\Omega}_{\rm Reco})}$ as the error in the reconstruction, and
the angular resolution as the value where the cumulative distribution of the
reconstruction’s error reaches 68%. We shall refer to this value as
$\gamma_{68}$.

Figure 15:  The angular resolution as a function of the zenith angle for the
Dragon-configuration of the JEM–EUSO mission pointing to nadir for proton
(dark blue) and iron (red) primaries with an energy of 5$\times$1019 eV (a),
and 1020 eV (b). Panel c) shows in violet the angular resolution for photons
of 1020 eV. Previous results with the HTV-configuration are also shown in
light blue. Image adapted from guzman-icrc2015 .

The results using the Dragon option indicate that the angular resolution of
the detector is not affected too much from the larger fluctuations of the
proton-induced showers as the iron induced EASs have similar reconstruction
performance. Fig. 15 displays also results obtained with the HTV configuration
which have been studied in mernik-ea . The better performance of the Dragon
option compared to the HTV option is mainly due to stricter cuts applied in
the selection performed with the PWISE algorithm particularly visible in the
significant improvement obtained for protons at 30∘. However, this comparison
shows the possibility to improve the quality of the reconstructed events by
applying more stringent cuts at the price of a reduced statistics
($\sim$50$\%$ at 30∘). In a real experiment all the triggering events will be
reconstructed with coarser selection cuts. A series of refinements will allow
high quality events to be reconstructed with higher performance still keeping
the high statistics. The event selection and reconstruction strategy is still
in definition. In the case of photons as primary particle we experience a low
triggering ratio for the showers that exhibit a strong Landau-Pomeranchuk-
Migdal (LPM) effect lpm1 ; lpm2 . Showers with the LPM effect appear less
bright, as a consequence of their extended longitudinal profile. It works as a
selection filter allowing only the brightest photon showers to trigger the
detector. Again this is mostly relevant at the lower zenith angles, whereas
for higher zenith angles the impact is less dramatic. A more detailed
discussion of this analysis can be found in guzman-icrc2015 .

The angular resolution is studied also for configurations in tilt mode with
the Dragon option in case of proton showers mernik-icrc2015 . The standard
procedure described in mernik-ea  is applied here. EASs are generated using
the SLAST-GIL simulator with fixed energies between 5$\times$1019eV and
5$\times$1020eV and fixed zenith angles between 30∘ and 75∘. All azimuth
angles are picked randomly between 0∘ and 360∘. The shower cores have been
placed within a rectangular area of x[-550km;+100km] $\times$ y[-250km;+250km]
for $\xi$ = 20∘ tilt angle and x[-1300km;0km] $\times$ y[-400km;+400km] for
$\xi$ = 40∘. These areas are considerably larger than the actual FoV of the
tilted instrument. For each energy/zenith angle combination the number of
triggering events is of the order of 2000 or higher.

Figure 16:  The angular resolution of the 20∘ (a) and 40∘ (b) tilted JEM–EUSO
telescope. Image adapted from mernik-icrc2015 .

Results are presented in Fig. 16. As expected, the angular resolution of the
telescope tilted by $\xi$ = 20∘ gets worse by approximately 2.5∘ when compared
to the nadir mode operation (see Fig. 15). The effect mainly depends on the
zenith angle of the showers and to a smaller extent on the energy. Especially
the low zenith angles are affected. When we tilt the telescope by $\xi$ = 40∘,
the resolution gets worse compared to the previous 20∘ case. Again, the effect
mainly depends on the zenith angle of the showers and to a smaller extent on
the energy. The loss of the angular resolution is about 1.5∘ compared to the
$\xi$ = 20∘ tilted case. As expected from the analysis of the signal
behaviour, we can observe a worsening of the angular resolution due to the
fact that less light per EAS reaches the telescope. The instrument resolution
capability is determined by four limiting factors, three of which are related
to the distance of the shower from the detector. The first one is the
proximity effect. Events injected nearby the telescope appear brighter than
those farther away, since the number of photons reaching the telescope is
scaled by a factor of $1/d^{2}$, where $d$ represents the distance between the
telescope and the location of the emitted photon. The second comes from the
projected pixel size on ground as it determines the minimum theoretically
reachable air shower resolution of the telescope. Pixels in the outer parts of
the FoV observe a larger volume of air than the ones at the centre. The third
one is due to optics throughput. Events occurring in the outer parts of the
FoV face stronger optical losses, due to a lower transmittance of the optical
system. The probability of being attenuated or defocused by the telescope
optics is higher. The last one is related to the skimming effect. Shower
tracks can skim the field of view and appear only partially on the FS. This
effect increases when the nadir FoV is deformed by tilting the detector.

The question whether or not to tilt a JEM–EUSO-like instrument in space
strongly depends on the primary objective of the mission. When the emphasis is
put on high exposure for the highest energy events, a tilting of the
instrument might be useful. When the focus lies on accuracy for direction
determination, the nadir mode is the preferred operation mode.

Similar studies have been conducted also in regards to the energy and
$X_{\max}$ resolutions. We report here those performed for the HTV
configuration in nadir mode adopting the SLAST-GIL shower generator fenu-ea ,
as they were conducted in a more detailed way. This is the standard procedure
adopted also for similar studies conducted with POEMMA and K–EUSO. An analysis
using different primaries (p, Fe and photons) and using CONEX shower simulator
can be found in guzman-icrc2015 . After the retrieval of the signal identified
by the pattern recognition we start the correction of the inefficiencies of
the detector and of the absorption in atmosphere and compute an estimate of
the fluorescence yield. The reconstruction of the geometry is done following
either of two methods: the slant depth or the Cherenkov method. As final
result we obtain a shower profile which we will fit with some predefined
shower function. In this way we obtain the energy and $X_{\max}$ of the
shower. An example of the reconstructed profile with the related fit is shown
in Fig. 17a. This event has an energy of $3\times 10^{20}$ eV and a
reconstructed energy of $3.2\times 10^{20}$ eV. We see the Cherenkov
reflection peak in the right part of the profile.

Figure 17: Panel a): the simulated (black line) and reconstructed (points)
shower electron curve. The GIL fit is shown as a red line. The simulated
proton event has an energy of 3$\times$1020 eV, a zenith angle of 50∘and an
$X_{max}$ of 915 g cm-2. The reconstructed parameters for this fit are
3.2$\times$1020 eV and 873 g cm-2. The $\chi^{2}$/DOF of this event is 0.905.
The shaded areas show the points which are excluded from the fit. Panel b):
the energy reconstruction performance is shown here for the all–event sample
extracted on the full FoV ($\pm$270,$\pm$ 200) km and energy range
2$\times$1019 – 2$\times$1020 eV. The sample with cuts DOF$>$ 4,
$\chi^{2}$/Ndf $<$ 3 is shown here. Panel c): The energy resolution in terms
of the $\sigma_{R}$ factor (see text for details), in percent, is shown. Here,
we plot the results for various zenith angles and energies. All the events are
impacting in the central part of the field of view (namely in the inner
($\pm$20,$\pm$20) km). The geometry has been reconstructed with the slant
depth method. Panel d): Same as in c) but adopting the Cherenkov method. Image
adapted from fenu-ea ,fenu-icrc2015 .

Using the reconstruction procedure discussed in the previous section, a study
of the energy resolution of the JEM–EUSO mission has been performed. The
impact point is selected in the central part of the field of view (namely in
the inner ($\pm$20,$\pm$20) km). Showers are generated according to the GIL
parameterization. We simulated 8000 events for each point and we applied
quality cuts DOF$>$ 4, $\chi^{2}$/DOF $<$ 3 on all the data. The cut on the
degrees of freedom implies a minimum number of 7 points to be fit. Such a cut
is a minimal requirement to ensure that events with too much light loss
because of gaps are rejected. The cut on the $\chi^{2}$ rejects instead the
catastrophically failing fits. Under such conditions more than 80% of the
events above 1020 eV are selected.

To estimate the resolution, we define the parameter $R$ for each event as:

$R=\frac{E_{\rm reco}-E_{\rm real}}{E_{\rm real}}.$ (2)

The distribution of parameter 2 for all the events which survived the cuts has
then been fitted with a Gaussian curve. The $\sigma_{R}$ parameter of such
Gaussian fit is reported in panels b), c) and d) of Fig. 17. As can be seen in
Fig. 17c), the energy resolution tends to improve toward the higher zenith
angles and with the increasing energy due to the better quality of the signal.
Generally, the slant depth method will always have a resolution under 20%. At
the most extreme energies, the resolution reaches 10% or even lower. In Fig.
17d), the energy resolution obtained with the Cherenkov method is shown.
Again, the highest energies allow the best performance, while a clear
improvement depending on the zenith angle cannot be seen anymore. This is due
to the worsening quality of the Cherenkov peak at the highest zenith angles.
In fact, the Cherenkov peak will be much more difficult to recognize at large
zenith angles due to the larger spread of the reflection spot. In Fig. 17b)
the energy resolution, estimated using the slant depth method, is shown for
events distributed in the range ($\pm$270,$\pm$ 200) km and for energies in
the range 2$\times$1019 – 2$\times$1020 eV. The events have zenith angles
between 0∘ and 90∘ distributed as sin(2$\cdot\theta$). Here, we also apply DOF
$>$ 4, $\chi^{2}$/DOF $<$ 3 quality cuts on $\sim$ 104 events. The resolution
ranges from $\sim$30% at 2$\times$1019 eV to 15–20% at $\sim$1020 eV.
Systematics have not been corrected and may still be contributing to the
distribution width.

A similar study has been performed for the $X_{\max}$ parameter. Using the
same samples generated for the study of the energy resolution, we have
calculated the distribution of the slant depth of the maximum. Fig. 18 shows
the JEM–-EUSO $X_{\max}$ resolution for fixed conditions of zenith angle and
energy. Similarly to the case for the energy, we evaluate the parameter
$X_{\max}^{\rm reco}$ \- $X_{\rm\max}^{\rm real}$ for all the events. Then we
fit the distribution with a Gaussian and we plot the $\sigma$ parameter. Fig.
18a) displays the reconstruction performance for the slant depth method. As
can be seen, the $X_{\max}$ resolution improves with the energy. At the lowest
energies, it ranges from 90 to 120 g cm-2 while at the highest energies, from
60 to 80 g cm-2. The higher zenith angles also yelds better resolution, due to
the better angular resolution. Moreover, the higher altitude of such events
implies higher luminosity at the detector. The complete profile can be totally
fitted not being cut by the ground impact. Fig. 18b), shows the same plot
obtained with the Cherenkov method. In this case the performance is
significantly better ranging from 80–100 g cm-2 at the lowest energies to
50–60 g cm-2 at the highest ones. At the highest zenith angles the Cherenkov
reflection peak will however not be recognizable. For this reason, the plots
will not extend above 60∘. We reiterate that at these energies the difference
between p and Fe $X_{\max}$ is of the order of 100 g cm-2 yushkov-icrc2019 ;
abbasi-composition

Figure 18: The $X_{max}$ resolution is shown for various zenith angles and
energies of proton events. All the events are impacting in the central part of
the field of view (namely in the inner ($\pm$20,$\pm$20) km). The geometry has
been reconstructed with the slant depth method in panel a) and with the
Cherenkov method in panel b). For the lowest energy bin the reconstruction
procedure adopting the Cherenkov method very often fails due to lack of
signal, therefore, it can not be applied. Image adapted from fenu-icrc2015 .

Comparable results have been obtained on the resolution of the $X_{\rm max}$
distributions using the CONEX simulator for either proton or iron showers, and
slightly larger resolution for photon showers in all three cases distributed
within the full FoV. However, an offset in Xmax was observed in this case
indicating a need for a fine tuning of the reconstruction algorithms. Despite
the fact that on a single event the uncertainty on Xmax is large, by
collecting a large sample the uncertainty on the average value will reduce
significantly (in principle by a factor of 10 with a statistics of 100 events,
under the condition of purely statistical errors). This allows obtaining
meaningful results in terms of the evolution of the average mass composition
as a function of energy at energies which are not reachable yet by ground-
based experiments due to the limited duty cycle and relative exposure.

###  5.2 The K–EUSO configuration

We present in the following the performance results in terms of aperture,
exposure, angular, energy and Xmax resolutions obtained adopting the latest
configuration designed for the K-EUSO mission as reported in Section 2.

For this purpose, N = 4500 showers were simulated in the energy range E = 1019
eV - 3$\times$1020 eV, from all directions uniformly in azimuth and with
$\sin(2\theta)$ zenith dependence in the entire field of view of the detector.
The yearly exposure as a function of energy is shown in Fig. 13. As it can be
seen, at the plateau, which is reached at around 1020 eV, K–EUSO achieves an
exposure of $\sim$18000 km2 sr yr. The 50% efficiency is reached at $\sim
4\times 10^{19}$ eV. Assuming the spectrum recently published by the Auger
collaboration auger , the expected rate of triggered events has been
calculated to be of the order of 4 events/year above 1020 eV and 65
events/year above 5$\times 10^{19}$ eV.

As discussed in keuso , and shown in Table 2 by adopting the so called
Numerical Exact 1 method mernik-ea , K–EUSO achieves an angular resolution
between 3∘ to 7∘ at small zenith angles and improves to 1–2∘ for nearly-
horizontal events in the energy range between $5\times 10^{19}$ and 3$\times
10^{20}$ eV. There is a clear improvement trend as the energy increases.

Table 2: Angular, energy and $X_{\max}$ resolutions of the K–EUSO detector for proton EASs of different energies and zenith angles. The angular and energy estimations are done at fixed angles and full FoV while in case of $X_{\max}$ they are performed at one single angle (30∘) and refer to the center of the FoV. Energy | Energy res. (%) | Angular res. (${}^{\circ})$ | Xmax res.
---|---|---|---
[EeV] | 30∘ | 45∘ | 60∘ | 75∘ | 30∘ | 45∘ | 60∘ | 75∘ | [g/cm2] 30∘
50 | 25 | 25 | 22 | 16 | 6.8 | 6.8 | 4.0 | 1.6 | 110
70 | 27 | 24 | 20 | 14 | 5.6 | 4.6 | 3.0 | 1.6 | 83
100 | 27 | 24 | 20 | 13 | 4.8 | 3.0 | 2.0 | 1.0 | 69
300 | 21 | 16 | 13 | 7 | 4.2 | 1.6 | 1.0 | 0.63 | 41

Estimations of the energy resolution of K–EUSO for UHECRs with different
energies arriving at various zenith angles are shown in Tab. 2. Similarly to
the analysis related to the angular resolution, 2500 showers were simulated at
fixed energies and zenith angles, both for the center and for the full FoV of
the detector. The resolution was estimated as the standard deviation of the R
distribution as shown in the previous section. It can be seen that the energy
resolution is around 25% at low zenith angles and improves to around 15% for
nearly horizontal events, with a small improvement for higher energies. No
significant improvement of the performance has been observed if events are
simulated on the central part of the FoV.

Reconstruction of the $X_{\rm max}$ of an EAS is also performed according to
fenu-ea  and is obtained from the fit of the reconstructed shower profile. In
this work, we only show a few examples of the reconstruction performance
obtained in some specific condition. The method we use here considers only
events with a visible Cherenkov reflection peak. In this way, the impact point
of the shower can be identified in the profile and therefore a clear
constraint can be put onto the shower geometry. An overview of the performance
in few conditions is given in Table 2. The resolution is always around 50–90
g/cm2 for the center while similar values are obtained for the whole FoV.

These results have to be regarded as a first indication of the performance.
Improvements will be possible when the K-EUSO design is frozen and the
algorithms will be optimized for this specific configuration.

Fig. 19 shows a comparison between JEM–EUSO, K–EUSO and POEMMA performance in
terms of angular and energy resolutions at 1020 eV for different zenith
angles.

Figure 19:  Comparison between JEM–EUSO, K–EUSO and POEMMA performance in
terms of angular (panel a) and energy (panel b) resolutions for 1020 eV proton
EASs with different zenith angles. The POEMMA angular resolution in stereo
mode is obtained without the use of ESAF, as it implies a stereoscopic vision,
while the energy resolution has been extrapolated from the monocular mode
derived with ESAF. The dashed lines represent the result of the cumulative
resolution obtained for all theta angles. The better performance of JEM–EUSO
is due to the smaller pixel footprint at ground and by a dedicated
optimization of the reconstruction algorithms. POEMMA and K–EUSO adopted the
same algorithms developed for JEM–EUSO with only limited optimizations.
Moreover, in case of POEMMA a parametric simulation of the optics has been
considered instead of a ray-tracing code. The comparison between JEM–EUSO and
POEMMA shows also the margin of improvement which is in principle obtainable
with a dedicated fine tuning of the reconstruction algorithms. At the same
time the significant improvement of a stereoscopic configuration is clear when
the mono and stereo performance of POEMMA are compared.

###  5.3 The POEMMA configuration

A first estimation of POEMMA performance in terms of trigger exposure and
quality of event reconstruction has been assessed using the ESAF code assuming
a clear atmosphere (details can be found in poemma-prd ). Because the POEMMA
PFC baseline design employs the PDMs and electronics developed for the
JEM–EUSO mission, the JEM–EUSO trigger algorithms and reconstruction
procedures have been considered to evaluate the POEMMA performance. Proton
showers have been simulated using the SLANT-GIL shower generator. The POEMMA
optics response was implemented in ESAF using the parametric model. ESAF
doesn’t allow yet a stereoscopic vision, therefore, monocular mode performance
has been determined at first and then extrapolated to the stereoscopic view
for what concerns the energy resolution. Instead an independent approach (as
detailed in poemma-prd ) has been adopted for the estimation of the angular
and Xmax resolutions in stereo mode. The simulations were performed assuming a
standard UV night glow background level of 500 photons m-2 ns-1 sr-1 in the
300–500 nm band. Taking into account the POEMMA detector response, this
corresponds to an average equivalent count rate of 1.54 counts $\mu$s-1
pixel-1. The study presented here assumes a 2.5 $\mu$s GTU, used as reference
for the different projects. Preliminary tests using the independent approach
discussed in poemma-prd , with short time resolution indicate a significant
impact on the angular and Xmax resolutions, while negligible on the energy
resolution. For this reason the stereo reconstruction adopted the 1 $\mu$s GTU
while for the monocular mode studies the 2.5 $\mu$s resolution was considered.
The present results have, therefore, to be considered conservative, in terms
of POEMMA performance. In Fig. 20 we show the photoelectron (left) and track
profile (right) on the PFC focal plane induced by a proton EAS of 1020 eV,
inclined 60∘ from the nadir.

Figure 20: A 1020 eV, 60∘ zenith angle proton EAS. On the left: the
photoelectron profile for the POEMMA detector. On the right: the image on the
POEMMA’s focal surface. Image taken from fenu-icrc2019 .

To estimate the exposure curve of POEMMA, an overall set of 20,000 proton EASs
was simulated with ESAF in the energy range 5$\times$1018 eV – 5$\times$1020
eV uniformly in azimuth and with the same zenith dependence as in K–EUSO
simulations over a sampling area that is almost twice the size of that in the
FoV ($S_{FoV}\sim$145,000 km2). The exposure $\mathcal{E}(E)$ was then
determined using equation 1 under similar assumptions. In case of POEMMA only
the first level trigger was applied. Based on JEM–EUSO simulations, it was
estimated that the effect of the second level trigger is to increase the
exposure curve by $\sim$10% at higher energies. The exposure was estimated
also for different tilt angles as shown in Fig. 13. The annual exposure in
monocular mode reaches $\sim$70000 km2 yr sr, while it reduces by about a
factor of two if the stereo mode is applied with the satellites separated by
300 km poemma-prd .

The triggered EASs were passed through the JEM–EUSO pattern recognition and
reconstruction chain using both the slant depth and Cherenkov methods to
evaluate the exposure for reconstructed events. To perform a reconstruction,
the same cuts as described in the JEM-EUSO section (5.1) were applied. The
slant depth method successfully reconstructed $\sim$84% of the triggered
events with almost constant efficiency above log(E/eV) $>$ 19.6, while for the
Cherenkov method only about half of the events were reconstructed. As
mentioned before, this is due to the fact that this method is usable up to
zenith angles $\sim$50∘ (the value depends on the EAS energy and location on
the FS). At higher zenith angles the Cherenkov signal is spread and too dim to
be isolated from background fluctuations.

The performance of the angular reconstruction for POEMMA was evaluated at
fixed zenith angles ($\theta$ = 30∘, 45∘, 60∘, and 75∘) for three different
energies (E = 7$\times$1019, 1020 and 3$\times$1020 eV). The same methodology
defined for the JEM–EUSO reconstruction was applied to POEMMA, with a fine-
tuning of the parameters of the PWISE algorithm. Results are presented in Tab.
3 in terms of $\gamma_{68}$ parameter. It is important to underline that a
more detailed study of the bias should be performed. The reduction of the bias
would improve the overall performance of $\gamma_{68}$ as it includes both
statistical and systematic uncertainties.

Table 3: Angular and energy resolutions of the POEMMA detector for proton EASs
of different energies and zenith angles obtained with ESAF under different
assumptions. The angular resolution is obtained at fixed energy in monocular
mode. The energy resolution is in monocular mode and is presented for two
cases: results in the first column have been obtained with the assumption that
the angular reconstruction was provided in stereo mode with an angular
resolution of 1∘ in both zenith and azimuth angles while in the second column
we put results without assumption of 1∘. Assuming a stereo vision the energy
resolution improves by $\sqrt{2}$, assuming no bias or similar bias between
the two telescopes.

Energy | Energy res. (%) |  Angular res. (∘)
---|---|---
[EeV] |  All angles (1∘ res.) | All angles |  30∘ |  45∘ |  60∘ |  75∘
50 | 26 | 30 | 12 | 6.2 | 5.5 | 5.2
70 | 25 | - | 9.9 | 6.4 | 3.9 | 5.1
100 | 24 | 27 | 9.1 | 4.2 | 3.5 | 4.1
300 | 23 | - | 6.2 | 2.3 | 2.1 | 1.4

The stereoscopic vision of POEMMA allows a much better angular reconstruction
than does monocular vision. In stereo mode the reconstruction of the EAS
trajectory is robust, yielding a much better angular resolution, which is
$\sim 1.5^{\circ}$($\sim 1^{\circ}$) or better above 5$\times$1019 (1020) eV
(see poemma-prd  for more details).

For the energy resolution study, we present here the results for two
situations: assuming that the EAS direction has been pre-determined using the
stereo approach with a 1∘ resolution in both zenith and azimuth angles and
without this assumption. The results are shown in Tab. 3. With 1∘ assumption,
for 5$\times$1019 eV, the energy resolution is 26% with a +3.5% bias, while
for 1020 eV the energy resolution is 24% with a -1.5% bias. Since the two
POEMMA telescopes provide independent measurements of each EAS, the combined
resolution is obtained by dividing by $\sqrt{2}$, assuming no bias or similar
bias between the two telescopes, yielding 18% at 5$\times$1019 eV and 17% at
1020 eV.

A preliminary study of the $X_{\max}$ resolution was performed as well
indicating resolutions of the order of those obtained for JEM–EUSO. However,
similarly to the angular case, an estimate of the $X_{\max}$ resolution in
stereo mode was conducted. The total $X_{\max}$ resolution of POEMMA,
including both angular resolution and photoelectron statistics, is about 31 g
cm-2 at 3$\times$1019 eV for events below 60∘ (72% of the data sample) and 39
g cm-2 below 70∘ (91% of the data sample). At 1020 eV the resolution is 17 and
21 g cm-2, respectively (see poemma-prd  for more details). These results
indicate the much better performance of a stereoscopic detector compared to a
monocular vision.

###  5.4 The TUS configuration

The ESAF code has been used to study the TUS performance and comparison to
data with two different approaches and simulation codes. The first one is ESAF
coupled with the TUSSIM program package developed at the Joint Institute for
Nuclear Research, Dubna (Russia) esaf-tussim . ESAF is used to generate the
EAS cascade and the fluorescent radiation which is propagated at TUS optics
level. Then, the TUSSIM program simulates the TUS detector performance
including the Fresnel mirror optical parameters, the light concentrator of the
photo detector, the front-end and trigger electronics. In the second approach
tus-mario , the TUS detector is implemented directly into the ESAF simulation
code. Regarding the optics simulation, approaches similar to JEM–EUSO have
been adopted. The standard one, which was used in this work, adopts a
parametric simulation module that analytically calculates the position of the
photon on the FS and adds a Gaussian spread around this position. This is
intended to be a fast working tool to test the features of different optics
designs in an approximate way. Once the photons reach the FS, they are
transported through the filter and the optical adapter before reaching the
photocathode. All the relevant effects including geometrical losses,
inefficiencies of the adapter and of the UV filters are taken into account. A
parameterization of the photo-multiplier response is included in the
electronics part. All the effects like quantum efficiency, dependence on the
incident angle of photons, collection efficiency and cross-talk are also taken
into account. The signal is then amplified by a parameterized gain and the
resulting output current is collected and treated by the front-end electronics
module. Fig. 21 shows an example of the light profile and shower track
expected to be detected from a 1021 eV, 60∘ zenith angle proton EAS.

Figure 21:  A simulated 1021 eV, 60∘ zenith angle proton event. Left panel:
the photoelectron profile for the TUS detector. Right panel: the photoelectron
image for TUS. Image taken from fenu-icrc2019 .

During its operation, TUS has detected about $8\times 10^{4}$ events that have
been analyzed offline to select those satisfying basic temporal and spatial
criteria of UHECRs. A few events passed this first screening. Those that
exhibited some EAS-like characteristics were compared to ESAF simulations to
understand if they were consistent with an UHECR origin. One specific event,
which was registered in perfect observational conditions, was deeply
scrutinized (see Fig. 22). Its phenomenology and the possible interpretations
were reported in detail in tus-jcap . Thanks to the comparison with ESAF
simulations, it was possible to demonstrate that the PMT waveforms and the
light curve of the event show similarities with expectations from an EAS.
However, the amplitude corresponds to UHECR energies $E$ $\gtrsim$ 1021 eV,
which makes the cosmic ray origin of this event highly unlikely as TUS
accumulated exposure is two orders of magnitude lower than accumulated
exposure collected by ground-based experiments and no event was detected so
far above 3$\times$1020 eV Bird:1994uy . Another important phenomenological
feature of the event is that it develops very high in the atmosphere. The
duration of the signal and its slow attenuation lasting $\sim$60 $\mu$s lead
to an estimate of $X_{\max}$ $\sim$550 g cm-2, which corresponds to the
altitude of $\sim$7.5 km. On the other hand, if EASs are simulated with an
inclination around 45∘, which corresponds to the reconstructed direction of
the TUS event, the Xmax has values in the range 915 - 985 g cm-2 which are
much deeper in the atmosphere. Moreover, the EAS profile of the TUS event is
closer to a 60∘ inclined event which again doesn’t provide a good matching
between shower profile and direction reconstruction. An even higher altitude
($\sim$8.5 km) of the signal maximum is obtained if one assumes the narrow
peak at around 150 $\mu$s to be Cherenkov reflection. These values are in a
contradiction with expectations from the ESAF simulation of a ZeV event (see
Fig 22). This inconsistency indicates that the peak around 150 $\mu$s might be
due to other reasons, including a random fluctuation of the signal or an
artifact of the electronics or due to an anthropogenic source on ground. A
similar peak was indeed observed also in other events which showed an apparent
movement of the signal. These were later on associated with the presence of
airports (sharakin-tus-airports ). On the ocean 15 EAS-like events in total
were found, four of which had at least three active channels and were
registered in good observational conditions. However, for none of them it was
possible to reconstruct the arrival direction of the light source accurately,
either for the limited number of hit pixels or because they occurred at the
edge of the FoV (tus-mario ). This shows the importance of ESAF not only to
understand the performance of an instrument but also to inspect experimental
events through simulations. Mini-EUSO results, as the detector features
similar FoV per pixel, even though a higher energy threshold, will help
understanding the expected random imitation rate of this kind of EAS-like
signals.

Figure 22: Left panel: The light curve of the TUS161003 event as the signal of
the ten hit channels stacked together. The insert shows positions of the hit
pixels on the focal surface. Right panel: An expected TUS detector response to
an EAS from a 1 ZeV proton arriving at the zenith angle $\theta\approx
50^{\circ}$. Image adapted from tus-jcap .

ESAF was also used to perform a detailed analysis of the TUS exposure and
sensitivity to UHECRs tus-francesco . Two thousand EASs were injected in an
area $A_{\text{simu}}$ larger than the FoV ($\pm 150$ km) to avoid border
effects. The TUS trigger logic was implemented in ESAF. Several trigger
thresholds used in the mission were tested with an airglow rate of $\sim 18$
photoelectrons per frame. As a result of our preliminary estimation, we
obtained a trigger threshold $\gtrsim 5\times 10^{20}$ eV. However, this
estimation is affected by large uncertainties due to an accident that occurred
during the first days after launch (described in tus-jcap ), when 20% of the
PMTs were destroyed and sensitivities of the remaining PMTs changed compared
to the pre-flight measurements. Despite a number of in-flight calibration
attempts, considerable uncertainties still remain on the PMT gains. Moreover,
the TUS trigger algorithm is more efficient for horizontal showers leading to
a higher fraction of high zenith angle events. The majority of the events
could indeed trigger only above $40^{\circ}\text{--}50^{\circ}$. This is a
consequence of the persistence condition of the trigger that rejects all
events lasting for a short time.

Secondly, the efficiency of the trigger in cloudy conditions was evaluated.
The cloud condition for each trigger has been estimated based on MERRA data
(see tus-mario  for details). One thousand EASs at fixed energy have been
simulated for each cloud top height condition in similar way as for clear sky.
An estimate of the overall reduction of the exposure during the whole flight
can be given by an average of the trigger efficiency weighted by the fraction
of triggers in each condition. This leads to 57% of what is expected for the
clear sky case. By taking into account the above factors the geometrical
exposure in clear sky conditions amounts to $\sim$1550 km2 sr yr at plateau
energies, reducing to $\sim$884 km2 sr yr at $2\times 10^{21}$ eV taking into
account the cloud impact. It is important to recall that the estimation of the
exposure might have a cloud dependence due to the interplay of the brightness
of the shower and the location of its maximum. For the same cloud location, at
lower energy a lower value for the exposure is expected.

###  5.5 The Mini–EUSO configuration

The Mini–EUSO configuration has been incorporated in ESAF including its
trigger logic mini-trigger . Proton showers have been simulated using the
SLAST-GIL shower generator. A ray trace code of the Mini-EUSO optics response
is included in ESAF. Fig. 23 shows an example of a 1021 eV, 60∘ zenith angle
simulated proton event. Mini-–EUSO is at the detection threshold at such
energies. The signal looks dim. Background has not been simulated but it is
expected to be at a level of $\sim$1 count/pixel/GTU(2.5 $\mu$s) in standard
observational conditions.

Figure 23: A 1021 eV, 60∘ zenith angle proton event. Left: the photoelectron
profile for the Mini–-EUSO detector. Right: the photoelectron image. Image
taken from fenu-icrc2019 .

The trigger efficiency curve and aperture have been studied in a way similar
to that used for the other instruments. Fig. 24 shows the derived trigger
efficiency and the aperture curves.

Figure 24: The trigger efficiency (on the left axis, in black) and geometrical
aperture (on the right axis, in red) are shown as a function of the EAS
energy, E, in eV. A UV background level of 1 count/pixel/GTU(2.5 $\mu$s) was
considered in both cases.

The experimental data taken by Mini–EUSO allow a first comparison with the
assumed background levels in JEM–EUSO, K–EUSO and POEMMA to verify that the
estimated performance is based on justified assumptions. Table 4 shows
Mini–EUSO results on the average UV emissions in different conditions: clear
and cloudy conditions, sea and land, various lunar phases as reported in
minieuso-uv . As explained in minieuso-uv  the presence of clouds is derived
from the US National Weather Service Global Forecast System (GFS) GFS .
Assuming no-moon conditions and typical land/ocean and clear/cloudy atmosphere
ratios equal to 30/70, the average background level is $\sim$1.3
counts/pixel/GTU.

In order to re-scale this value to the JEM–EUSO (JE) case a full simulation of
JEM–EUSO and Mini–EUSO detectors was performed with ESAF. In case of Mini–EUSO
(ME) the overall efficiency of the detector was fine-tuned in ESAF, mainly
acting at the level of MAPMT response, to match the measured one
$\epsilon_{ME}$ = 0.080 $\pm$ 0.015 (see minieuso-uv ) for a point-like source
on ground. A flat diffused UV emission in the range $\lambda$ = 300 - 400 nm
was simulated at the detector’s aperture either with a range of zenith
directions much larger than the FoV of the instrument ($\pm$ 60∘ for both
detectors) or just within the FoV of the detectors ($\pm$30∘ for JEM–EUSO and
$\pm$22∘ for Mini–EUSO). The measured background ratio (R(ME/JE)) between
Mini–EUSO and JEM–EUSO at FS level was R(ME/JE) = 0.98 - 1.04 slightly
depending on the range of zenith angles. This indicates that the expected
photon counts for JEM–EUSO should be similar to Mini–EUSO one $\sim$(1.3 $\pm$
0.2) counts/pixel/GTU taking into account the uncertainty in the estimation of
Mini–EUSO efficiency. This result indicates that the average value of
$\sim$1.1 counts/pixel/GTU assumed in JEM–EUSO simulations is within the
current estimation and confirms the robustness of the hypotheses undertaken
with ESAF.

Table 4: Average emission values in counts/(pixel$\cdot$GTU) for Mini-EUSO for sea and ground for various lunar phases and cloudiness. In the table ‘cloudy all’ indicates the weighted average of the counts in ‘cloudy land’ and ‘cloudy sea’. Half-moon includes Moon fractions between 0.4 and 0.5, and full-moon includes fractions between 0.9 and 1. The brightest pixels (above the 99th percentile) were excluded when calculating the mean and standard deviation to mitigate the effects from bright anthropogenic sources. For conditions with multi-modal distributions, the mode closest to the average is displayed. Table adapted from minieuso-uv . | clear sea | clear land | cloudy sea | cloudy land | cloudy all
---|---|---|---|---|---
No-moon | 0.9 | 1.4 | 1.3 | 1.7 | 1.4
Half-moon | 1.8 | 2.8 | 13.0 | 8.1 | 9.7
Full-moon | 37.6 | 35.1 | 50.7 | 51.1 | 51.0

ESAF simulations are performed to test the UHECR origin of short bright
signals detected by Mini–EUSO with time duration in the range of EASs. So far
all the investigated candidates are not compatible in pulse shape and track
image with those expected from EAS. Those showing a periodic behaviour can be
immediately discarded as anthropogenic sources, while non-repetitive ones
require a more detailed analysis. One of the most interesting examples in the
Mini–EUSO data sample is shown in Fig. 25. It has been detected off the coast
of Sri Lanka. The trigger was issued by the event in the red circle. The
lightcurve presents the characteristic bi-gaussian shape of an EAS, with a
faster rise and a slower decay time. The event was compared to different
simulated EASs with variable energy and zenith angle. No simulated EAS is
compatible with both the image size and the time duration of the light
profile. In fact, the light spot is compatible with a nearly vertical event,
but the duration is much longer than the time needed by a vertical shower to
develop in atmosphere and reach the ground. This event has, therefore, a
different nature which is currently under investigation. A detailed
description of the onboard performance of the Mini–EUSO first level trigger
and search for EAS-like events can be found in matteo-asr .

Figure 25: Left panel: one frame of an event triggered off the coast of Sri
Lanka. The blue circle (upper right) encloses a static, bright light source to
be discarded. The trigger was issued by the event in the red circle. Bottom
left pane: the lightcurve of a 3$\times$3 pixel box that contains the event.
The lightcurve presents the characteristic bi-gaussian shape, with a faster
rise and a slower decay time. Center and right panels: Two proton EAS
simulated through ESAF at two different energies and zenith angles (top part
presents the image of the events while the bottom part the corresponding light
profiles). Center panel shows a simulation at zenith $\theta$ = 50∘ and energy
E = 5$\times$1021 eV. The signal persists on few pixels for $\sim$30 GTUs,
much shorter than the measured one, the sharp cutoff is given by the shower
reaching the ground. Right side is a simulation at zenith $\theta$ = 80∘ and
energy E = 2$\times$1022 eV. The signal is much longer in time but the
footprint on the focal plane is much more elongated. Image adapted from
matteo-asr .

Among Mini–EUSO scientific objectives there is also the study of slower events
such as meteors and fireballs, and the proof-of-principle of space debris
observation with absolute magnitude of M $\lesssim$ +5 using the albedo from
the Sun ebisu-debris . In optimal dark conditions, at the detection threshold
M=+5, the signal (integrated at steps of 40.96 ms) will exceed the UV-
nightglow level by 3–4$\sigma$. These events will be detected using offline
trigger algorithms on ground hiroko-debris .

Fig. 26 shows an example of a simulated meteor track having absolute magnitude
M = +5 crossing the field of view of Mini–EUSO with a 45∘ inclination with
respect to the nadir axis. The meteor speed is 70 km s-1 and its duration is 2
s. The center and right panels show two different meteor candidates detected
by Mini–EUSO. In Mini–EUSO data, there are tens of thousands of meteor
candidates with different brightness and time duration which can be simulated
with ESAF.

Figure 26: Left panel: ESAF simulated light track of a meteor of absolute
magnitude M = +5 and 45∘ inclination in Mini–EUSO (the effects of UV-nightglow
are not included and the threshold is 30 counts). Bottom: Expected light
profile. Each time bin on the x-axis corresponds to an integration time of
40.96 ms. Center & right panels: Example of meteors detected by Mini–EUSO. In
the Mini–EUSO data, there are meteors with different brightness and time
duration. Image taken from hiroko-icrc2021 .

As pointed out in ebisu-debris , a detector like Mini–EUSO is also potentially
capable of detecting space debris, if not directly exposed to sunlight. Under
this assumption, Mini–EUSO would be effectively a high-speed camera with a
large FoV and could be used as a prototype for the detection of space debris
during the twilight periods of observation. It will detect debris when they
are illuminated by the Sun. In the current simulation with ESAF, the photon
flux of the Sun in the 300–400 nm has been considered to be $10^{20}$ photons
m-2 s-1. The debris are assumed to have a spherical shape of diameter $d$ and
a variable reflectance. Therefore, the event appears as a spot of light moving
through the field of view with slowly variable light profile.

Fig. 27 shows the potential of Mini–EUSO to detect space debris. On the left
side a simulated object with 3 cm radius flying at 360 km height (40 km from
Mini–EUSO) with a speed 7.7 km/s is displayed. A study of the sensitivity of
Mini–EUSO to space debris in terms of size and relative distance has been
carried out. The trigger threshold requires a signal at least 3$\sigma$ above
background for at least 5 consecutive frames of 40.96 ms each. The UV
background has been assumed to be the same as in the other simulations at 1
count/pixel/GTU. However, it is possible that for this specific measurement,
the background could be higher due to the presence of some sunlight. Results
are displayed on the right side of Fig 27.

Figure 27: Left panel: An example of space debris detection simulated with
ESAF. Right panel: maximum distance of space debris observable by Mini–EUSO
from the ISS as a function of reflectance and size of the debris, derived from
ESAF simulations using the standard background level adopted for UHECR
detections. Image adopted from hiroko-icrc2021 .

Usually, Mini–EUSO detects on continents ground flashers. They are often
associated with airport lights (but not always). These types of lights are
simulated in ESAF as point-like sources with a rising and decaying curve
following the specifications of commercial flashers. In parallel we are also
testing the response of ESAF to the light emitted by flasher systems that have
been built in the framework of the JEM–EUSO collaboration to provide an in-
flight instrument calibration. The flasher consists of a 100 W COB-UV LEDs, DC
power supply and an Arduino circuit. The flasher campaign has been done at
Piana di Castelluccio, Italy, at 1500 m above sea level (lat. 42.766, lon.
13.190), in the clear night sky conditions of May 3rd \- 4th, 2021 when
Mini–EUSO was operational while ISS was flying over central Italy. After
including in ESAF the estimation of the detector sensitivity obtained with
ground tests, simulations were performed. The top panel of Fig. 28 shows the
Mini–EUSO data. The left plot is the raw data image of one D3 frame (GTU=40.96
ms) while the central one shows the light curve of the integrated counts of
3$\times$3 pixels around the peak count pixel inside the red circle. The right
plot shows the zoomed in image of the green circled part of the center plot,
corresponding to the timing and duration of the ESAF simulation. The bottom
panel shows the simulated flasher event with a background level of 2.5
counts/pixel/GTU which is resulting in $\sim$15$\%$ difference between
simulated and real background. The center shows the integrated counts of
3$\times$3 pixels around the peak pixel inside the red circle in the left
plot, with background photons, while the right shows the integrated counts of
the same pixels but without background photon counts to see the total signal
contribution. The tendency of signal fading as the flasher moves in the FoV is
clearly visible in both Mini–EUSO and ESAF data. As a preliminary result, the
number of expected detections obtained by ESAF matches well to the detected
number by Mini–EUSO. More details can be found in hiroko-icrc2021 .

Figure 28: Top: Mini–EUSO flasher campaign event. The central panel shows the
light evolution of summed counts of 3$\times$3 pixels around the peak count
pixel, indicated by the red-circle on the left plot, for a cycle of 1600 ms
pulse (GTU=40.96ms). The transit of the 1600 ms pulse preceded and followed by
400 ms off is clearly seen. Right panel: the zoomed in plot to the duration
and timing where ESAF simulated the same event, as shown in the bottom plots.
Bottom: Simulated flasher campaign event by ESAF. The central panel shows the
light evolution of summed counts of 3$\times$3 pixels around the peak count
pixel, indicated by the red-circle on the left plot with a background level of
2.5 counts/pixel/GTU, which is resulting in $\sim$15$\%$ difference between
simulated and real background. The right panel is the same as the central one
without background to see the signal contribution.

###  5.6 EUSO Balloons configuration

EUSO–Balloon and EUSO–SPB1 have been implemented in ESAF while EUSO–SPB2 in
its final configuration is currently implemented only in
$\overline{\mbox{Off}}\underline{\mbox{Line}}$. EUSO–Balloon and EUSO–SPB1
share the same configuration in ESAF. Only parameters such as quantum
efficiency of MAPMTs, balloon height, etc. change depending on the performed
simulation. A ray trace code configuration for the optics response has been
implemented as well together with the parametric option. The adopted trigger
logic can be activated too. Fig. 29 shows an example of a light profile and
shower track for a proton simulated EAS of 1019 eV energy and 45∘ of zenith
angle.

Figure 29: A 1019 eV, 45∘ zenith angle simulated proton event. Left: the
photoelectron profile for the EUSO–SPB1 detector. Right: the photoelectron
image for EUSO–SPB1. Image adapted from fenu-icrc2019 .

A significant difference compared to space-based missions is the much shorter
distance between the detector and cascade in the atmosphere. As a result, most
of the EAS tracks are not fully contained in the FoV. To perform an estimation
of the energy range of sensitivity to UHECRs and of the expected number of
events under specific assumptions of the balloon configuration, a new
methodology has been adopted to compute the aperture of the instrument which
speeds up the simulation by a factor of 10 at least. We defined a cylindrical
volume $\mathcal{V}$ (8 km radius on ground) around the FoV where EAS must
pass before being fully simulated by ESAF (see Fig. 30). Showers not passing
through this volume are guaranteed to never cross the FoV (which is much
smaller, $\pm$4 km side on ground) and therefore are not simulated.

Figure 30: Panel a): To speed up the simulation process in balloon
configurations, EASs are fully simulated if crossing a cylindrical volume
$\mathcal{V}$ which includes the balloon FoV. EAS not crossing this volume are
not simulated. Panel b): trigger efficiency as a function of proton EASs
energy for different heights of the balloon.

We define the exposure $\mathcal{E}$ as:

$\mathcal{E}(E)=<\epsilon>(E)\int_{A_{\rm
simu}}dA\int_{\Omega}d\Omega\int_{t_{\rm acq}}dt$ (3)

The average efficiency $<\epsilon>(E)$ is therefore computed as:

$<\epsilon>(E)=\frac{\int_{A_{\rm simu}}dA\int_{\Omega}d\Omega\frac{N_{\rm
trigg}(E,x,y,\theta,\phi)}{N_{\rm simu}(E,x,y,\theta,\phi)}}{\int_{A_{\rm
simu}}dA\int_{\Omega}d\Omega}k,$ (4)

where $k$ represents the average correction factor for the efficiency taking
into account the fraction of events passing through the volume $\mathcal{V}$
with respect to the events on the entire solid angle $N_{\rm test}$:

$k=\frac{\int_{A_{\rm simu}}dA\int_{\Omega}d\Omega\frac{N_{\rm simu}}{N_{\rm
test}}}{\int_{A_{\rm simu}}dA\int_{\Omega}d\Omega},$ (5)

The right panel of Fig. 30 presents an example of the trigger efficiency as a
function of proton EAS energy for different heights of the balloon. Finally,
the number of events is calculated as

$N(E)=\mathcal{E}(E)\Psi(E),$ (6)

where $\Psi(E)$ is a fit to the Pierre Auger spectrum auger . We see in Fig.
31 the triggered spectrum as expected by EUSO–SPB1 floating at an altitude of
30 km in clear sky and for a mission duration $t_{\rm acq}$ of 118 hours. This
was the total dark time expected prior to launch on the moon phase of March -
April 2017. The total number of events has been calculated by integrating the
number of events on the entire energy range. The spectrum is peaked at
energies around 3$\times$1018 eV. It is important to point out that this is
the energy at which EUSO–SPB1 was 50% efficient in EAS triggering according to
the field tests performed at EUSO–TA site in October 2016, prior to flight
mario-nim2019  (see sec. 5.7).

Figure 31: The expected number of triggered EAS for EUSO–SPB1 floating at an
altitude of 30 km assuming clear sky condition and a flight duration
corresponding to 118 hours of dark time. Image adapted from fenu-icrc2017 .

By implementing the cloud distribution in ESAF according to satellite
databases along the trajectories of previous NASA-SPB flights and by assuming
30 hours of acquired data, due to the short EUSO–SPB1 flight, ESAF provided a
preliminary expected number of $\sim$1 UHECR along the flight right after the
conclusion of the mission. Successive studies which employed both
$\overline{\mbox{Off}}\underline{\mbox{Line}}$ and ESAF, and took better into
account the effective detector performance, the measured background level and
the effective presence of clouds showed that this preliminary estimation
eser_icrc19 ; kenji_icrc19 ; spb1  has to be decreased by a factor of $\sim$2
(0.4 events in 25 hours of effective good quality data taking). This shows the
usefulness of ESAF either as a tool for quick performance studies or for more
accurate data analyses. Additionally, EAS tracks generated with ESAF were
extensively used in neural network algorithms to train the networks to search
for EAS tracks. No track was found in the data vrabel_icrc19 .

At the very beginning of the flight, low energy cosmic rays directly
interacting in the detector drew the attention as they looked like very fast
linear tracks, faster than normal EAS events. During one single GTU the entire
PDM is crossed by such a light pulse. An example of this class of events is
shown in Fig. 32. The left side shows the typical light track of a direct
cosmic ray quasi-planar to the PDM. The signal lasts one GTU. The right side
of the figure shows the attempted production of a similar track with an EAS
generated by an UHECR proton. The track shown in the figure is generated by a
highly inclined EAS with $\theta$ = 89∘ and energy E = 5$\times$1018 eV, with
the first interaction point at 280 km from the nadir position at 30 km
altitude, and crossing the detector FoV at a distance of $\sim$4.5 km from the
detector. The EAS event appears much dimmer than the experimental one. This is
due to two different reasons. The first is that at high altitudes the light
emission is smaller due to the much lower atmospheric density. The second is
related to the fact that the signal crosses the pixel FoV in $\sim$80 ns as
the pixel FoV is $\sim$25 m wide at 4.5 km distance from the balloon. Taking
into account a double-pulse resolution of 6 ns, the signal can not exceed a
few counts/pixel/GTU as seen in the ESAF event. It is, therefore, extremely
difficult to reproduce such a bright and fast signal in the camera with an
UHECR event. On the other hand, a direct cosmic ray can produce de-excitation
in the glass filter or photo-cathode with a decay time comparable to 1 GTU and
the signal can be much brighter. This study was carried out during the days
just after this event was detected and shows the utility of ESAF also as a
quasi-online tool to interpret the data.

Figure 32: Left side: direct cosmic ray triggering the EUSO–SPB1 detector.
Right side: simulated proton EAS of energy E = 5$\times$1018 eV crossing the
balloon FoV at $\sim$25 km altitude with a zenith angle of $\theta$ = 89∘.
They both correspond to 1 GTU data.

A first attempt to adapt the JEM–EUSO reconstruction algorithms to the balloon
configuration was performed. Fig. 33a shows an example of reconstructed shower
profile for EUSO–Balloon. We can see here the real (black line) and
reconstructed profile (points). The GIL fit to the reconstructed points marked
in red is represented as a continuous red line. As the figure shows, the
reconstructed profile is slightly overestimated (as in the case of JEM–EUSO)
due to the lack of backscattered Cherenkov correction. The profile is cut
above $\sim$1090 $g/cm^{2}$ due to the impact with the ground. The resulting
Cherenkov reflection feature is also visible in the reconstructed profile. The
shower of energy 1019 eV and 25∘ zenith angle has been reconstructed as
1.1$\times$1019 eV. The $\chi^{2}$/DoF is 0.97 and the number of degrees of
freedom of the fit is 12.

Figure 33: Panel a): we show here an example of an event reconstructed by
EUSO–Balloon. The continuous black line indicates the real simulated shower
profile (the number of charged particles in the shower at each slant depth).
The black points show the reconstructed profile as obtained by the algorithms.
The points which are accepted as fit data are indicated by red circles and the
GIL fit applied to these points is shown by the continuous red line. We
clearly see how the automatic fit correctly excluded the Cherenkov mark
visible at the end of the curve. The fitting range and the minimal threshold
automatically chosen by the algorithms are also shown as black straight lines.
Panel b): an example of the $R$ reconstruction parameter fitted over a sample
of events with a gaussian function. The sigma of the distribution is 0.16,
with a mean value of $\sim$0.15 showing a clear overestimation of the energy
due to the lack of the backscattered Cherenkov correction. Image adapted from
fenu-balloon-icrc2015 .

Fig. 33b shows a sample of reconstructed events with energy 1019 eV and 25∘
zenith angle. As in JEM–EUSO, we calculated the parameter $R$ (2) for each
event. A gaussian fit has been performed for the resulting distribution and
represented as a red continuous line. The sigma of this distribution is 0.16
providing an estimation of the resolution for this energy and angle. At
energies around 3–5$\times$1018 the resolution worsens to 30% while for 45∘
inclined EAS a further 10% decrease in resolution is observed. This is
opposite to the JEM–EUSO case, where the reconstruction of inclined EAS gives
better performance. This behaviour is due to the relatively small FoV of the
balloon leading to only partial containment within the FoV for inclined
showers and hence much larger uncertainties in the reconstruction. Concerning
the angular resolution, the $\gamma_{68}$ analysis provides resolutions which
are $\sim$4∘ for 1019 eV and 25∘ zenith angle. At 3–5$\times$1018 eV the
resolution worsens to around 5∘. On average the angular resolution for 45∘
inclined EAS worsens by $\sim$2∘. These results are consistent with the energy
reconstruction, giving again an indication that the different kinematics of
the signal may be affecting the reconstruction. The fraction of events that
can be reconstructed, even if with modest angular and energy resolutions, is
$\sim$70% at energies E $>$ 3$\times$1018 eV and angles between 25∘ and 45∘.
This is promising for the future balloon flights as it demonstrates that for a
significant fraction of detected events a reconstruction procedure could be
applied to derive a reasonable energy estimation.

We present in Fig. 34 results related to the angular reconstruction in EUSO-
Balloon. Over 12300 EAS were simulated in the energy range between 1018 and
1019 eV. The zenith angles were chosen between 10∘ and 60∘. All events were
distributed randomly having their impact point within an area of 10 $\times$
10 km2 around nadir position. The FoV projected on ground corresponds to an
area of 8.4 $\times$ 8.4 km2. The lower limit in zenith angle is due to the
fact that the track on the FS is too short to be fitted. For zenith angles
exceeding about 50∘, the shower track does not fit entirely on the PDM.
Slightly fewer than 2500 events were successfully triggered and reconstructed.
The angular reconstruction is evaluated in terms of mean value and standard
deviation between reconstructed and simulated angles ($\Delta\Theta$ =
$\Theta_{\rm rec}-\Theta_{\rm sim}$ and $\Delta\Phi$ = ($\Phi_{\rm
rec}-\Phi_{\rm sim})\cdot\cos(90-\Theta)$ ). The direction of the EAS can be
measured sufficiently well when the zenith angle is between 10∘ and
approximately 50∘. The resolution of $\gamma$, the opening angle between the
true shower direction and the reconstructed direction, is found to be
$\gamma<5$ for EAS contained within the FoV increasing and saturating at about
8 deg for uncontained showers. Obviously, the probability that parts of the
signal are lost increases at the edge of the FoV, increasing the uncertainty
in the arrival direction reconstruction. More details of this analysis can be
found in mernik-balloon-icrc2013 .

Figure 34: Mean value and standard deviation of $\Delta\Theta$ =
$\Theta_{rec}-\Theta_{sim}$ (left) and $\Delta\Phi$ =
($\Phi_{rec}-\Phi_{sim})cos(90-\Theta)$ (right) plotted against the true
zenith angle (inclination) for EUSO–Balloon. Image adapted from mernik-
balloon-icrc2013 .

###  5.7 EUSO–TA configuration

The EUSO–TA configuration has been included in ESAF as well. An example of a
simulated 1019 eV, 45∘ zenith angle event impacting at a distance of 25 km
from the detector is shown in Fig. 35.

Figure 35: A 1019 eV, 45∘ zenith angle simulated proton event impacting at 25
km distance from the detector. Panel a): the photoelectron profile for the
EUSO-–TA detector. Panel b): the photoelectron image for EUSO–-TA. Image taken
from fenu-icrc2019 .

EUSO–TA was also the first detector implemented in
$\overline{\mbox{Off}}\underline{\mbox{Line}}$. Therefore, at the very
beginning several efforts were made to cross-check the detector
implementations and EAS simulations in the two software packages, by comparing
the expected number of detected events and their characteristics with those
predicted by simulations. Fig. 36 shows a comparison between an UHECR event
observed by EUSO–TA and a proton simulated with ESAF assuming the EAS
parameters provided by the TA reconstruction of the event (E = 2.4$\times$1018
eV, zenith $\theta$ = 41∘). In this phase EUSO–TA events were acquired through
an external trigger from TA fluorescence detectors. The background is added to
the EAS simulation using real data. Taking account of reconstruction
uncertainties, the simulated event reasonably reproduces the detected one.

Figure 36: Comparison between an UHECR event observed by EUSO–TA (left) and a
proton shower simulated with ESAF (right) assuming the EAS parameters provided
by the TA reconstruction of the event (E = 2.4$\times$1018 eV, zenith $\theta$
= 41∘). No longitudinal distribution is provided for this event as its
duration is confined in 2 GTUs. The background is added to the EAS simulation
using real data. The dashed line is just guidance to recognize the event
track. Data collected in two following GTUs are added together, reducing
signal over noise ratio. The white squares include 1 full EC and 1 MAPMT not
operational at that time as well as low efficiency pixels.

The ESAF software was also used at the beginning to cross-check the measured
number of UHECRs with expectations from simulations francesca-icrc2017 . In
this analysis the following assumptions were made: 1) the TA trigger
efficiency was assumed to be 100%; 2) the cosmic ray power spectrum was
simulated with an E-1 differential spectrum in the range 1017 $\leq$ E $\leq$
1019 eV to have higher statistics of sample for calculating the trigger
efficiency for every energy bin. The spectrum was later on re-weighted
according to the IceTop measurements icetop  in the 1017 \- 5$\times$1017 eV
energy range and with the Auger spectrum auger  at higher energies; 3) EASs
were uniformly generated in azimuth angle with a $\sin(2\cdot\theta)$
distribution in zenith angle; 4) the impact point on ground of the shower axis
was generated uniformly within a radius $R$ $\leq$ 50 km around the telescope.
The number of EASs within the EUSO–TA FoV with an impact parameter 1 $\leq$
$R_{p}$ $\leq$ 10 km was then estimated. A selection was made to require at
least 200, 400, or 600 counts in the detector integrated over 3 consecutive
GTUs. EASs in EUSO–TA are detected on average at even closer distances
compared to the balloon configuration, so the signal can last no more than 1
GTU. Fig. 37 shows the relation between the EAS energy and the impact
parameter $R_{p}$. Among 1000 simulated events with a power spectrum E-1, 229,
118, and 67 EASs generated more than 200, 400, and 600 counts in the EUSO–TA
detector, respectively.

Figure 37: Relation between the EAS energy and the impact parameter $R_{p}$.
1000 proton events were simulated, and among them 229, 118, and 67 events
generated more than 200, 400, and 600 counts over 3 consecutive GTUs in the
EUSO–TA detector, respectively. In this plot a cosmic ray power spectrum E-1
has been considered: more events at high energies are present in the plot than
expected in reality, for which the average spectrum scales by about E-3. Image
taken from francesca-icrc2017 .

This number of events was then rescaled by taking into account the IceTop and
Auger fluxes. The results indicate that under the assumption of an acquisition
time of 120 hours, the total acquisition time in 2015, EUSO–TA can detect
$\sim$6 events with a signal of at least 600 counts integrated over 3
consecutive GTUs. This signal is in the range of the photon-counts excess over
the background level, typically measured in the events detected by EUSO–TA.

These results, extrapolated to 140 hours of effective data taking by EUSO-TA
would predict 7 detectable events which is a number compatible with the 9
effectively detected events by EUSO-TA in similar amount of time, thus
confirming the capability of ESAF to reproduce the EAS detected by the EUSO-
TA.

##  6 Conclusions and perspectives

The JEM–EUSO program is an international effort devoted to the study of UHECRs
from space. The program consists of a series of missions some completed and
some in preparation, in space, on stratospheric balloons, or on ground. All
such detectors demand an extensive simulation work to estimate the performance
and to support the data analysis. The original ESAF package developed in the
framework of the EUSO project evolved within the JEM–EUSO collaboration. A new
branch was created which includes the detector configurations of almost all
the missions which have been conceived, performed, or under development in the
program: JEM–EUSO, K–EUSO, POEMMA, TUS, Mini–EUSO, EUSO–Balloon, EUSO–SPB1,
and EUSO–TA. Along the years, the ESAF code was an essential tool to assess
the expected performance of the missions, to fine tune their objectives and to
drive the technological developments in order to satisfy the scientific
requirements as well as to help in the interpretation of the collected
experimental data. In fact, thanks to the missions of the JEM–EUSO program,
for the first time the ESAF simulated data have been compared to experimental
measurements. Moreover, the large panel of scientific objectives of missions
like Mini–EUSO and TUS, required the implementation in ESAF of simplified
versions of a large variety of luminous transients aside from EASs, such as
elves, meteors, space debris and flashers which were not present in the
original ESAF version. In conclusion, evaluation of the expected performance
of future space-based missions and interpretation of the experimental data
with ESAF simulations indicate that a space-based UHECR detector has a
satisfactory performance to contribute in unveiling the origin of the
extremely energetic particles of the Universe.

ESAF is expected to remain an essential tool for further developments of the
planned missions of the program and for the interpretation of the data they
will acquire.

Acknowledgments This work was partially supported by Basic Science
Interdisciplinary Research Projects of RIKEN and JSPS KAKENHI Grant (22340063,
23340081, and 24244042), by the ASI-INAF agreement n.2017-14-H.O, by the
Italian Ministry of Foreign Affairs and International Cooperation, by the
Italian Space Agency through the ASI INFN agreements Mini-EUSO n. 2016-1-U.0,
EUSO-SPB1 n. 2017-8-H.0, OBP (n. 2020-26-Hh.0) and EUSO-SPB2 n. 2021-8-HH.0.
by NASA award 11-APRA-0058, 16-APROBES16-0023, 17-APRA17-0066, NNX17AJ82G,
NNX13AH54G, 80NSSC18K0246, 80NSSC18K0473, 80NSSC19K0626, 80NSSC18K0464 and
80NSSC22K1488 in the USA, by the French space agency CNES, by the Deutsches
Zentrum für Luft- und Raumfahrt, the Helmholtz Alliance for Astroparticle
Physics funded by the Initiative and Networking Fund of the Helmholtz
Association (Germany), by Slovak Academy of Sciences MVTS JEM–EUSO, by
National Science Centre in Poland grants 2017/27/B/ST9/02162 and
2020/37/B/ST9/01821, by Deutsche Forschungsgemeinschaft (DFG, German Research
Foundation) under Germany Excellence Strategy - EXC-2094-390783311, by Mexican
funding agencies PAPIIT-UNAM, CONACyT and the Mexican Space Agency (AEM), as
well as VEGA grant agency project 2/0132/17, by grant S2018/NMT-4291 (
TEC2SPACE-CM ) ”Desarrollo y explotación de nuevas tecnologías para