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A&A
Volume 684, April 2024
Article Number A66
Number of page(s) 7
Section Interstellar and circumstellar matter
DOI https://doi.org/10.1051/0004-6361/202346473
Published online 05 April 2024

© The Authors 2024

Licence Creative CommonsOpen Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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1 Introduction

Cosmic rays (CRs) are energetic particles originating from astro-physical accelerators and continuously arriving at Earth. The all-particle CR spectrum exhibits a spectral softening at ~1-3 PeV, which is known as the ‘knee’ and is generally understood to indicate the start of the transition from Galactic to extragalac-tic accelerators being responsible for the bulk of CRs (Ginzburg & Syrovatskii 1964; Hillas 2006; Apel et al. 2013; Parizot 2014). Astrophysical sources capable of accelerating particles to PeV energies are known colloquially as ‘PeVatrons’. γ rays produced as a consequence of particle interactions at the source typically have energies of a factor of ~1/10 that of the parent particle population (Blumenthal & Gould 1970). Hence, the detection of γ rays with E > 100 TeV indicates the presence of particles with PeV energies, corresponding to the CR ‘knee’.

Definitive evidence for the presence of PeVatrons in our galaxy has, however, proven elusive. Although diffusive shock acceleration of CRs at supernova remnants (SNRs) can account for the energy budget of CRs in our galaxy, their γ-ray spectra cut off at energies below 100 TeV (Bell 1978; Lagage & Cesarsky 1983; Bell 2013; H.E.S.S. Collaboration 2018). This indicates that active acceleration of particles to PeV energies is not occurring at these SNRs, although the detection of the characteristic ‘pion-bump’ signature of neutral pion decay in several SNRs indicates that the emission is hadronic in origin (Bell et al. 2013; Ackermann et al. 2013; Jogler & Funk 2016).

Indications for PeVatron activity from the Galactic centre were found (H.E.S.S. Collaboration 2016), yet only in recent years have experimental facilities been capable of measuring γ rays with energies > 100 TeV. Water Cherenkov and particle-detector-based facilities in particular, such as the High Altitude Water Cherenkov Observatory (HAWC, Abeysekara et al. 2017), the Large High Altitude Air Shower Observatory (LHAASO, Aharonian et al. 2021), and the Air Shower array Tibet-ASγ (Amenomori et al. 2009) have contributed significantly to this advance.

Until 2023, the ultra-high-energy (UHE, >100 TeV) γ-ray sky only comprised ~ 15 sources, with the Crab nebula being one of the first identified (Amenomori et al. 2019; LHAASO Collaboration 2021). A further 31 UHE sources were announced in the first LHAASO catalogue (Cao et al. 2024). Twelve UHE sources were reported by LHAASO in 2021 (Cao et al. 2021c), the majority of which are spatially coincident with known very-high-energy (VHE; ≳100 TeV) γ-ray sources. In particular, there are several associations with energetic pulsar wind nebulae from which the emission is understood to be dominantly lep-tonic in origin. Despite the Klein-Nishina suppression of inverse Compton scattering at the highest energies, this suppression is relaxed in the case of high-radiation field environments, and a leptonic scenario remains a viable interpretation for the UHE sources associated with known energetic pulsars (Vannoni et al. 2009; Breuhaus et al. 2021, 2022). There is, however, one source reported in Cao et al. (2021c) for which the γ-ray emission was first discovered at UHE and without any known counterpart accelerators, such as pulsars or SNRs. LHAASO J2108+5157 is an enigmatic source that is spatially coincident with molecular clouds yet with the accelerator mechanism remaining unidentified (Cao et al. 2021b). In the wake of the LHAASO discovery, follow-up observations were conducted by several facilities, including in the radio and X-ray bands as well as by γ-ray experiments. The Fermi-LAT source 4FGL J2108.0+5155 is spatially coincident with the UHE emission, but due to the differing spectral properties a physical association remains unclear (Abdollahi et al. 2020). A re-analysis of the Fermi-LAT data found a potential spatial extension of a 0.48° angular size of the source, designated as 4FGL J2108.0+5155e (Cao et al. 2021b).

A 3.7σ signal of γ-ray emission was measured at E > 3 TeV by the Large Sized Telescope (LST-1), a prototype telescope for the forthcoming Cherenkov Telescope Array (CTA) (Acharya et al. 2013). They derived upper limits in the 0.32–100 TeV energy range that considerably constrain model scenarios for the origin of the emission (Abe et al. 2023).

The HAWC observatory recently reported an ~7 σ detection in ~2400 days of data (Kumar et al. 2023). However, observations and analysis by the VERITAS imaging atmospheric Cherenkov telescope array did not result in a detection, with constraining upper limits being reported; said observations are consistent with those from the LST-1 (Kumar et al. 2023; Abe et al. 2023).

Although there is little observational evidence for SNRs currently acting as PeVatrons, it remains feasible that SNRs act as PeVatrons only for a comparatively short period during their lifetimes, such that the rate of currently detectable SNR PeVatrons is low (Cristofari et al. 2020). Particle escape from the shock region occurs in an energy-dependent manner, such that the most energetic particles will also be the first to leave the shock region (Celli et al. 2019a). Evidence for PeV particles may therefore be found not at the location of the accelerator, but rather from subsequent interactions of these particles with target material in the ambient medium such as nearby molecular clouds (Gabici & Aharonian 2007; Morlino et al. 2009; Inoue et al. 2012; Celli et al. 2019b). This scenario has been proposed as a possible explanation for the UHE emission from LHAASO J2108+5157 (Cao et al. 2021b; Kar & Gupta 2022; De Sarkar 2023; Abe et al. 2023).

In contrast to previous models for LHAASO J2108+5157, in this study we scanned the parameter space in two free variables, namely SNR age and the distance between the cloud and the SNR, to determine the range of plausible values for the required properties of the responsible SNR. We investigated the influence of uncertainties in the cloud properties on the resulting γ-ray flux for the best-matched models. We estimated the corresponding expected neutrino flux and discuss the plausibility of the best-matched models in this paper.

2 Method

We adopted the model of Mitchell et al. (2021, 2023), based on Aharonian & Atoyan (1996) and Kelner et al. (2006), to investigate the scenario of a SNR illuminating molecular clouds as a possible explanation for LHAASO J2108+5157. Whilst there are several clouds identified in the vicinity, we focused on clouds that are spatially coincident with the γ-ray emission and located closest to the best-fit centroid of LHAASO J2108+5157 at (l = 92.2148°, b = 2.9359°). Cloud 4607 from the Miville-Deschênes et al. (2017) catalogue based on data from the 12CO survey of Dame et al. (2001) has been considered in previous models of the region (Kar & Gupta 2022; De Sarkar 2023), while a newly identified cloud was recently detected in the region (de la Fuente et al. 2023). Adopting the convention of prior works, we henceforth refer to these two clouds as MML[2017]4607 and FKT[2022], respectively. Table 1 summarises the key physical properties of the clouds relevant for this study.

For convenience, we summarise the key features of the model from Mitchell et al. (2021, 2023) adopted for this work. Protons are accelerated impulsively with a power-law spectrum of slope α. The particle probability density function ƒ(E, r′, t′) is taken from Eq. (3) of Aharonian & Atoyan (1996) and is a function of the particle energy E, distance travelled from the SNR r′, and time since escape from the SNR t′. The SNR radius, RSNR, expands with time (t) adiabatically during the Sedov-Taylor phase as RSNR ∝ t2/5 (Truelove & McKee 1999). Particles escape from the SNR at a time tesc in a momentum-dependent manner, following tesc ∝ (p/pM)1/β, where pM is the maximum particle energy reached, assumed to be 3 PeV c−1 at the Sedov time, tsed (Celli et al. 2019a). Particles are either transported diffusively through the ISM to reach the cloud or are injected directly into the cloud if the SNR is sufficiently expanded. Diffusion within the intervening ISM is assumed to be slow with respect to the Galactic average value due to the local accelerator activity (Gabici et al. 2007). Within the cloud, diffusion is suppressed with respect to the ISM by a factor of χ that relates to local turbulence. For our default scenario, the Sedov time is assumed to commence at 1.6 kyr corresponding to the case of type II supernovae. In the case of type Ia supernovae, the Sedov time commences at a mere 234yr, which is considered as an alternative scenario (Celli et al. 2019a).

Details of the SNR forward-shock interaction with the cloud, in the case where the SNR is in close proximity and sufficiently evolved, are neglected. The diffusion coefficient D(E) is considered to have a power-law dependence on the energy E as: D(E)=χD0(E/GeVB(n)/3μG)δ,$D(E) = \chi {D_0}{\left( {{{E/{\rm{GeV}}} \over {B(n)/3\mu {\rm{G}}}}} \right)^\delta },$(1)

where δ and χ relate to the properties of the magnetic field turbulence in the region, and B(n) describes the dependence of the magnetic field strength B on the cloud density n (see Mitchell et al. 2021). Values adopted for δ, χ, and the diffusion coefficient normalisation D0 at 1 GeV are listed in Table 2. Within the ISM, χ is taken to be 1, whilst a value of 0.1 is adopted to account for suppressed diffusion within the clouds. From the above ingredients, the particle spectrum as a function of energy E, age t, and distance from the accelerator r is obtained: f (E, r′, t′).

Experimental measurements are, however, bound to neutral messengers such as γ rays and neutrinos as the signatures for the presence of energetic hadronic particles. For comparison to data, the proton spectrum can then be converted into a γ-ray emissivity Φγ(Eγ, r′, t′) (in ph cm−3 s−1 TeV−1) using the expressions from Kelner et al. (2006): Φγ(Eγ,r′,t′)=cn∫Eγ∞σinel (E)f(E,r′,t′)Fγ(EγE,E)dEE,${\Phi _\gamma }\left( {{E_\gamma },{r^\prime },{t^\prime }} \right) = cn\int_{{E_\gamma }}^\infty {{\sigma _{{\rm{inel }}}}} (E)f\left( {E,{r^\prime },{t^\prime }} \right){F_\gamma }\left( {{{{E_\gamma }} \over E},E} \right){{{\rm{d}}E} \over E},$(2)

for which we adopted the parameterisation of the inelastic cross-section for proton-proton interactions σinel(E) from Kafexhiu et al. (2014); moreover, we note that due to high uncertainties below ~ 100 GeV, we take this as an energy threshold and restrict our model predictions to energies > 100 GeV only.

Lastly, we obtain the γ-ray flux F(Eγ, t) at a distance d from the cloud (i.e. at Earth) taking into account the volume of the molecular cloud traversed by particles Vc via F(Eγ,t)=Φγ(Eγ,t)Vc/(4πd2).$F\left( {{E_\gamma },t} \right) = {\Phi _\gamma }\left( {{E_\gamma },t} \right){V_{\rm{c}}}/\left( {4\pi {d^2}} \right).$(3)

The diffusive Galactic CR flux permeates the entire Galaxy, and as such will also contribute to the total particle flux interacting with the molecular clouds. To take this contribution into account, we include the proton flux as measured by the Alpha Magnetic Spectrometer on the International Space Station (Aguilar et al. 2015). This flux is added to the particle flux arriving at the cloud, f in Eq. (2), enabling the relative contributions of accelerator and the diffuse CR sea to be evaluated.

Kelner et al. (2006) also provided expressions for the neutrino production via charged pion and muon decay via Fv(EvE,E)${F_v}\left( {{{{E_v}} \over E},E} \right)$ for the total production of electron and muon neutrinos from the same proton interactions. By analogy with Eqs. (2) and (3), the corresponding total neutrino flux can be obtained.

In the next section, we discuss how we used this model to generate predictions for the γ-ray flux arising from a hypothetical SNR illuminating the molecular clouds identified in the vicinity of the LHAASO J2108+5157. Additionally, we considered the contribution from the Galactic CR sea to establish whether it is sufficient to account for the observed γ-ray emission without requiring a nearby accelerator. The model is compared to measurements from LHAASO and HAWC, and upper limits from the LST-1 and VERITAS1 (Cao et al. 2021b; Abe et al. 2023; Kumar et al. 2023).

Table 1

Properties of the molecular clouds considered in this study.

Table 2

Assumed parameters of the model.

3 Results

3.1 Scan over SNR parameter space

As the properties of the molecular clouds are known (Table 1), we varied the properties of a hypothetical SNR to investigate the required values to account for the γ-ray flux of LHAASO J2108+5157. We assumed that the SNR is located at the same distance from Earth as the cloud. The SNR age is varied in ten logarithmically spaced steps between 1 kyr and 500 kyr, for a fixed separation distance between the SNR and cloud of 24 pc. Similarly, the separation distance is independently varied in ten logarithmically spaced steps between 10 pc and 500 pc for a fixed SNR age of 4 kyr. For type Ia supernovae, the fixed reference values were reduced to 10 pc and 1 kyr. These curves are shown in Figs. 1 and 2 for type II and type Ia supernovae, respectively.

In the case of type II supernova remnants shown in Fig. 1, the predicted flux is comparable to the data for cloud FKT[2022]; yet, the flux predicted for MML[2017]4607 consistently falls below the measured flux. Younger ages are preferred, with the flux at energies ≲ 1 TeV becoming over-predicted between ~7 kyr and 30 kyr for FKT[2022]. The key features of the model are that the highest energy particles escape the SNR at earlier times and are first to arrive at the cloud. The spectral energy distribution hence rises at the highest energies at earlier times (and for shorter distances). The particle distribution then cools as a function of age, with the peak shifting towards lower energies.

In the case of type Ia supernova remnants shown in Fig. 2, a separation distance larger than 24 pc is required for FKT[2022] to avoid over-predicting the flux in the <10 TeV range. MKT[2022]4607 is better able to account for the γ-ray flux in the type Ia scenario, yet only for an optimum combination of low distance and young age. As tsed is lower for the type Ia scenario, the spectral energy distribution is more highly populated at an earlier stage.

3.2 Contribution from the Galactic CR sea

As described above, the contribution from diffusive Galactic CRs is included in the model, assuming that the particle flux is comparable to that measured at Earth (Aguilar et al. 2015). From the parameter scan, we find that the contribution from the nearby SNR dominates over that from Galactic CR sea in most cases. Indeed, the contribution from diffusive Galactic CRs only exceeds that from the SNR if either the cloud-SNR distance is ≳200 pc (for young ≲10 kyr SNRs), or if the SNR is old, ≳400 kyr (for nearby ≲50 pc SNRs).

In order to test whether the diffuse Galactic CR sea could be solely responsible for the measured γ-ray flux, the normalisation of the Galactic flux contribution was varied when no hypothetical SNR was considered. To match the observed emission at TeV energies using the molecular clouds considered, the normalisation must be of the order of ~103 higher than that measured at Earth. This enhancement is unlikely to be achieved without the presence of an accelerator nearby.

Next, we considered all possible combinations of SNR age and separation distance within the aforementioned ranges. A chi-square evaluation of the model curve to the LHAASO data points only is used to establish which model curves provide the closest match to the data. Due to the large number of free parameters entering into the model, we did not perform a minimisation, as there will be multiple local minima in the parameter space able to account for the data. Instead, we aim to provide a plausible range of allowed values for the specific case of this model, with assumed fixed parameters as in Table 2.

thumbnail Fig. 1

Dependence of γ-ray flux on properties of a type II supernova. Left: variation in supernova age for a fixed distance of 24 pc. Right: variation with distance between the SNR and the cloud for a fixed age of 4 kyr. Solid lines correspond to MML[2017]4607 and dashed lines correspond to FKT[2022].
thumbnail Fig. 2

Dependence of γ-ray flux on properties of a type Ia supernova. Left: variation in supernova age for a fixed distance of 10 pc. Right: variation with distance between the SNR and the cloud for a fixed age of 1 kyr. Solid lines correspond to MML[2017]4607 and dashed lines correspond to FKT[2022].

3.3 Best-matched models

3.3.1 Clouds MML[2017]4607 and FKT[2022]

For each cloud, model curves corresponding to the two best matching combinations of SNR age and separation distance are shown in Fig. 3. Model curves for MML[2017]4607 were consistently below the data points for χ = 0.1 within the cloud, as seen in Figs. 1 and 2. To obtain parameter values within comparable agreement with the data as for FKT[2022], we neglected the suppressed diffusion within the cloud for MML[2017]4607 (and for this section only) by setting χ = 1. This corresponds to the most optimistic case in which CRs can freely penetrate the cloud, although we note that δ was kept fixed at 0.5 and we did not investigate the effect of altering the energy dependence of the diffusion coefficient in Eq. (1).

The best matching combinations are summarised in Table 3. In general, the SNR age was found to have a stronger influence on the curve shape and, hence, the quality of the match to LHAASO data than the separation distance. FKT[2022] yielded more parameter combinations with a lower χ2 than MML[2017]4607, where model curves for the same age yet for smaller distances were essentially consistent. This is supported by Figs. 1 and 2. For a fixed age, provided the distance is sufficiently small that CRs have had time to traverse the cloud, the γ-ray flux remains constant with decreasing distance. Equivalently, the γ-ray flux drops with increasing distance. Overall, the type Ia scenario (i.e. a lower tsed) is preferred.

One might ask whether or not a finer resolution of values covering the reasonable parameter space would lead to a model that better matched the data. While this may be the case, we first considered the effect of propagating the uncertainties in the measured properties of the clouds (Table 1) through the model. An upper bound to the flux is obtained by adopting the 1 σ deviation d − σd and n + σn, while a lower bound is similarly obtained from the model evaluated with d + σd and n − σn, where we intrinsically assume that the uncertainties are Gaussian distributed. Increasing n increases the target material and, hence, the flux, as per Eq. (2); while increasing d decreases the flux as per Eq. (3). For FKT[2022], uncertainties are reported in de la Fuente et al. (2023); for MML[2017]4607, uncertainties are not provided in the case that near and far estimates agree (Miville-Deschênes et al. 2017). We therefore adopted a 20% uncertainty in d and n for MML[2017]4607 as a rough estimate, given that the true uncertainty and subsequent variation in the model is unknown. Resulting uncertainty bands corresponding to the parameter combinations reported in Table 3 are shown in Fig. 3.

Figure 3 clearly illustrates that the uncertainty introduced to the model from experimental measurements (or the adopted 20% uncertainty) on the cloud properties leads to variation in predicted flux comparable to that seen by varying the input age and distance of the parameter scan. Therefore, a more finely resolved exploration of the SNR parameter space is not justified.

thumbnail Fig. 3

Model curves corresponding to parameter combinations that best match data as listed in Table 3. Left: type II supernova remnant. Right: type Ia supernova remnant. Solid lines and shaded uncertainty band correspond to MML[2017]4607. Dashed lines and hatched region correspond to FKT[2022].
Table 3

Combinations of SNR age, t and separation distance, Δd for the model curves that best match the LHAASO data, listed in ranked order according to χ2.

3.3.2 Corresponding neutrino flux

For two of the best matching models from Table 3, we show the corresponding total neutrino flux in Fig. 4. For MML[2017]4607, this is for t = 1 kyr and Δd = 37 pc, while for FKT[2022] we show t = 4 kyr and Δd = 57 pc; both are for the SN Ia case. Although Δd = 37 pc yielded a lower χ2 for FKT[2022] with respect to the LHAASO data, this curve is disfavoured as it exceeds the upper limits provided by LST-1 (upper dashed curve in Fig. 3). These curves essentially scale with the γ-ray flux, yet they still lie at least an order of magnitude in flux below the sensitivity of current neutrino experiments suited for the detection of astrophysical neutrinos, such as IceCube (Aartsen et al. 2019).

thumbnail Fig. 4

γ-ray and neutrino fluxes for two of the best-matching scenarios for a type Ia SN from Table 3. Solid lines correspond to the expected γ-ray flux, and dashed lines correspond to the neutrino flux.

4 Discussion

LHAASO J2108+5157 is an intriguing UHE γ-ray source with no known counterparts, yet it is spatially coincident with molecular clouds. In this study, we investigated a scenario whereby the molecular cloud is illuminated by energetic protons accelerated at a SNR in the vicinity. By scanning the parameter space of SNR age and separation distance between the hypothetical SNR and the cloud, we obtain model predictions that can be compared to data, thereby constraining the most likely SNR properties. Consistently, we find that a comparatively young (< 10 kyr) and nearby (d ≲ 40–60 pc) SNR is required.

There are currently no known SNRs matching this description. From the SNR catalogue (Ferrand & Safi-Harb 2012), the two closest SNRs are G094.0+01.0 and G093.7-00.2, at angular distances of more than 1.4° from LHAASO J2108+5157. At the 3.28 kpc distance of MML[2017]4607, this corresponds to a 140 pc and 190 pc separation from the cloud, respectively, while at the 1.7 kpc distance of FKT[2022] the SNRs are situated 80 pc and 110pc away from the cloud. Additionally, G094.0+1.0 has an estimated age of 25 kyr, far older than the SNR ages preferred by our model. We conclude that neither SNR is associated with LHAASO J2108+5157.

Nevertheless, it remains plausible that there are further, as yet undiscovered SNRs located in the region. Recent results from the EMU/POSSUM survey performed using the Australian Square Kilometer Array Pathfinder (ASKAP) observed a region of the Galactic plane containing seven known SNRs and found 21 candidates, 13 of which were new discoveries (Ball et al. 2023). This supports the notion that radio surveys to date may not be sufficiently sensitive to detect all SNRs within a given region.

Several molecular clouds have been identified in the region, two from Miville-Deschênes et al. (2017) based on Dame et al. (2001) (MML[2017]4607 and MML[2017]2870) and most recently a new cloud FKT[2022] reported by de la Fuente et al. (2023). Model parameters were explored for the two clouds spatially coincident with LHAASO J2108+5157, namely MML[2017]4607 and FKT[2022].

Both type II and type Ia supernova explosion scenarios were considered, where the main difference is in the assumed time for transition to the Sedov-Taylor phase (tsed). Although a better match could be achieved under the type Ia scenario, we consider this unlikely. Type Ia supernovae occur in older systems where at least one member of a binary system has sufficiently evolved to become a white dwarf, and this generally corresponds to environments not rich in molecular material. Type II supernovae, however, occur in younger environments where an abundance of molecular material can be expected, similar to that observed in the vicinity of LHAASO J2108+5157. Hence, we interpret these results as indicating that an earlier transition into the Sedov-Taylor phase is preferred, which may reflect, for example, properties of the ambient medium rather than the nature of the progenitor (Truelove & McKee 1999).

In all model curves, the highest energy data point at ~500 TeV could not be well matched with a maximum energy of the proton spectrum of 1 PeV. Therefore, throughout this study we assumed a maximum energy at the Sedov time of 3 PeV.

For MML[2017]4607 to account for the data, we neglected an additional suppression within the cloud due to turbulence compared to the ISM (i.e. χ = 1). With χ = 0.1 within the cloud, MML[2017]4607 consistently under-predicted the data in our model (Figs. 1 and 2). Our model assumed locally suppressed diffusion compared to the Galactic average also in the intervening medium between the SNR and the cloud, a reasonable assumption for regions of active particle acceleration (Gabici et al. 2007; D’Angelo et al. 2018; Inoue 2019).

Suppressed diffusion and a young SNR age as preferred model parameters is in agreement with the 4.5 kyr age obtained by Kar & Gupta (2022), although De Sarkar (2023) suggested an older SNR age of 44 kyr, obtained with a different spectral index for the particle population. A young SNR may still be a comparatively weak producer of synchrotron emission, or it could be small in size and remain embedded within (or obscured by) molecular clouds in the region. Given the angular size of the molecular clouds, a young SNR could be completely hidden behind the clouds along the line of sight. Using the relation RSNR ∝ t2/5 for evolution in the Sedov-Taylor phase, an SNR younger than 12 kyr for MML[2017]2870 and 19 kyr for FKT[2022] would be small enough to be obscured by the cloud. This is consistent with the preferred < 10 kyr SNR age.

Nonetheless, other scenarios for the origin of LHAASO J2108+5157 remain plausible. Young stellar clusters have been hypothesised as suitable Galactic PeVatrons, with particle acceleration occurring at the termination shock of the collective wind (Aharonian et al. 2019; Morlino et al. 2021). There are two known young stellar clusters nearby LHAASO J2108+5157; although, the distance to Kronberger 80 is known to be at least 4.8 kpc or larger (Kharchenko et al. 2016; Cantat-Gaudin & Anders 2020), disfavouring an association with the molecular clouds in the region, and the distance to Kronberger82 remains unknown (Kronberger et al. 2006). As such, a stellar cluster is a potential alternative accelerator also capable of illuminating molecular clouds with CRs, but not well justified in this region.

Given the spatial correlation of LHAASO J2108+5157 with molecular clouds a leptonic scenario for the emission seems unlikely; nevertheless, it has been demonstrated that powerful pulsar wind nebulae are capable of accelerating leptons to beyond 1 PeV and can account for UHE γ rays, especially in high radiation field environments (Vannoni et al. 2009; Breuhaus et al. 2022). The lack of a pulsar counterpart, or of X-ray synchrotron emission that would indicate the presence of a pulsar wind nebula also in cases where the pulsed emission is mis-aligned, disfavours such a scenario.

With the advent of current generation detectors such as LHAASO sensitive to UHE γ rays, we may expect other enigmatic sources to emerge, corresponding to clouds illuminated by unknown accelerators. Other unidentified γ-ray sources for which no known counterpart has been identified to date, such as LHAASO J0341+5258, may have a similar origin (Cao et al. 2021a). The first LHAASO catalogue reported no fewer than seven further new sources that seem to be ‘dark’ in nature, without any known counterparts (Cao et al. 2024). Undoubtedly, further follow-up studies, both in terms of observation and interpretation, are necessary to determine the origin of these enigmatic γ-ray sources.

5 Conclusion

LHAASO J2108+5157 is a dark UHE γ-ray source spatially coincident with two molecular clouds. We find that the γ-ray emission can be accounted for in terms of molecular cloud illumination by CRs from a nearby (≲40–60 pc) young (< 10 kyr) SNR. Although no SNR is currently known that fulfills these criteria, such an SNR could be obscured by other material along the line of sight, or simply lie below the detection threshold of previous surveys (Ball et al. 2023). Interactions of the diffuse Galactic CR sea with the molecular clouds is found to be insufficient to explain the observed γ-ray flux.

As the exposure of current survey instruments increases, and with the advent of future facilities such as CTA and SWGO, we can anticipate further such discoveries, potentially unveiling a population of UHE sources tracing the presence of PeV particles (Acharya et al. 2013; Albert et al. 2019; Casanova 2022; Cao et al. 2024). The key to identifying PeVatrons may lie not in emission from the accelerators themselves, but rather from evidence of energetic particles that have escaped the source region.

Acknowledgements

The author is grateful to G. Rowell and C. van Eldik for fruitful discussions and especially to A. Specovius for reading the manuscript. This work is supported by the Deutsche Forschungsgemeinschaft, DFG project number 452934793.

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1

Very Energetic Radiation Imaging Telescope Array System.

All Tables

Table 1

Properties of the molecular clouds considered in this study.

In the text
Table 2

Assumed parameters of the model.

In the text
Table 3

Combinations of SNR age, t and separation distance, Δd for the model curves that best match the LHAASO data, listed in ranked order according to χ2.

In the text

All Figures

thumbnail Fig. 1

Dependence of γ-ray flux on properties of a type II supernova. Left: variation in supernova age for a fixed distance of 24 pc. Right: variation with distance between the SNR and the cloud for a fixed age of 4 kyr. Solid lines correspond to MML[2017]4607 and dashed lines correspond to FKT[2022].
In the text
thumbnail Fig. 2

Dependence of γ-ray flux on properties of a type Ia supernova. Left: variation in supernova age for a fixed distance of 10 pc. Right: variation with distance between the SNR and the cloud for a fixed age of 1 kyr. Solid lines correspond to MML[2017]4607 and dashed lines correspond to FKT[2022].
In the text
thumbnail Fig. 3

Model curves corresponding to parameter combinations that best match data as listed in Table 3. Left: type II supernova remnant. Right: type Ia supernova remnant. Solid lines and shaded uncertainty band correspond to MML[2017]4607. Dashed lines and hatched region correspond to FKT[2022].
In the text
thumbnail Fig. 4

γ-ray and neutrino fluxes for two of the best-matching scenarios for a type Ia SN from Table 3. Solid lines correspond to the expected γ-ray flux, and dashed lines correspond to the neutrino flux.
In the text

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