# The expected potential of hadronic PeVatron searches with spectral
$\gamma$-ray data from the Southern Wide-field Gamma-ray Observatory

Ekrem Oğuzhan Angüner<EMAIL_ADDRESS>Tülün Ergin

###### Abstract

The presence of a spectral softening, occurring at $\sim$3 PeV energies, seen
in the local cosmic-ray energy spectrum provides an evidence that our Galaxy
hosts astrophysical objects, known as ’hadronic PeVatrons’, that are capable
of accelerating hadrons to PeV energies and above. Recent results from ground-
based particle detector array experiments have provided conclusive evidence
that these facilities are essential to explore the ultra-high-energy (UHE,
E$>$100 TeV) $\gamma$-ray domain and pinpoint the location of PeVatrons in the
Galaxy. The Southern Wide-field Gamma-ray Observatory (SWGO) is proposed next-
generation ground-based extensive air shower observatory planned for
construction in the Southern Hemisphere, which holds great scientific
potential for UHE observations. In this study, we investigate the expected
potential of SWGO to search for hadronic PeVatrons, based on the publicly
available preliminary SWGO straw-man instrument response functions (IRFs). By
using these straw-man IRFs, it can be shown that the SWGO detection of
$\gamma$-ray spectral cutoffs between 30 TeV and 100 TeV, at a 95$\%$
confidence level, is possible for faint $\gamma$-ray sources of $\sim$5 mCrab
given that the spectral index is hard ($\Gamma\lesssim$ 2.0), while spectral
cutoffs from softer sources with $\Gamma\cong$2.3 can be detected for sources
brighter than $\sim$11$-$12 mCrab. The reconstructed SWGO PeVatron detection
maps demonstrate that the future SWGO experiment can probe large parts of the
investigated PeVatron parameter space, providing a robust detection and/or
rejection of presence of spectral signatures associated with hadronic
PeVatrons. A dedicated study on the promising Southern-sky PeVatron
candidates, the Galactic Center region, Westerlund 1, HESS J1702$-$420 and
HESS J1641$-$463, shows that the SWGO will have a great potential to confirm
or exclude PeVatron nature of these candidate sources at a robust significance
level after 5-years of observation. In addition, it is shown that controlling
systematic errors will be necessary to reach full potential of the SWGO
experiment for PeVatron searches.

###### keywords:

Gamma rays: general , Cosmic rays , Galactic PeVatrons , Methods: data
analysis , Methods: statistical

††journal: Astroparticle Physics

[1]country=TÜBİTAK Research Institute for Fundamental Sciences, 41470 Gebze,
Turkey [2]Department of Physics and Astronomy, Michigan State University, East
Lansing, MI, USA [3]Middle East Technical University, Northern Cyprus Campus,
99738 Kalkanli via Mersin 10, Turkey

##  1 Introduction

Cosmic Rays (CRs) are charged particles, roaming in our Galaxy with
relativistic speeds and arriving the Earth’s atmosphere isotropically from
outer space. Decades of measurements have shown that the composition of CRs
consist mainly of protons ($\sim$90$\%$) followed by Helium nuclei
($\sim$9$\%$), while the rest are heavier ions and electrons (see Blasi
(2013); Amato (2014); Amato and Blasi (2018) for detailed review). The energy
spectrum of CRs measured on Earth ranges from a few MeVs to beyond 1020 eV.
Above $\sim 30$ GeV energies, it was historically described by a smooth power-
law spectrum with an index of $-$2.7 up to the so called "knee" feature,
emerging at $\sim$3 PeV (1 PeV=$10^{15}$ eV), where the spectrum steepens
significantly to $-$3.1 above these energies. When only the cosmic Hydrogen
and Helium spectra are considered, there is an evidence that the respective
knee is below 1 PeV, at energies around 700 TeV (ARGO-YBJ Collaboration et
al., 2015). The detailed CR measurements have provided evidence of spectral
hardening around 100$-$300 GeV energies and re-softening at higher energies
around $\sim$100 TeV for all type of nuclei (Adriani et al., 2011; Aguilar et
al., 2015b, a; Adriani and CALET Collaboration, 2022; Cardillo and Giuliani,
2023), especially for protons and Helium. These unique spectral
characteristics suggest that a rigidity-dependent acceleration mechanism is at
work in Galactic CR sources, allowing heavier nuclei to be accelerated to
higher energies (Amato and Blasi, 2018; Amato and Casanova, 2021).
Consequently, the knee feature observed in the CR spectrum can be interpreted
as a sum of different nuclei types, each showing their unique cutoff in their
respective spectra. As a result, the overall CR spectrum exhibiting more or
less a smooth power-law up to 3 PeV energies provides a strong evidence that
the sources in our Galaxy must accelerate CRs at least up to PeV energies and
even well beyond. The existence of a "second knee" feature seen at $\sim$100
PeV energies, which is thought to be originated from the heaviest nuclei, such
as Fe (Z=26), further supports this idea (Schroder, 2019; Coleman, 2019;
Cristofari, 2021). Given this scenario, it is believed that the second knee
structure marks the lower bound of the energy region where transition from
Galactic to the extra-galactic CRs occurs. Additionally, the recent detection
of ultra-high-energy (UHE, E$>$100 TeV) diffuse $\gamma$-ray emission from the
Galactic plane (Amenomori et al., 2021a; Cao et al., 2023a) offers an
alternative indirect way to study the distribution and propagation of global
CRs in the Galaxy, when compared to local CR observations performed on Earth.
More detailed reviews on the topic of CRs can be found in Amato (2014); Amato
and Blasi (2018); Amato and Casanova (2021); Cristofari (2021); Di Sciascio
(2022); Vink (2022); Casanova (2022).

In this context, the term "PeVatron" stands for astrophysical sources which
can energize CRs at least up to PeV energies and beyond. Various astrophysical
source classes, such as supernova (SN) Remnants (SNRs) (Bell, 1978; Gabici and
Aharonian, 2007; Celli et al., 2019), massive star clusters (MSCs) (Aharonian
et al., 2019; Morlino et al., 2021), core-collapse SNe (Tatischeff, 2009; Bell
et al., 2013; Zirakashvili and Ptuskin, 2016; Marcowith and et al., 2018),
pulsar wind nebulae (PWNe) (Amato, E. et al., 2003; Ohira et al., 2018;
Guépin, Claire et al., 2020; Amato and Olmi, 2021), TeV halos (Linden et al.,
2017; Fang, 2022), star formation regions (SFRs) (Bykov et al., 2020),
microquasars (Abeysekara et al., 2018) and superbubbles (Higdon and
Lingenfelter, 2003; Binns et al., 2005; Vieu et al., 2022), are expected to be
promising PeVatron candidates. PeVatrons are categorized as "hadronic
PeVatrons" or "leptonic PeVatrons" depending on whether the accelerated
particles are primarily hadrons or leptons, respectively. The definition of
PeVatron focuses on the maximum achievable energy of an accelerator,
identifying the PeVatron nature based on the highest energy reached by
individual particles at the acceleration site. This definition establishes a
strict energy threshold of ’1 PeV’, distinguishing between PeVatron and non-
PeVatron nature of the source, consequently making the 1 PeV energy threshold
the primary property of a PeVatron. The detection of UHE $\gamma$-rays above 1
PeV from the Crab Nebula (LHAASO Collaboration et al., 2021), a known host of
leptons with PeV energies for over a decade (Amato and Olmi, 2021), and the
Cygnus Cocoon region (Cao and others, 2021), a superbubble surrounding a
massive star formation region (Ackermann et al., 2011), implies the existence
of particles accelerated to PeV energies at these sites, regardless of whether
the emission has hadronic or leptonic origin, making the Crab Nebula and
Cygnus Cocoon robust Galactic PeVatron sources according to the definition
given above. The question of the origin of CRs, specifically the astrophysical
accelerators capable of energizing CRs up to the observed knee feature around
$\sim$3 PeV energies, stands as one of the top scientific questions in
astrophysics. Within this context, the investigation into the origin of CRs is
directly linked to hadronic PeVatrons, as the contribution of leptons to the
observed CR spectrum is negligible ($\sim$1-2$\%$). To account for the knee
feature around $\sim$3 PeV, CR sources must efficiently accelerate bulk of
hadrons well beyond 1 PeV energies. Consequently, the hadronic spectrum
produced by the accelerator should extend beyond 1 PeV energies without
exhibiting a spectral cutoff.

From the experimental point of view, observed high-energy (HE, E$>$100 MeV)
and UHE $\gamma$-ray emission are the primary means to explore the origins of
CRs. When $\gamma$-rays are created from proton-proton (pp) interactions
followed by subsequent pion decay, the energy of $\gamma$-rays is typically
around 10 times lower than the energy of parent protons (Kelner et al., 2006;
Kafexhiu et al., 2014; Celli et al., 2020), and can create spectral features
in the $\gamma$-ray spectrum, providing clear signatures of hadronic
interactions. For example, the AGILE and Fermi-LAT results (Giuliani, 2011;
Ackermann, 2013) demonstrated that Galactic SNRs can accelerate CRs, producing
low energy (MeV$-$GeV) $\gamma$-rays showing up as a "pion-bump" feature111The
pion bump is a characteristic spectral feature observed in the spectral energy
distribution of $\gamma$ rays, seen in between 100 MeV and 1 GeV energies.
This feature is a result of hadronic interactions between accelerated CRs with
the surrounding gas. Please refer to Yang, R. et al. (2018) for more details.
in the observed SNRs’ energy spectra. On the other hand, regardless of whether
they are hadronic or leptonic, significant UHE emission is one of the main
characteristics of PeVatron sources and must be detected for a robust claim of
PeVatron nature. In the hadronic case, correlation with target material, in
which accelerated particles can interact with, is expected. It is important to
note that the target region, where CR interactions take place, is an evidence
of PeVatron activity, but the region does not necessarily host the PeVatron
source itself. In addition, neutrino emission is a clear indication of
hadronic interactions (Kelner et al., 2006; Anchordoqui et al., 2014).
However, the sensitivities of current neutrino experiments, i.e. IceCube
(Abbasi and et al., 2009) and Baikal-GVD (Zabarov and the Baikal-GDV
Collaboration, 2021), are not sufficient to put strong constraints on
significant discrimination between hadronic and leptonic nature of PeVatrons
(Abbasi et al., 2023), while the future neutrino observatories, such as
IceCube-Gen2222https://www.icecube-gen2.de/index-eng.html and
KM3NeT333https://www.km3net.org/, are expected to reach such high
sensitivities.

The first indication of the presence of a Galactic PeVatron at the Galactic
center (GC) region is discussed in HESS Collaboration et al. (2016). Detection
of the GC PeVatron was claimed based on the derived 95$\%$ confidence level
(CL) lower limits on the parent proton spectral cutoff of 0.4 PeV, together
with the strong correlation observed between the very-high energy (VHE, 0.1
TeV$<$E$<$100 TeV) $\gamma$-ray emission and distribution of molecular gas.
After this pioneering study, interpreting PeVatron nature of a source based on
95$\%$ CL lower limits of the proton spectral cutoff became a standard
approach in PeVatron searches (Spengler, G., 2020; Abdalla, H. et al., 2021).
In the following years, ground-based water Cherenkov detector (WCD)
experiments, Tibet AS-gamma (Amenomori et al., 2019, 2021b) and the High-
Altitude Water Cherenkov Observatory (HAWC) (Abeysekara et al., 2020),
reported significant detection of Galactic UHE photons and sources,
respectively. Finally, the discovery of 12 Galactic UHE source by the LHAASO
collaboration marked a major milestone in PeVatron searches, and completely
reshaped our understanding of the PeVatron concept, as many of these sources
are plausibly associated to leptonic accelerators like pulsars and PWNe (Cao
and others, 2021). The recently published first LHAASO catalogue of
$\gamma$-ray sources have revealed 43 UHE sources detected above 100 TeV with
significance greater than 4$\sigma$ (Cao et al., 2023b).

These experimental results have provided clear evidence that ground-based
WCDs, e.g. HAWC and LHAASO, due to their enhanced high energy flux
sensitivities above $\sim$10 TeV, are the key facilities to explore the UHE
regime and locate PeVatrons in the Galaxy, therefore making them "PeVatron
hunters". However, up to date, no Galactic source that has been firmly proven
to accelerate hadrons to PeV energies and above could be identified. This is
due to the fact that discrimination between hadronic and leptonic PeVatrons,
using current observational data, are extremely challenging. On the other
hand, angular resolution of WCD experiments ($\sim$0.2∘-0.3∘) is a factor of
3$-$4 worst when compared to current generation imaging atmospheric Cherenkov
telescopes (IACTs). Such a disadvantage causes source confusion to become a
major problem for the ground-based WCD observations, consequently making it
impossible to pin down the astrophysical origin of the observed emission from
morphology studies. The synergy between future VHE and UHE $\gamma$-ray
instruments such as the Cherenkov Telescope Array (CTA) (Acharya and et al.,
2013; Hofmann and Zanin, 2023) and the Southern Wide-field Gamma-ray
Observatory (SWGO) (Albert, A. et al., 2019) will play a critical role for
robust identification of Galactic PeVatrons which can contribute significantly
to the CR knee feature. In addition, future neutrino experiments, like KM3NeT
and IceCube-Gen2, will be able to provide sensitive measurements that can
resolve the ambiguity between leptonic and hadronic PeVatrons. More detailed
reviews on the topic of PeVatrons can be found in Amato and Casanova (2021);
Amato and Blasi (2018); Amato (2014); Di Sciascio (2022); Casanova (2022);
Cristofari (2021); Vink (2022); Sudoh and Beacom (2023); la Fuente et al.
(2023); Cardillo and Giuliani (2023); Angüner (2023); Cao et al. (2023c).

Throughout this paper, we focus on the hadronic PeVatrons, namely source of
CRs at energies around the knee of the CR spectrum. Consequently, the leptonic
PeVatrons are out of the scope of this study. The paper is structured as
follows. The next-generation SWGO experiment is briefly introduced in Sec. 2.
Simulations of the SWGO observations and the data analysis methods employed in
this study are discussed in Sec. 3. The results on the investigation of SWGO’s
sensitivity in $\gamma$-ray spectral cutoff detection are provided and
discussed in Sec. 4. The general ability of SWGO to identify PeVatron sources
is quantified in Sec. 5. Simulation results of the SWGO observations of the
promising PeVatron candidates in the Southern-sky are provided and discussed
in Sec. 6. Finally, the discussions and conclusions are summarized in Sec. 7.

##  2 The Southern Wide-field Gamma-ray Observatory

SWGO is a proposed next-generation ground-based Extensive Air Shower (EAS)
observatory to be built in the Southern Hemisphere, designed to scan large
parts of the sky with a large field of view (FoV) at a very high duty cycle
($>$95$\%$), and measure $\gamma$-rays within the range spanning from a few
hundred GeVs to PeV energies (Albert, A. et al., 2019). Expected to start full
operations by 2026, SWGO is set to maintain its operational capacity for a
minimum of 10 years. The fundamental structure of SWGO consists of ground-
based WCDs, positioned in the Southern Hemisphere at an altitude exceeding
4400 m above sea level (Conceiç$\tilde{\rm{a}}$o and SWGO Collaboration, 2023;
Barres de Almeida and SWGO Collaboration, 2022). These WCDs are designed to
optimize and enhance both signal collection and particle recognition
capabilities through the exceptionally precise time resolution ($\Delta$t
$\approx$ 2 ns) and advanced signal reconstruction techniques, respectively.
One of the proposed detector designs is a dual-layered water Cherenkov tank,
which will enable reconstructing the number of muons and separating primary
CRs, therefore both increasing the background rejection rate and allow CR
anisotropy measurements (Lang and SWGO Collaboration, 2023), respectively.

The scientific potential and capabilities of ground-based EAS arrays have
already been demonstrated by the current generation observatories like HAWC
(Abeysekara, A.U. et al., 2017) and LHAASO (Vernetto and for the LHAASO
Collaboration, 2016), both of which are located in the Northern Hemisphere.
Despite the Southern-sky holds great scientific potential, there is currently
no operational EAS observatory in the Southern Hemisphere. In this regard,
SWGO will serve as a complementary to the currently existing ground-based EAS
observatories in the Northern Hemisphere, and to the next-generation IACT
project, the CTA observatory. Through a five-year data collection with SWGO,
it is expected that the sensitivity of detecting point-like $\gamma$-ray
sources at energies exceeding 10 TeV will be better when compared to 50 hours
of CTA data (Albert, A. et al., 2019). This advantage, together with its large
FoV, makes SWGO an ideal observatory to search for $\gamma$-ray sources above
several 10 TeV. Such capability is particularly important for revealing
sources of Galactic CR acceleration and the systematic investigation of
transient events at these high energies. Furthermore, SWGO has the potential
to play a key role in subsequent follow-up observation campaigns in case of
transient alerts and multi-messenger triggers, both by mapping the
distribution of transient and by extending the simultaneous sky coverage of
$\gamma$-ray monitoring facilities, e.g. HAWC, LHAASO, and CTA (La Mura et
al., 2020), respectively. In addition, strategic location of SWGO close to the
Southern Tropic (Albert, A. et al., 2019) ensures efficient coverage of the
declination band of transient events that might be associated to neutrino
alerts from current neutrino observatories, e.g.
IceCube444https://icecube.wisc.edu/science/real-time-alerts/ (Meneguolo et
al., 2023), future neutrino observatories like KM3NeT and IceCube-Gen2, and
gravitational wave observatories, such as LIGO
555https://emfollow.docs.ligo.org/userguide/early-warning.html (Magee and et
al., 2021).

The search for the location of the SWGO construction site has been in progress
as a part of the research and development phase, and is expected to reach its
conclusion by the end of 2024. Up to date, the SWGO collaboration has been
systematically gathering detailed information regarding the potential sites
under consideration, which are located in Argentina, Chile, and Peru (Doro and
SWGO Collaboration, 2022). The selection of these candidate sites was based on
various factors including altitude, local topology, environmental conditions,
site access, transport costs, as well as the availability and cost of
essential resources like water, power, and network connectivity (Santander and
SWGO Collaboration, 2023).

Figure 1: A comparison of differential point-like source sensitivities between
the SWGO (the 1 year straw-man, solid-orange, taken from Albert, A. et al.
(2019)), Fermi-LAT (10 years P8R3-SOURCE-V3, solid-brown, taken from Ajello et
al. (2021)), CTA (50 h Southern array prod5.v0.1, solid-blue, taken from CTA
Observatory and Consortium (2021)), HAWC (507 days, solid-magenta, taken from
Abeysekara, A.U. et al. (2017)) and LHAASO WCDA (1 year, solid-gray) and
LHAASO KM2A (1 year, solid-black) taken from Chen et al. (2022); della Volpe
(2023). The yellow, red and blue shaded bands indicate the foreseen phase-
space exploration of the low-energy, mid-energy and high-energy enhancement,
respectively, for the SWGO experiment. The figure is adapted from Hinton and
SWGO Collaboration (2022).

Figure 1 shows the differential point-like source sensitivity curves from
various experiments, along with the sensitivity of the SWGO for 14 different
detector and array layout configurations, which are indicated with shaded
bands featuring different colors. The selection of these configurations
follows a detailed investigation of array and detector parameters, including
dimensions of the detector station, number and size of photo-sensors placed
inside the detector, and the distribution of the dense inner (for lower
energies) and sparse outer array (for higher energies), as well as the
correspondence between them. The solid orange sensitivity curve shown in Fig.
1 represents the preliminary baseline configuration of SWGO, which is referred
as the straw-man design throughout this paper. This straw-man design
configuration comprises a compact inner array with a 160 m radius and a fill
factor of $\sim$80$\%$, which is surrounded by a less dense outer array,
having a radius of 300 m and a fill factor of $\sim$5$\%$. The detector units
in both the inner and outer arrays, resembling a two-compartment cylindrical
tank with a diameter of 3.8 m, are identical and resulting in a total of 6600
detector units (Schoorlemmer and SWGO Collaboration, 2022). The sensitivity of
the straw man design was evaluated between 20 GeV up to 500 TeV by
extrapolating the published HAWC performance metrics (Abeysekara, A.U. et al.,
2017), such as the angular and energy resolution to be $\sim$0.15∘ and
$\sim$25$\%$ at 30 TeV, respectively, as well as the passing rate of the gamma
and hadron cut to be $\sim$2$\times 10^{-3}$ (see Fig. 11 of Abeysekara, A.U.
et al. (2017)).

The sensitivity curve of SWGO shown in Fig. 1 serves as a guiding reference to
direct the design studies, rather than being a definite measure of SWGO
performance. The comprehensive exploration of the complete parameter phase-
space is expected to be completed in 2024. The differently colored shaded
regions in Fig. 1 represent various design options aimed at improving the
sensitivity of the straw man design. Potential enhancements in low-energy
performance (shaded yellow region) are achievable by lowering the individual
unit thresholds and the exploration of higher elevation sites. In the mid-
energy range (shaded red region), it has been shown that significant
enhancements in both angular resolution and background rejection can be
achieved (Hofmann, 2020; Kunwar, 2021; Conceição et al., 2021). The lower
limit of the color band, marked by the dashed line, corresponds to a 30$\%$
improvement in the point spread function (PSF) and a tenfold increase in
background rejection efficiency. Particularly, ongoing investigations focus on
compact detector units with dedicated muon tagging capabilities to further
enhance background rejection efficiency. For the high-energy range (shaded
blue region), performance improvements can be achieved by implementing a low-
density, large outer array with a size of a few square kilometers, coupled
with effective background rejection capabilities. As it was evident from the
LHAASO results (Cao and others, 2021), it is possible to implement a square
kilometer array with a background efficiency of $\sim$10-5. These studies will
provide valuable insights for identifying the most favorable SWGO design
configurations to consider, subsequently followed by the production of the
official SWGO instrument response functions (IRFs). Therefore, we explicitly
mention that the results and conclusions presented throughout this paper are
not based on any official IRFs or tools provided by the SWGO collaboration.
Additionally, the results and conclusions derived in this paper are
conservative with regard to their dependence on the assumed differential
sensitivity.

##  3 Simulations and data analysis

The expected potential of identifying point-like PeVatron sources using the
forthcoming SWGO experiment data is evaluated through Monte-Carlo (MC)
simulations, based on the differential straw-man sensitivity666The
differential straw-man sensitivity curve data are taken from
https://github.com/harmscho/SGSOSensitivity. outlined in Albert, A. et al.
(2019). This straw-man SWGO sensitivity curve is provided with an energy
binning approach. Each bin, indexed with $i$ and centered at the energy value
of $E_{i}$, in principle, determines the minimum detectable $\gamma$-ray flux
level $\Phi_{\mathrm{Sens}}(E_{i})$ within it, ensuring a $5\sigma$ detection
significance, assuming observation times of both 1 year and 5 years. For each
specific $E_{i}$, the simulated $\gamma$-ray flux points $\Phi(E_{i})$ are
generated based on SWGO straw-man sensitivity curve with
$\sigma(E_{i})=\Phi_{\mathrm{Sens}}(E_{i})/5$ as the standard deviation, and
are distributed normally around $\Phi_{\mathrm{True}}(E_{i})$ representing the
predicted $\gamma$-ray spectrum from astrophysical sources. Spectral data
points exhibiting a relative error $\sigma(E_{i})/\Phi(E_{i})$ exceeding
100$\%$ are excluded from subsequent analyses. This exclusion is due to the
intention of deriving flux upper limits for such data points in practical
analysis applications.

In the subsequent sections, either the simulated SWGO $\gamma$-ray flux data
or publicly available spectral $\gamma$-ray flux data obtained from H.E.S.S.
observations of various Galactic PeVatron candidate sources are analyzed
within the framework of gammapy (Deil et al., 2020). The analysis procedure is
based on fitting the respective flux data sets to $\gamma$-ray emission
models. The model parameters that best describe the data are determined by
minimizing the $\chi^{2}$ statistic.

When dealing with the publicly available H.E.S.S. flux data, which may include
asymmetric statistical errors represented by $[\sigma_{-},\sigma_{+}]$, the
symmetric statistical errors given by
$\sigma_{\mathrm{stat}}=\mathrm{max}\\{\sigma_{-},\,\sigma_{+}\\}$ are
conservatively adapted instead of directly incorporating the asymmetric
errors. Additionally, relative systematic flux error of
$\sigma_{\mathrm{sys}}=\xi\,dN/dE$ with $\xi$=20$\%$ is taken into account for
the H.E.S.S. data (Aharonian et al., 2006). To explore the potential impact of
systematic errors on the PeVatron searches with SWGO, relative systematics of
$\xi$=5$\%$ (optimistic case) and $\xi$=10$\%$ (conservative case) are assumed
in the simulated SWGO flux points. These assumptions are based on the 7$\%$
flux systematics observed in the LHAASO experiment (Aharonian et al., 2021).
Finally, the overall error associated with the analyzed flux data points is
determined by selecting the larger value as
$\sigma=\mathrm{max}\\{\sigma_{\mathrm{sys}},\,\sigma_{\mathrm{stat}}\\}$.
This combined error estimation ensures a conservative consideration of the
uncertainties in the analysis.

The differential spectrum of $\gamma$-ray sources are modeled as exponential
cutoff power law (ECPL) model formulated as follows

$\Phi_{\mathrm{ECPL}}(E)=\Phi_{0}\mathrm{(E_{0})}\cdot\left(\frac{E}{E_{0}}\right)^{-\Gamma_{\gamma}}\cdot\exp{\left(-\lambda_{\gamma}\;E\right)}\,\mathrm{,}$
(1)

where $\lambda_{\gamma}$=(1/$E_{cut,\,\gamma}$) is the inverse $\gamma$-ray
cutoff energy with $E_{cut,\,\gamma}$ representing the cutoff energy of
$\gamma$-ray spectrum, $\Gamma_{\gamma}$ is the spectral index and
$\Phi_{0}$($E_{0}$) is the source flux normalization at the reference energy
$E_{0}$. Likewise, the differential energy distribution of accelerated protons
is also assumed to follow an ECPL model expressed as

$J_{\mathrm{p}}(E_{\mathrm{p}})\sim
E_{\mathrm{p}}^{-\Gamma_{\mathrm{P}}}\;\exp\left(-\left(\lambda_{\mathrm{p}}\;{E_{\mathrm{\mathrm{p}}}}\right)^{\beta}\right)\,\mathrm{,}$
(2)

where $\lambda_{\mathrm{p}}$=(1/$E_{\mathrm{cut,\,\mathrm{p}}}$) is the
inverse proton cutoff energy $E_{\mathrm{cut,\,p}}$ and $\Gamma_{\mathrm{P}}$
is the proton spectral index. The parameter $\beta$ describes the degree of
sharpness in the exponential cutoff, and for the analyses presented in this
paper, it is fixed to $\beta$=1. This choice adequately captures the particle
spectra characteristics in scenarios involving hadronic acceleration as
discussed in Schure and Bell (2013); Cristofari et al. (2020); Angüner et al.
(2023). The likelihood test statistics,

$\mathrm{TS}_{\gamma,\mathrm{p}}=-2\ln\frac{\hat{L}(\lambda_{\gamma,\mathrm{p}}=0)}{\hat{L}(\lambda_{\gamma,\mathrm{p}})},$
(3)

where $\hat{L}(\lambda_{\gamma,\mathrm{p}})$ and
$\hat{L}(\lambda_{\gamma,\mathrm{p}}=0)$ are the maximum likelihoods over the
full parameter space, either for $\gamma$-rays
($\lambda_{\gamma},\,\Phi_{0,\gamma},\,\Gamma_{\gamma}$) or protons
$(\lambda_{\mathrm{p}},\,\Phi_{0,\mathrm{p}},\,\Gamma_{\mathrm{p}})$, used for
quantifying the statistical significance of $\gamma$-ray spectral energy
cutoffs
($\mathrm{S}_{\mathrm{cut,\gamma}}$=$\sqrt{\mathrm{TS}_{\mathrm{\gamma}}}$)
and protons spectral cutoffs
($\mathrm{S}_{\mathrm{cut,p}}$=$\sqrt{\mathrm{TS}_{\mathrm{p}}}$),
respectively. The PeVatron Test Statistics (PTS) method, as introduced in
Acero, F. et al. (2023) and formulated as

$\mathrm{PTS}=-2\ln\frac{\hat{L}(E_{\mathrm{cut,\,p}}=1\,\mathrm{PeV},\boldsymbol{\theta}|D)}{\hat{L}(E_{\mathrm{cut,\,p}},\boldsymbol{\theta}|D)}\,\mathrm{,}$
(4)

offers a likelihood ratio test that enables the measurement of the deviation
of the best-fit hadronic energy cutoff, denoted as $E_{\mathrm{cut,\,p}}$,
extracted from a specific set of observed data ($\mathrm{D}$), from a fixed
proton cutoff energy threshold set at 1 PeV. Throughout this paper, only flux
data $\Phi(E_{i})$ with errors $\sigma(E_{i})$ in energy bins $E_{i}$ are
analyzed, and the adopted likelihood function is given by

$L(E_{\mathrm{cut,\,p}},\,\boldsymbol{\theta}|D)=-2\sum_{i}\left(\frac{\Phi_{\gamma}(E_{i}|E_{\mathrm{cut,\,p}},\,\boldsymbol{\theta})-\Phi(E_{i})}{\sigma(E_{i})}\right)^{2}\,\mathrm{,}$
(5)

where $\boldsymbol{\theta}=(\Gamma_{\mathrm{P}},\Phi_{0,\mathrm{p}})$. This
paper consistently employs the statistical significance of the PTS
($S_{\mathrm{PTS}}=\mathrm{sign}(E_{\mathrm{cut,\,p}}-1\,\mathrm{PeV})\sqrt{\mathrm{PTS}}$)
to gauge the level of statistical significance regarding the identification of
spectral PeVatron signatures. The ecpli package (Spengler, G., 2022) is used
to derive lower limits for both hadronic and $\gamma$-ray cutoff energies
associated to a given source, following the methods as explained
comprehensively in the appendix provided in Acero, F. et al. (2023). The
analysis presented in this paper does not include the impact of the
attenuation of $\gamma$-ray emission due to pair creation, i.e. the process
$\gamma\gamma\rightarrow e^{+}e^{-}$. This exclusion is due to the focus on
simulated spectral $\gamma$-ray flux points with energies below 200$-$300 TeV.
As outlined in Vernetto and Lipari (2016), it is assumed that the flux
attenuation due to pair creation is negligible ($<$ 10$\%$) below these
energies. Nevertheless, it is important to mention that when simulating SWGO
data without accounting for systematic errors ($\xi=0$), the impact of pair
creation can become significant, particularly depending on the location of the
source in the Galaxy and its distance.

##  4 Investigating SWGO’s sensitivity in $\gamma$-ray spectral cutoff
detection

The SWGO Collaboration has defined a set of science benchmarks, encompassing
the key target scientific objectives of the SWGO project, with the aim of
exploring performance parameters that are crucial for the best possible
optimization of the forthcoming SWGO experiment (Hinton and SWGO
Collaboration, 2022). One of them is directly related to PeVatron searches and
defined under the ’Galactic accelerators’ science case. The benchmark is
described as "Maximum exponential-cutoff energy detectable at 95$\%$ CL in 5
years for a $\gamma$-ray source with spectral parameters of $\Phi_{0}$(1
TeV)=5 mCrab777The Crab unit is taken as the differential Crab flux level at 1
TeV of 3.84 $\times$ 10-11 cm-2 s-1 TeV-1 following Table 6 of Aharonian et
al. (2006) and $\Gamma_{\gamma}$=2.3" (Hinton and SWGO Collaboration, 2022).
In this section, results of a dedicated simulation study utilizing 5-years
straw-man SWGO sensitivity curve are presented. The aim of this study is to
explore and provide an estimation of the maximum detectable energy cutoff at a
95$\%$ CL over a 5-year observation time as defined in the respective SWGO
science benchmark.

Figure 2: A comparison is shown between $\gamma$-ray spectral models with
different spectral indices of $\Gamma$=2.3 (red), $\Gamma$=2.0 (yellow) and
$\Gamma$=1.7 (blue), for a source exhibiting a flux normalization $\Phi_{0}$
of 5 mCrab at 1 TeV, and a fixed $\gamma$-ray spectral cutoff energy of 100
TeV. Additionally, the flux points derived from SWGO simulations, following
the procedure detailed in Sec. 3, are shown in their corresponding colors,
accounting only for 1$\sigma$ statistical errors ($\xi=0$). The solid black
line outlines the 5-year SWGO straw-man sensitivity curve. Figure 3: The
$\gamma$-ray spectral cutoff detection maps reconstructed from 5-years of SWGO
observations are shown for a fixed flux normalization of $\Phi_{0}$(1 TeV)=5
mCrab (left) and for a fixed gamma-ray spectral index of $\Gamma$=2.3 (right).
The x-axes show$\gamma$-ray spectral cutoff energies, while the y-axes show
the $\gamma$-ray spectral index (left) and flux normalization at 1 TeV (right)
of the simulated ECPL model given in Eq. 1, respectively. For the
reconstruction of the cutoff energy axis, a total of 29 equally spaced
logarithmic bins between 10 and 300 TeV energies have been used. As for the
spectral index and flux normalization axes, eight bins cover the range of
$\Gamma$=[1.7, 2.4], and 13 bins cover the flux range of $\Phi_{0}$(1
TeV)=[3.0, 15.0] mCrab, respectively. Within each ($\rm{\Phi_{0}}$, $\Gamma$,
Ec,γ) combination bin, a set of 500 simulations of SWGO flux points is
performed based on the corresponding $\gamma$-ray model, and the distribution
of $\mathrm{TS}_{\gamma}$ is generated. The detection probabilities of the
spectral cutoffs, represented on the z-axis, are calculated by assuming a
cutoff detection threshold of $\mathrm{TS}_{\gamma}$ $\geq$ 25 (5 $\sigma$)
and taking the fraction of the distribution above this threshold, as initially
introduced in (Acero, F. et al., 2023). The yellow and black contours indicate
lower bounds of the parameter space in which the 95$\%$ CL cutoff detection
can be established assuming the cutoff detection threshold of
$\mathrm{S}_{\mathrm{cut,\gamma}}$=5$\sigma$ and
$\mathrm{S}_{\mathrm{cut,\gamma}}$=3$\sigma$, respectively. The white dashed
lines in figures indicate location of the reference source cited in SWGO
science benchmark, with parameters of $\Phi_{0}$(1 TeV)=5 mCrab and
$\Gamma$=2.3, on the phase space.

In principle, detecting a $\gamma$-ray spectral cutoff, or equivalently,
robust determination of a spectral shape, requires reasonably broad energy
coverage and sufficient event statistics within that energy range. Figure 2
illustrates a comparison between different $\gamma$-ray spectral models with
various spectral indices, originating from a 5 mCrab source exhibiting a 100
TeV $\gamma$-ray spectral cutoff, together with the simulated respective SWGO
flux points following the method detailed in Sec. 3. The figure clearly
reveals that detecting a 100 TeV $\gamma$-ray cutoff from a 5 mCrab and
$\Gamma$=2.3 source (dashed red line) encounters challenges due to both
insufficient statistics and the limited ability of the SWGO 5-year straw-man
sensitivity curve to effectively capture the cutoff feature. Conversely, a
source with a comparable flux level but showing a harder spectral index of
$\Gamma$=1.7 benefits from comprehensive coverage, making the detection of a
100 TeV cutoff feature possible. A preliminary investigation of the simulated
5 mCrab and $\Gamma$=2.3 source did not conclusively result in a detection of
any spectral cutoff feature up to energies of 300 TeV at a 95$\%$ CL.
Consequently, the simulation study is extended further to production of
spectral detection maps, introduced in Acero, F. et al. (2023), which
encompass a wide range of the $\gamma$-ray spectral parameter space and can be
used to investigate the detectable cutoff energies at a desired CL.

Figure 3 shows the reconstructed $\gamma$-ray spectral cutoff detection map
using 5-years of SWGO observations for a fixed flux normalization of
$\Phi_{0}$(1 TeV)=5 mCrab (left) and a fixed $\gamma$-ray spectral index of
$\Gamma$=2.3, together with 95$\%$ CL contour lines assuming
$\mathrm{S}_{\mathrm{cut,\gamma}}$=5$\sigma$ (yellow) and
$\mathrm{S}_{\mathrm{cut,\gamma}}$=3$\sigma$ (black) cutoff detection
thresholds given in Eq. 3, respectively. As evident from the figures, the
reference source cited in the SWGO science benchmark fails to achieve a 95$\%$
CL detection for any spectral cutoff value spanning from 10 to 300 TeV when
taking the straw-man design sensitivity curve into account. By analyzing the
characteristics of the reference source parameters separately, it becomes
apparent that $\gamma$-ray spectral cutoff energies ranging from 30 to 100 TeV
can be confidently detected (at 5$\sigma$ level) for a 5 mCrab source, given
that the $\gamma$-ray spectral index is hard ($\Gamma$ $\leq$ 2.0). The
probabilities of detecting these cutoff energies exhibit a relatively flat
structure between 30 TeV and 100 TeV. On the other hand, when considering
$\gamma$-ray sources with a spectral index of $\Gamma$=2.3, robust detection
of their spectral cutoffs can become possible only if the flux $\Phi_{0}$(1
TeV) is larger than $\sim$11 mCrab. In this case, the capability to identify
spectral cutoffs attains its peak performance at Ec,γ=$\sim$30 TeV, and the
maximum energy at which a cutoff can be detected increases as the source gets
brighter. If a less strict cutoff detection threshold of
$\mathrm{S}_{\mathrm{cut,\gamma}}$=3$\sigma$ is assumed, the minimum
prerequisites for spectral parameters become less conservative, enabling the
potential detection of spectral cutoffs even for a 5 mCrab source with
$\Gamma$=$\sim$2.1, as well as for a $\sim$8 mCrab and $\Gamma$=2.3 source.

##  5 Exploration of PeVatron parameter space

Figure 4: Estimated probability maps for exclusion (left panels) and detection
(right panels) of a PeVatron source with a robust statistical significance of
$5\sigma$ with SWGO data. This estimation is based on the assumed SWGO straw-
man sensitivity curve (Albert, A. et al., 2019) taken from
https://github.com/harmscho/SGSOSensitivity. The reconstruction of maps
follows the methodology introduced in Acero, F. et al. (2023). The x-axis and
the left and right y-axes represent the assumed parameter values for the true
observed $\gamma$-ray flux normalization $\Phi_{0}$ at $10$ TeV originating
from pp interactions observed from Earth, the spectral index of the hadronic
particle distribution ($\Gamma_{\mathrm{p}}$), and the corresponding spectral
index of ECPL $\gamma$-ray emission ($\Gamma_{\mathrm{\gamma}}$),
respectively. The color bar indicates the probability of either exclusion
(left panels) or detection (right panels) of a PeVatron with a statistical
significance of $5\sigma$, using the PTS method. The top panels present the
results for 1 year of SWGO observations, whereas the bottom panels shows 5
year observations. The cutoff energy for the hadronic particle spectrum in the
left panels, representing exclusion power at a $5\sigma$ significance for non-
PeVatron sources, is assumed to be $E_{\mathrm{cut,p}}$=$300$ TeV. On the
other hand, $E_{\mathrm{cut,p}}$=$3$ PeV is used for the right panels, which
demonstrate SWGO’s power to robust detection of a PeVatron. The contours
representing detection and rejection probabilities of 0.5, 0.7, and 0.9 are
shown with solid black lines.

As it was discussed in Acero, F. et al. (2023); Angüner (2023), it is
important to highlight that establishing a direct relationship between the
’detection or absence of $\gamma$-ray spectral cutoffs’ and the
’identification of PeVatron spectral signatures’ is not always
straightforward. Indeed, the presence of a significant $\gamma$-ray spectral
cutoff observed at UHEs (i.e. E$>$100 TeV) could potentially be interpreted as
a sign of PeVatron detection assuming that the observed $\gamma$-ray emission
originates from hadronic interactions. Conversely, a source that does not
exhibit a clear $\gamma$-ray spectral cutoff within the energy range of the
instrument, i.e. due to its very high underlying hadronic spectral cutoff,
would clearly display a more promising spectral PeVatron signature, only if
this spectral behaviour is significant. The recently introduced PTS method
(Acero, F. et al., 2023) offers a gauge to quantitatively assess the
statistical significance of such spectral behaviors.

In this section, the potential of SWGO observations to decide whether a given
source is associated with a PeVatron or not is estimated based on the straw-
man design configuration for general point-like $\gamma$-ray sources, assuming
1 year and 5 years of simulated SWGO observations. The investigation
encompasses a wide range of parameters, denoted as $\rm{\Phi_{0}}$ which
corresponds to true $\gamma$-ray flux observed from Earth, resulting from pp
interactions followed by subsequent $\pi^{0}$ decay, and proton spectral index
$\Gamma_{\mathrm{P}}$, associated with PeVatron sources. The SWGO flux points
are simulated using $\gamma$-ray emission models from hypothetical PeVatrons
characterized by a proton cutoff energy of $E_{\mathrm{cut,p}}=3$ PeV, as well
as from non-PeVatron sources having a proton cutoff energy of
$E_{\mathrm{cut,p}}=300$ TeV, taking into account various combinations of
($\rm{\Phi_{0}}$, $\Gamma_{\mathrm{p}}$) parameters. Since SWGO’s sensitivity
is expected to be more pronounced at higher energies (E$\gg$1 TeV, see Fig.
2), the flux normalization of the maps is established at a reference energy of
10 TeV, deviating from the typical value of 1 TeV generally used in VHE
astronomy. The probability to detect a PeVatron and, respectively, to exclude
that a hadronic $\gamma$-ray source is a PeVatron, with a statistical
significance of more than robust $S_{\mathrm{PTS}}$=$5\sigma$ level, is
estimated by taking the fraction of simulated sources for which the PTS is
larger than 25 and, respectively, smaller than $-25$ as it was discussed and
detailed in Acero, F. et al. (2023); Angüner (2023).

Figure 4 shows the SWGO PeVatron detection (right panels) and exclusion (left
panels) maps, revealing that the sensitivity achieved with the SWGO straw-man
design configuration is already promising for exploring significant portions
of the investigated parameter space of PeVatron sources. For the purpose of
relative performance comparison with future VHE experiments, such as the CTA
(Acero, F. et al., 2023), similar maps reconstructed using the flux
normalization at $\Phi_{0}$ at 1 TeV (in mCrab units) are also provided in A.
Considering the straw-man design configuration, it becomes evident that the
PeVatron detection capability of SWGO after 1 year of observations is
comparable to what can be achieved with 50 hours of CTA observations.
Consequently, 1-year SWGO observations can provide much higher PeVatron
detection sensitivity with respect to what can be expected from the planned
CTA scan of the Galactic plane (Cherenkov Telescope Array Consortium et al.,
2019; Abe et al., 2023), which is estimated to have an average exposure of
$\sim$10 hours. Moreover, extending observations to 5 years with SWGO yields a
relatively better PeVatron detection sensitivity compared to 100 hours of
deeper follow-up CTA observations. However, this comparison neglects the fact
that a source which appears as point-like for SWGO, considering its angular
resolution of $\sim 0.15^{\circ}$ above $30$ TeV, will indeed not display
point-like characteristics for the CTA due to its superior angular resolution.
It is important to point out that the comparison based on the analysis results
do not include systematic errors. The conclusions can change depending on the
extent of systematic uncertainties. The power of PeVatron detection and
exclusion, derived from observations with SWGO as shown in Fig. 4 (and also in
Fig. 7), diminishes by a factor of 2$-$8, depending on the source brightness
and spectral index, when a conservative systematic flux error of $\xi=10\%$ is
assumed. The effect is more pronounced for the weak and soft sources,
consequently shifting the transition regions888Transition region is the part
of the parameter space in which the detection (or exclusion) probabilities are
between 0.5 and 0.9 contour lines. to higher flux levels. This confirms that
the control of systematic errors is an important prerequisite to reach the
full potential of SWGO.

##  6 Probing promising PeVatron candidates of the Southern-sky with SWGO

Figure 5:  The SWGO visibility plot for the Southern-sky assuming the observatory situated at 23∘ South latitude, which is a similar latitude location of the H.E.S.S. experiment (Aharonian et al., 2006). The gradient of blue colors illustrates the visibility of objects at different observation zenith angles, while the red shaded areas indicate sky regions where the observation zenith angle is between 40∘ and 50∘, which are generally considered as sub-optimal observation conditions for obtaining reliable data. The black solid and dashed orange lines correspond to the sky visibility at the zenith angles of 0∘ and 30∘, respectively. The yellow and magenta dots highlighted on the plot mark the position of the LHAASO sources showing significant (SUHE $\geq$ 4$\sigma$) E$>$100 TeV $\gamma$-ray emission regions (Cao et al., 2023b) and VHE sources detected in the H.E.S.S. Galactic Plane Survey (H. E. S. S. Collaboration et al., 2018), respectively. The green stars mark the location of promising E$>$100 TeV Southern sky sources, namely the GC diffuse emission region, HESS J1702$-$420A, Westerlund 1 and HESS J1641$-$463, discussed extensively in Sec. 6. The plot is produced using the swgo-plot module provided in https://swgo-collaboration.gitlab.io/swgo-plot/. Table 1: Spectral characteristics of the promising Southern-sky E$>$100 TeV $\gamma$-ray sources, the GC diffuse emission region (HESS Collaboration et al., 2016), HESS J1702$-$420A (Abdalla, H. et al., 2021), Westerlund 1 (Aharonian, F. et al., 2022) and HESS J1641$-$463 (Abramowski et al., 2014a). The differential flux at 1 TeV is provided in both TeV-1cm-1s-1 and mCrab units in the second and third columns, while the corresponding differential flux at 10 TeV is given in the fourth column. Details regarding the best-fit $\gamma$-ray spectral indices, spectral cutoffs (if detected), and the favored $\gamma$-ray models are provided in the fifth, sixth, and seventh columns, respectively. We note that the $\Phi_{0}$(1 TeV) value of HESS J1702$-$420A is derived by extrapolating the $\gamma$-ray model described in Abdalla, H. et al. (2021) down to 1 TeV energy. The EMax column gives the energy of the highest significant flux point, while the energy of the highest flux upper limits (if exists) are provided in parentheses. Source |  $\Phi_{0}$(1 TeV) |  $\Phi_{0}$(1 TeV) |  $\Phi_{0}$(10 TeV) | Spectral | Ecut,γ | Preferred | EMax
---|---|---|---|---|---|---|---
Name | (TeV-1cm-1s-1) | (mCrab) | (TeV-1cm-1s-1) | Index | (TeV) | Model | (TeV)
GC diffuse emission | (1.92$\pm$0.08)$\times$10-12 |  $\sim$50 |  $\sim$9.2$\times$10-15 | 2.32$\pm$0.05 | $-$ | PL | 39.6 (58.8)
HESS J1702$-$420A |  $\sim$1.6$\times$10-13 |  $\sim$4 |  $\sim$4.7$\times$10-15 | 1.53$\pm$0.19 | $-$ | PL | 84.8 (130.1)
Westerlund 1 | (1.00$\pm$0.03)$\times$10-11 |  $\sim$260 |  $\sim$4.0$\times$10-14 | 2.30$\pm$0.04 | 44${}^{+17}_{-11}$ | ECPL | 80.6
HESS J1641$-$463 | (3.91$\pm$0.69)$\times$10-13 |  $\sim$10 |  $\sim$3.3$\times$10-15 | 2.07$\pm$0.11 | $-$ | PL | 23.4 (68.7)

In this section, the analysis results of SWGO simulations based on the public
spectral $\gamma$-ray data from four promising Southern-sky Galactic PeVatron
candidate sources, the GC diffuse emission999The GC diffuse emission spectrum
is extracted from an annulus centred at Sgr A* (see right panel of Fig. 1 in
HESS Collaboration et al. (2016)) with inner and outer radius of 0.15∘ and
0.45∘, respectively, and a solid angle of 1.4$\times$10-4 sr. region at the
center of the Galaxy (HESS Collaboration et al., 2016), the young massive
stellar cluster Westerlund 1 (Aharonian, F. et al., 2022), and unidentified
hard $\gamma$-ray sources HESS J1702$-$420A (Abdalla, H. et al., 2021) and
HESS J1641$-$463 (Abramowski et al., 2014a), are presented and discussed in
the framework of the SWGO straw-man configuration design. All four of these
$\gamma$-ray sources detected at VHEs are considered as promising E$>$100 TeV
emitters, either due to their fluxes detected at high-energies (such as
$\sim$81 TeV for Westerlund 1 and $\sim$85 TeV for HESS J1702$-$420A) or from
their observed power-law characteristic that exhibit hard spectral features
without showing any clear indications of spectral cutoffs (GC diffuse emission
region and HESS J1641$-$463). Such unique spectral features, which are listed
in Table 1, make these sources particularly intriguing as potential Southern-
sky PeVatron candidates, as the possibility of hadronic emission scenarios
cannot be ruled out for any of them. Location of these Southern-sky PeVatron
candidates are marked with green dots in the SWGO Southern-sky visibility plot
shown Fig. 5. As illustrated, all of these sources can be observed under ideal
conditions, with zenith angles smaller than 30∘, assuming the observatory
being situated $\sim$23∘ South latitudes. These promising candidates discussed
in this section are presumed to be spatially isolated and are treated as
point-like sources for SWGO. The assumption of a point-like source holds true
for HESS J1702$-$420A and HESS J1641$-$463, since their spatial extensions of
$0.06^{\circ}\pm 0.02^{\circ}\,(\mathrm{stat})\,\pm
0.03^{\circ}\,(\mathrm{sys})$ (Abdalla, H. et al., 2021) and an upper limit of
$0.05^{\circ}$ (Abramowski et al., 2014a) degrees, respectively, are
significantly smaller than SWGO’s design angular resolution of $\sim$0.15∘
above 30 TeV. However, the GC diffuse emission region is defined with an outer
radius of $0.45^{\circ}$ (HESS Collaboration et al., 2016), and the emission
region around Westerlund 1 extends up to a diameter of $\sim$2∘ (Aharonian, F.
et al., 2022), clearly deviating from the point-like source assumption for
SWGO. Additionally, it’s important to note that all sources are actually not
"spatially isolated" and they potentially suffer from the effects of source
confusion, where the presence of multiple nearby $\gamma$-ray sources
complicates the analysis in practice. We explicitly state that due to these
idealized assumptions, the following estimates can only serve as first
benchmarks within simplified conditions.

###  6.1 The GC diffuse emission region and the unidentified source HESS
J1702$-$420A

The PTS analysis of the available VHE $\gamma$-ray data from the H.E.S.S.
experiment for the GC diffuse emission and HESS J1702$-$420A regions was
presented and extensively discussed in Angüner et al. (2023), resulting in
non-significant $\mathrm{S}_{\mathrm{PTS}}$ values of 0.4$\sigma$ and
1.0$\sigma$, respectively. Assuming $\xi=20\%$ systematic error in the
H.E.S.S. data sets, the corresponding $95\%$ CL cutoff lower limits were
calculated for the underlying hadronic spectra, yielding 172 TeV for the GC
diffuse emission region and 436 TeV for HESS J1702$-$420A. Due to these
results, it was not possible to draw any statistically significant conclusions
regarding the PeVatron nature of these sources. However, it was discussed that
the potential impact of forthcoming observatories, particularly the SWGO
experiment, is crucial since both sources lack UHE data above 100 TeV, and
data from such future observatories could provide crucial insights on
determining whether these sources can be classified as Galactic PeVatrons.

###  6.2 Westerlund 1: The young massive stellar cluster

One of the regions in the Southern-sky showing potential promise for emitting
UHE $\gamma$-rays above 100 TeV is the Westerlund 1 region, which stands out
as the most massive young stellar cluster (YMC) within our Galaxy, estimated
to be around 4$-$5 Myr old according to Clark, J. S. et al. (2005). The YMC
environments in our Galaxy serve as fertile grounds for star formation,
containing stars in the early stages of formation, surrounded by cosmic gas
and dust. As a result of such conditions, these environments become efficient
regions for accelerating particles which can interact with the surrounding
gas, and are considered as promising Galactic PeVatron candidates (Morlino et
al., 2021). A recent detailed VHE analysis of the region using H.E.S.S. data
revealed the presence of an extended and complex shell-like $\gamma$-ray
emission spanning up a diameter of $\sim$2∘. The authors mentioned that even
though there is not a clear spatial correlation between the structures of
interstellar gas and the observed VHE $\gamma$-ray emission, the possibility
of a scenario involving hadronic interactions is still possible due to the
lack of energy-dependent morphology and uncertainties of the gas distribution
(Aharonian, F. et al., 2022).

The ECPL model, given in Eq. 1, was fitted to the $\gamma$-ray flux data
points of Westerlund 1, considering systematic errors of $\xi=20\%$, resulting
in $\Phi_{0}$(1 TeV)=(1.02$\pm$0.07)$\times$10-11 TeV-1cm-1s-1,
$\Gamma_{\gamma}$=2.33$\pm$0.08 and Ecut,γ=44.2$\pm$21.4 TeV, which are
consistent with the findings presented in Aharonian, F. et al. (2022). In this
context, the statistical significance of the $\gamma$-ray spectral cutoff
feature is found to be $\mathrm{S}_{\mathrm{cut,\gamma}}$=2.4$\sigma$, and the
corresponding lower limit for the $\gamma$-ray cutoff at the $95\%$ CL is
LLcut,γ=23 TeV. Assuming that the entire $\gamma$-ray emission arises from
interactions between accelerated protons, following the spectral shape defined
in Eq. 2, and target gas in the region, the spectral index and cutoff
parameters of the underlying parental proton spectral can be obtained as
$\Gamma_{\mathrm{p}}$=2.33$\pm$0.12 and $E_{\mathrm{cut,p}}$=300$\pm$188 TeV,
respectively. The statistical significance of the proton cutoff feature is
calculated as $\mathrm{S}_{\mathrm{cut,p}}$=2.4$\sigma$, while the $95\%$ CL
lower limit for the proton cutoff is derived at 127 TeV. The corresponding PTS
significance for the overall emission originating from the Westerlund 1 region
is estimated to be $\mathrm{S}_{\mathrm{PTS}}$=$-$1.4$\sigma$. When
considering only the available H.E.S.S. data, a conclusive determination
cannot be made regarding whether the emission from Westerlund 1 arises from
PeVatron activity. Consequently, further observations at UHE, particularly
above 100 TeV, are crucial to reach a conclusive determination of the PeVatron
nature of Westerlund 1.

###  6.3 The unidentified source HESS J1641$-$463

The unidentified source HESS J1641$-$463 in the Southern-sky presents another
promising region for the emission of E$>$100 TeV $\gamma$-rays. The source
exhibits a hard VHE $\gamma$-ray spectrum extending up to a few tens of TeV
without showing any significant spectral cutoff (Abramowski et al., 2014a;
Angüner et al., 2018). Similar to the situation with HESS J1702$-$420A, the
source is affected by source confusion due to the presence of the bright and
extended ($\sim$0.11∘) $\gamma$-ray source HESS J1640$-$465 (Abramowski et
al., 2014b), which is located $\sim$0.28∘ away and showing a significant
$\gamma$-ray cutoff in its spectrum at $\sim$6 TeV. There are dense molecular
clouds found toward the line of sight, along with two nearby supernova
remnants, SNR G338.3$-$0.0 and SNR G338.5$+$0, while the latter is found to be
spatially coincident with the source. These neighboring SNRs could potentially
serve as sources of accelerated protons, suggesting a plausible hadronic
scenario for the observed emission. By using the $\gamma$-ray flux data points
from HESS J1641$-$463 and assuming a $\xi=20\%$ systematic error, lower limits
for the $\gamma$-ray spectral cutoff at a 95$\%$ CL are derived as
LLcut,γ=12.4 TeV. Under the hypothesis that the entire $\gamma$-ray emissions
originates from a hadronic interactions, the spectral index of the parent
protons and the 95$\%$ CL lower limit for the proton cutoff parameters can be
determined as $\Gamma_{\mathrm{p}}$=2.03$\pm$0.15 and LLcut,p=64.1 TeV,
respectively, while the significance of the PTS is found to be
$\mathrm{S}_{\mathrm{PTS}}$=0.6$\sigma$. Similarly to the Westerlund 1 case,
robust conclusions on the PeVatron nature of HESS J1641$-$463 cannot be drawn
when taking into account only the H.E.S.S. data, emphasizing the need for
additional UHE data to provide further insights.

###  6.4 SWGO simulations and data analysis of the promising Southern-sky
PeVatron candidates

For all the sources discussed in this section, the available spectral H.E.S.S.
data assuming a minimum relative flux error of $\xi=20\%$ are fitted to the
hadronic emission model defined by Eq. 2. The resulting best-fit hadronic
models obtained from the analysis of H.E.S.S. data are adjusted and further
used in the SWGO simulations of each individual source under investigation. An
example simulation result of 5 years SWGO observations is shown in Fig. 6 for
the diffuse emission region in the vicinity of the GC (top left panel), the
unidentified $\gamma$-ray source HESS J1702$-$420A (top right panel),
Westerlund 1 region (bottom left panel) and HESS J1641$-$463 (bottom right
panel). The solid lines in Fig. 6 represent the hadronic models reconstructed
from H.E.S.S. data with an energy cutoff fixed at 3 PeV. These hypothetical
PeVatron models correspond to the expected $\gamma$-ray emission from Galactic
PeVatrons, which can significantly contribute to the knee structure observed
in the CR spectrum. On the other hand, the dashed lines in the figure
represent best-fit non-PeVatron models derived from the same H.E.S.S. data.
For these non-PeVatron models, the hadronic energy cutoff is fixed to the
derived $95\%$ CL lower limit of the underlying proton spectral cutoff
obtained from respective H.E.S.S. observations: 172 TeV for the GC diffuse
emission region, 436 TeV for HESS J1702$-$420A, 127 TeV for Westerlund 1, and
64 TeV for HESS J1641$-$463\. These non-PeVatron models, characterized by
proton cutoff energies fixed at their respective $95\%$ CL lower limits,
remain significantly below 3 PeV, consequently are not expected to
substantially contribute to the knee feature. To assess the impact of
systematic errors, the SWGO flux data for PeVatron and non-PeVatron models are
simulated considering statistical errors only ($\xi=0$), and with an
additional optimistic $\xi=5\%$ and conservative $\xi=10\%$ systematic errors.
The red SWGO flux data points shown in Fig. 6 account only for statistical
errors ($\xi=0$).

Figure 6: Simulated $\gamma$-ray spectra from 5 years of SWGO data for the GC diffuse emission region (upper left panel), HESS J1702-420A (upper right panel), Westerlund 1 (lower left panel) and HESS J1641$-$463 (lower right panel). The 5-year straw-man configuration sensitivity of SWGO taken from https://github.com/harmscho/SGSOSensitivity is used in simulations. Spectral $\gamma$-ray flux data from observations with H.E.S.S. are shown in blue stars with an assumed minimal relative flux error of $\xi=20\%$. Solid black lines show the best fit PeVatron models with a hadronic energy cutoff fixed at $3$ PeV, while the dashed black lines are the best-fit non-PeVatron models in which hadronic energy cutoffs are fixed the respective $95\%$ CL lower limit derived from the H.E.S.S. data. The SWGO flux points obtained from the simulation of the best fit PeVatron models are shown in red without considering any systematic errors ($\xi=0\%$). Table 2: Analysis results inferred from the SWGO simulations of four promising Southern-sky E$>$100 TeV sources. Each source instance is simulated 500 times and the results are obtained from the respective distributions of derived properties. The ’PeV’ and ’Non-PeV’ identifiers next to source names indicate whether the PeVatron (E${}_{\mathrm{cut,\,p}}$ fixed to 3 PeV) or Non-PeVatron (E${}_{\mathrm{cut,\,p}}$ fixed to derived 95$\%$ proton cutoff lower limits) hadronic models used when simulating the SWGO flux data, while $\xi$ is the assumed minimal relative flux error explained in Sec. 3. SPTS and LL${}_{\mathrm{cut,\,p}}$ denote the significance of the PTS and the $95\%$ CL lower limit on the hadronic energy cutoff E${}_{\mathrm{cut,\,p}}$, while $\mathrm{S}_{\mathrm{cut,p}}$ is the significance of the hadronic cutoff feature, respectively. Similarly, LLcut,γ and $\mathrm{S}_{\mathrm{cut,\gamma}}$ are the corresponding $95\%$ CL lower limit on the $\gamma$-ray cutoff energy E${}_{\mathrm{cut,\,p}}$ and the significance of the $\gamma$-ray cutoff feature. The derived reference properties, on which conclusions are based in this work, are highlighted in bold and shown in Fig. 6. Source Name | $\xi$ | $\mathrm{S}_{\mathrm{PTS}}$ | LLcut,p | $\mathrm{S}_{\mathrm{cut,p}}$ | Ecut,p | LLcut,γ | $\mathrm{S}_{\mathrm{cut,\gamma}}$ | Ecut,γ
---|---|---|---|---|---|---|---|---
| ($\%$) | ($\sigma$) | (TeV) | ($\sigma$) | (TeV) | (TeV) | ($\sigma$) | (TeV)
GC diffuse emission (PeV) | 0 | 11.7$\pm$1.0 | 2479$\pm$285 | 11.9$\pm$1.0 | 3020$\pm$391 | 244$\pm$21 | 11.5$\pm$1.0 | 282$\pm$28
GC diffuse emission (PeV) | 5 | 6.6$\pm$0.7 | 2153$\pm$314 | 6.6$\pm$0.8 | 3022$\pm$545 | 240$\pm$27 | 6.4$\pm$0.8 | 307$\pm$43
GC diffuse emission (PeV) | 10 | 4.1$\pm$0.6 | 1795$\pm$312 | 4.2$\pm$0.7 | 2969$\pm$759 | 220$\pm$26 | 4.1$\pm$0.8 | 316$\pm$58
GC diffuse emission (Non-PeV) | 0 |  $-$22.4$\pm$1.0 | 158$\pm$9 | 33.8$\pm$1.1 | 173$\pm$10 | 33$\pm$1 | 33.6$\pm$1.1 | 36$\pm$1
GC diffuse emission (Non-PeV) | 5 |  $-$12.8$\pm$0.7 | 148$\pm$9 | 18.8$\pm$0.7 | 172$\pm$11 | 34$\pm$2 | 18.6$\pm$0.7 | 37$\pm$2
GC diffuse emission (Non-PeV) | 10 |  $-$8.6$\pm$0.7 | 139$\pm$13 | 12.3$\pm$0.7 | 173$\pm$17 | 34$\pm$3 | 12.1$\pm$0.7 | 40$\pm$3
HESS J1702$-$420A (PeV) | 0 | 19.8$\pm$1.2 | 2593$\pm$243 | 25.2$\pm$0.9 | 3053$\pm$290 | 271$\pm$10 | 25.0$\pm$0.9 | 290$\pm$12
HESS J1702$-$420A (PeV) | 5 | 4.3$\pm$0.3 | 1773$\pm$329 | 7.2$\pm$0.5 | 3021$\pm$592 | 201$\pm$11 | 7.3$\pm$0.4 | 248$\pm$19
HESS J1702$-$420A (PeV) | 10 | 2.3$\pm$0.3 | 1250$\pm$332 | 4.1$\pm$0.5 | 3100$\pm$1012 | 166$\pm$12 | 4.2$\pm$0.4 | 236$\pm$24
HESS J1702$-$420A (Non-PeV) | 0 |  $-$11.0$\pm$1.0 | 427$\pm$7 | 45.5$\pm$1.0 | 441$\pm$21 | 102$\pm$3 | 44.0$\pm$1.0 | 107$\pm$3
HESS J1702$-$420A (Non-PeV) | 5 |  $-$4.9$\pm$0.7 | 415$\pm$9 | 18.2$\pm$0.7 | 449$\pm$32 | 97$\pm$3 | 17.7$\pm$0.7 | 107$\pm$4
HESS J1702$-$420A (Non-PeV) | 10 |  $-$2.8$\pm$0.5 | 397$\pm$10 | 10.2$\pm$0.5 | 453$\pm$48 | 86$\pm$4 | 10.0$\pm$0.4 | 102$\pm$5
Westerlund 1 (PeV) | 0 | 37.5$\pm$1.0 | 2805$\pm$109 | 34.6$\pm$1.0 | 2996$\pm$121 | 279$\pm$8 | 34.3$\pm$1.0 | 294$\pm$9
Westerlund 1 (PeV) | 5 | 8.5$\pm$0.5 | 2290$\pm$198 | 8.1$\pm$0.7 | 2899$\pm$313 | 281$\pm$18 | 7.9$\pm$0.7 | 344$\pm$27
Westerlund 1 (PeV) | 10 | 4.3$\pm$0.2 | 1832$\pm$126 | 4.1$\pm$0.3 | 2999$\pm$296 | 237$\pm$12 | 4.0$\pm$0.3 | 342$\pm$26
Westerlund 1 (Non-PeV) | 0 |  $-$141.3$\pm$1.0 | 126$\pm$1 | 197.7$\pm$1.3 | 128$\pm$1 | 28$\pm$1 | 196.5$\pm$1.3 | 29$\pm$1
Westerlund 1 (Non-PeV) | 5 |  $-$26.5$\pm$0.6 | 118$\pm$3 | 34.8$\pm$0.7 | 128$\pm$4 | 31$\pm$1 | 34.3$\pm$0.8 | 33$\pm$1
Westerlund 1 (Non-PeV) | 10 |  $-$16.2$\pm$0.6 | 113$\pm$6 | 20.5$\pm$0.6 | 128$\pm$7 | 32$\pm$2 | 20.1$\pm$0.6 | 36$\pm$2
HESS J1641$-$463 (PeV) | 0 | 6.7$\pm$1.0 | 2225$\pm$398 | 8.9$\pm$0.1 | 3050$\pm$625 | 219$\pm$25 | 8.3$\pm$1.0 | 268$\pm$37
HESS J1641$-$463 (PeV) | 5 | 5.2$\pm$0.8 | 2032$\pm$392 | 6.5$\pm$0.8 | 3045$\pm$717 | 211$\pm$25 | 6.1$\pm$0.8 | 273$\pm$41
HESS J1641$-$463 (PeV) | 10 | 3.6$\pm$0.6 | 1721$\pm$368 | 4.3$\pm$0.7 | 3065$\pm$930 | 191$\pm$23 | 4.0$\pm$0.7 | 275$\pm$50
HESS J1641$-$463 (Non-PeV) | 0 |  $-$18.5$\pm$1.0 | 56$\pm$4 | 24.7$\pm$1.1 | 65$\pm$7 | 21$\pm$1 | 24.5$\pm$1.2 | 23$\pm$1
HESS J1641$-$463 (Non-PeV) | 5 |  $-$14.8$\pm$0.9 | 55$\pm$4 | 19.2$\pm$0.9 | 65$\pm$8 | 21$\pm$2 | 19.1$\pm$0.9 | 23$\pm$2
HESS J1641$-$463 (Non-PeV) | 10 |  $-$10.0$\pm$0.7 | 54$\pm$4 | 12.9$\pm$0.7 | 66$\pm$10 | 20$\pm$2 | 12.7$\pm$0.7 | 23$\pm$3

In order to accumulate reliable statistics, the simulation procedure described
above is repeated 500 times for all examined sources, and $S_{\mathrm{PTS}}$
values are calculated assuming PeVatron and non-PeVatron models considering
systematic errors of $\xi=0$, $\xi=5\%$ and $\xi=10\%$ in each simulated SWGO
data set. In addition, the best fit proton and $\gamma$-ray spectral cutoff
energies (Ecut,p and Ecut,γ), statistical significance of the respective
proton and $\gamma$-ray cutoff features ($\mathrm{S}_{\mathrm{cut,p}}$ and
$\mathrm{S}_{\mathrm{cut,\gamma}}$) and the 95$\%$ CL of proton and
$\gamma$-ray spectral cutoff lower limits (LLcut,p and LLcut,γ) are derived
for each simulated SWGO data set. These characteristics derived from 500
simulations are then gathered into distributions, and their median values
along with standard errors are computed and summarized in Table 2.

The derived intrinsic properties mentioned above have the potential to provide
insights about the PeVatron characteristics of sources. The results of the
simulations clearly indicate that if the examined $\gamma$-ray sources are
associated to hadronic Galactic PeVatrons, which contribute to the knee
feature observed at 3 PeV energies, SWGO possesses substantial potential to
confirm their PeVatron nature at a robust CL ($\mathrm{S}_{\mathrm{PTS}}$
$\geq$ 5.0$\sigma$). Similarly, the absence of PeVatron characteristics can
also be robustly confirmed ($\mathrm{S}_{\mathrm{PTS}}$ $\leq$ $-$5.0$\sigma$)
for all sources, provided that the corresponding proton energy cutoffs are
well below 3 PeV. Given the specific cutoff values assigned to the assumed
respective proton spectra, the application of the PTS technique using spectral
data inferred from SWGO observations allow a robust determination of whether
the $\gamma$-ray emissions from these promising Southern-sky E$>$100 TeV
sources are Galactic PeVatrons in nature.

When a conservative $\xi=10\%$ SWGO systematic error is considered alongside
with otherwise unchanged simulation parameters, the median significances of
the PTS values are diminished to a marginal detection range of
$\mathrm{S}_{\mathrm{PTS}}\cong$3$-$4$\sigma$ for PeVatron cases, while the
instances where non-PeVatron characteristics can still be robustly confirmed,
with the exception of HESS J1702$-$420A. On the other hand, in the case of
$\xi=5\%$ SWGO systematic error, robust detection of both PeVatron and non-
PeVatron characteristics can be confirmed. These simulation results clearly
highlight the importance of inferred systematics, and show that the full
potential of SWGO in PeVatron searches can only be achieved when systematic
errors are carefully controlled and minimized as effectively as possible.
Especially, systematic flux error levels similar to LHAASO experiment or
better ($\xi=5-7\%$) can lead to significant detection of spectral PeVatron
characteristics. Furthermore, assuming point-like source morphology for the
extended GC diffuse emission and Westerlund 1 regions can have significant
impact on the results. As it was shown in (Acero, F. et al., 2023), both the
PeVatron detection and rejection probabilities decrease as the source
extension increases (see Ambrogi et al. (2018) for a detailed discussion on
extended source sensitivities). Consequently, the $\mathrm{S}_{\mathrm{PTS}}$
values (and lower limits, LLcut,p, LLcut,γ) obtained for these extended
sources tend to be overestimated.

##  7 Discussions and Conclusions

In practical applications, it is expected that the issue of source confusion,
which refers to the condition where multiple $\gamma$-ray sources exist within
an unresolved spatial distance, becomes a significant challenge when analysing
Galactic $\gamma$-ray data. This challenge is particularly pronounced when
dealing with $\gamma$-ray energies below 10 TeV, given that many Galactic VHE
sources are known either to exhibit cutoffs in their spectra below these
energies, or not to emit significant flux above 10 TeV due to soft power-law
spectral index of the emission. As a result, the problem of source confusion
becomes more relevant with decreasing $\gamma$-ray energy. One particular
example is the unidentified source HESS J1702$-$420 discussed in this paper.
The investigation of data from HESS J1702$-$420 has revealed two closely
positioned sub-components without the detection of significant energy cutoff
(Abdalla, H. et al., 2021). In this particular case, the component HESS
J1702$-$420A becomes more luminous than the second component, HESS
J1702$-$420B, above a few tens of TeV due to relative difference in their
power-law spectral indices. Another example comes from the observations of a
specific Galactic region encompassing the Boomerang PWN and SNR G106.3$+$2.7.
The observations of this region conducted by MAGIC provided compelling
evidence that supports the existence of two distinct power-law source
components (MAGIC Collaboration et al., 2023). The softer of the two
components, referred to as the ’head’, and the harder one, known as the
’tail’, both show no clear spectral cutoffs. Moreover, the observations
carried out by LHAASO in the same region (Cao and others, 2021) exclusively
detect a single source component emitting at UHEs, and as it was discussed in
Angüner et al. (2023), the UHE emission detected by LHAASO can be connected to
the tail emission detected by MAGIC. In contrary, when examining the case of
HESS J1641$-$463, which exhibits a hard power-law spectrum, the neighboring
source HESS J1640$-$465 shows a significant spectral cutoff in its spectrum
below 10 TeV. These examples show that $\gamma$-ray emission beyond several
tens of TeV can be well dominated by a single source even in the case of
source confusion, particularly either when no spectral cutoff is detected or
the spectral index of one component is significantly harder than for the
neighboring sources. Consequently, an unprecedented level of information on
comprehensive understanding of the PeVatron nature of sources can be acquired
from the synergy between the experiments like CTA and SWGO due to their
complementary capabilities, with CTA excelling in superior angular resolution
and SWGO enhancing flux sensitivity at high energies.

As evident from both Fig. 1 and Fig. 2, the flux sensitivity of SWGO will
offer a simple detection $\gamma$-ray sources at high energies, providing an
unprecedented level of statistical information beyond 10 TeV, at which
concerns related to source confusion is effectively eliminated. On the other
hand, the superior angular resolution of CTA will provide crucial information
for resolving individual sources below a few tens of TeV energies, at which
source confusion is expected to have more significant impact, and therefore
supplying key insights into the source component with which the observed UHE
emission can be associated. Such a clear association between a $\gamma$-ray
source exhibiting distinct PeVatron spectral signatures and any type of
Galactic CR accelerator is essential for robust determination of Galactic
objects which are truly the PeVatrons responsible for the knee feature
observed in the CR spectrum. As a result, such a synergy can potentially shed
light on the century-old enigma of the origin of Galactic CRs. However, when
addressing the issue of source confusion through a combined analysis of data
from different observatories, such as future CTA South and SWGO, the relative
systematic errors between the flux measurements of different observatories
must be carefully controlled.

In this paper, the expected potential of SWGO in PeVatron searches are
investigated using the straw-man design sensitivity curve. It was concluded
that the high energy $\gamma$-ray cutoffs between 30 TeV and 100 TeV can be
significantly detected for relatively faint 5 mCrab sources, when the spectral
index is hard ($\Gamma\lesssim$ 2.0), while the detection of spectral cutoffs
for the relatively soft $\Gamma\cong$2.3 sources can only be possible if they
are bright enough, i.e. $\Phi_{0}$ $\geq$ 11 mCrab. The reconstructed SWGO
PeVatron detection maps show that the SWGO can probe large parts of the
investigated PeVatron parameter space, providing a robust detection and/or
rejection power. A dedicated study on the promising Southern-sky E$>$100 TeV
sources gives similar results, concluding that the SWGO will have a great
potential to confirm or exclude their PeVatron nature at a robust significance
level after 5-years of observation. The study also demonstrates that the
control of SWGO systematic errors will be a necessary issue, and they should
be around $5-7\%$ in order to reach the maximized potential of detecting
spectral PeVatron characteristics. We explicitly mention that the results
presented in this paper do not reflect a fiducial performance of the planned
SWGO observatory, instead can provide a preliminary insight on the performance
of PeVatron searches with SWGO. The results presented in this paper are based
on straw-man design configuration, therefore they are conservative. Indeed,
with the low and high energy enhancements, together with improved PSF and
background rejection, the performance capabilities, especially SWGO abilities
to detect spectral cutoffs at high energies and PeVatron signatures will be
significantly improved.

## Acknowledgements

E.O.A. acknowledges financial support by TÜBİTAK Research Institute for
Fundamental Sciences.
We express our sincere gratitude to Gerrit Spengler for his extremely useful
active contributions and constructive feedback. We also express our sincere
gratitude to the SWGO Collaboration, especially the feedbacks provided by
Ulisses Barres, Ruben Conceição and Sidharth Sreeja Sadanandan, which greatly
enhanced the quality of the paper.

##  Appendix A Parameter scan at 1 TeV flux normalization

Figure 7: Estimated probability for exclusion and detection of a PeVatron
association at a respective statistical significance of $5\sigma$ with SWGO
data assuming the straw-man (Albert, A. et al., 2019) SWGO sensitivity taken
from https://github.com/harmscho/SGSOSensitivity. The abscissa, left and right
ordinate show the assumed parameters for the true observed $\gamma$-ray flux
normalization $\Phi_{0}$ at $1$ TeV originating from pp interactions observed
from Earth, the spectral index of the hadronic particle population
$\Gamma_{\mathrm{P}}$ and the corresponding spectral index of ECPL
$\gamma$-ray emission. The color bar indicates the probability to exclude
(left panels) and detect (right panels) a PeVatron with a statistical
significance of $5\sigma$ with the PTS. One year of SWGO observations is shown
in the upper panels, while 5 years of SWGO observations are shown in the lower
panels. The assumed hadronic cutoff energy for the left panels, which show the
exclusion power at a significance of $5\sigma$, is $E_{\mathrm{cut,p}}$=$400$
TeV. On the other hand, $E_{\mathrm{cut,p}}$=$3$ PeV is used for the right
panels, which show the respective SWGO PeVatron detection power.

The PeVatron detection and rejection maps provided in Sec. 5 uses the flux
normalization of sources at 10 TeV, which is much more suited for WCD
experiments that have enhanced high energy flux sensitivity. In order to
connect these maps to current and future VHE experiments which in general have
their maximized flux sensitivity at 1 TeV, the maps reconstructed using
$\Phi_{0}$ at 1 TeV are also provided in this appendix in Fig. 7.

List of Acronyms

CL: Confidence Level
CR: Cosmic Ray
CTA: Cherenkov Telescope Array
EAS: Extensive Air Shower
ECPL: Power-Law with Exponential Cutoff
FoV: Field of View
GC: Galactic Center
H.E.S.S.: High Energy Stereoscopic System
HAWC: High Altitude Water Cherenkov Observatory
HE: High Energy
IACTs: Imaging Atmospheric Cherenkov Telescopes
IRF: Instrument Response Function
LHAASO: Large High Altitude Air Shower Observatory
LL: Lower Limit
MAGIC: Major Atmospheric Gamma-Ray Imaging Cherenkov
MC: Monte-Carlo
PL: Power-Law
PSF: Point Spread Function
PTS: PeVatron Test Statistics
SN: Supernova
SNR: Supernova Remnant
SWGO: Southern Wide-field Gamma-ray Observatory
TS: Test Statistics
UHE: Ultra High Energy
VHE: Very High Energy
WCD: Water Cherenkov Detector
YMC: Young Massive stellar Cluster

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