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P. Cristofari

Publications and source records attributed to P. Cristofari.

At least 19 recordsLinked to original sources

Dust-driven streaming instability and magnetic field amplification downstream of supernova remnant shocks

The acceleration of cosmic rays up to PeV energies at supernova remnant shocks requires an amplification of the ambient magnetic field. The amplification mechanism must operate upstream of the shock, to prevent the escape of particles from the system. Observational evidence of field amplification has been indeed obtained by means of X-ray observations. However, such observations constrain the magnetic field strength downstream of the shock only. Here we describe a mechanism for magnetic field amplification that operates downstream of the shock. It is based on a plasma instability triggered by the drift of charged interstellar dust grains overtaken by the shock. We compute the growth rate of the instability, we estimate the level of magnetic field amplification expected downstream of supernova remnant shocks, and we compare our results with observations. In some cases (most notably Cas~A) this mechanism might explain the presence of the X-ray filaments observed at supernova remnant shocks, without requiring any amplification of the magnetic field upstream of the shock and therefore no acceleration of CRs to ultra-high energies.

astro-ph.HE

Chasing Gamma-Ray Signals from Binary Neutron Star Coalescences with the Cherenkov Telescope Array: Prospects and Observing Strategies

The detection of gravitational waves (GWs) from a binary neutron star (BNS) merger by Advanced LIGO and Advanced Virgo (GW170817), together with its electromagnetic counterpart, the short gamma-ray burst GRB~170817A, heralded the birth of multi-messenger astronomy. The detection of TeV emission from GRBs motivates follow-up observations with the Cherenkov Telescope Array Observatory (CTAO), ideal for detecting such signals due to its unprecedented sensitivity, rapid response, and wide-field survey capabilities. The aim of this work is to evaluate GeV--TeV GW follow-up strategies for CTAO using a multi-step simulation pipeline and to estimate the expected rate of joint GW-GRB detections during observing run O5. Using a simulated sample of BNS systems with corresponding GW detections, gamma-ray emission is simulated through phenomenological prescriptions based on the observed population of short GRBs, including off-axis jet scenarios. CTAO observations are simulated to account for instrument response, sky tiling strategies, integration times, and varying observing conditions. Strategies with variable and constant integration times are investigated. We find that, via an optimized follow-up strategy, about 5% of simulated GW-associated short GRBs produce GeV--TeV radiation detectable by CTAO. Detectability is strongly influenced by the jet opening angle and viewing angle, suggesting that even rough estimates of the viewing angle in GW alerts could enhance targeting. This framework motivates future follow-ups of GW-detectable events, including neutron star-black hole mergers, and further supports the development of advanced strategies incorporating galaxy distributions and synergies with future detectors such as the Einstein Telescope.

astro-ph.HE

Can a single supernova remnant account for the gamma-ray emission of G106.3+2.7?

SNR G106.3+2.7 is a complex TeV emitting source whose emission is still poorly understood. It has especially been at the center of numerous discussions on its potential for being a supernova remnant (SNR) PeVatron, since its gamma-ray spectra seems not to exhibit any significant suppression in the multi--TeV range, up to $\sim 600$ TeV, thereby indicating the presence of $\sim$ PeV particles. We study the hypothesis in which a SNR evolving in a clumpy or cloudy environment is powering the TeV gamma-ray emission, detected mainly from two regions, the "head" and the "tail". We discuss the implications of such an hypothesis. We rely on a simple physically motivated analytical modeling of the shock dynamics and of the content of accelerated particles and confront it to available gamma-ray observations. We find that the current observed TeV gamma-ray emission in the head and tail regions can be accounted for by an active single SNR, with a natural hardening of the spectrum due to the expansion in a clumpy medium or escaping to a dense region in the tail. However, in all scenarios, the broadband gamma-ray emission from the GeV range to the $\gtrsim 100$ TeV range is difficult to reconcile with a standard SNR - whether originating from a thermonuclear or a core-collapse supernova - and instead points toward an association with the pulsar.

astro-ph.HE

Very High Energy Gamma Rays from Ultra Fast Outflows

Context. Ultra fast outflows (UFOs) from active galactic nuclei (AGN) are expected to lead to the formation of sub-relativistic strong shocks expanding in a dense circumnuclear medium, and thus have the potential for being efficient particle accelerators, and to be proficient sources of gamma rays and neutrinos. Aims. We investigate the detectability of a sample of nearby identified UFOs in gamma rays and neutrinos with current and next- generation instruments. Methods. We model the acceleration of particles at the strong shocks of UFOs, and estimate the associated gamma-ray and neutrino signal. We adopt our model to investigate the prospects for detection with current and next-generation observatories. Results. We find that several UFOs could be detectable in the very-high-energy (VHE) domain - for example, by the Cherenkov Telescope Array Observatory (CTAO)- even if they remain undetected by Fermi-LAT in the high-energy range. Detectability is favored for hard proton spectra (spectral index {\alpha} \lessim 3.9), high acceleration efficiencies, and amplified magnetic fields. Our results suggest that next-generation VHE observatories could detect the first gamma-ray signatures of AGN UFOs, providing a new probe of particle acceleration in sub-relativistic shocks

astro-ph.HE

Characterizing planetary systems with SPIRou: questions about the magnetic cycle of 55 Cnc A and two new planets around B

One of the first exoplanet hosts discovered thirty years ago, the star 55 Cnc has been constantly observed ever since. It is now known to host at least five planets with orbital periods ranging from 17 hours to 15 years. It is also one of the most extreme metal rich stars in the neighbourhood and it has a low-mass secondary star. In this article, we present data obtained at the Canada-France-Hawai'i Telescope with the SPIRou spectropolarimeter on both components of the 55 Cnc stellar system. We revisit the long-period radial-velocity signals of 55 Cnc A, with a focus on the role of the magnetic cycle, and propose the existence of a sixth planet candidate, whose period falls close to that of the magnetic cycle, or half of it. The other massive outer planet has a revised period of 13.15 years and a minimum mass of 3.8 MJup. Although some uncertainty remains on these outer planets, the characterization of the four inner planets is very robust through the combination of many different data sets, and all signals are consistent in the nIR and optical domains. In addition, the magnetic topology of the solar-type primary component of the system is observed by SPIRou at the minimum of its activity cycle, characterized by an amplitude ten times smaller than observed during its maximum in 2017. For the low-mass component 55 Cnc B, we report the discovery of two exoplanets in the system, with a period of 6.799+-0.0014 and 33.75+-0.04 days and a minimum mass of 3.5+-0.8 and 5.3+-1.4 MEarth, respectively. The secondary magnetic field is very weak and the current data set does not allow its precise characterization, setting an upper limit of 10 G. The system 55 Cnc stands out as the sixth binary system with planetary systems around both components, and the first one with non equal-mass stellar components.

astro-ph.EP

The H.E.S.S. extragalactic sky survey with the first decade of observations

The results of the first extragalactic gamma-ray survey by the High Energy Stereoscopic System (H.E.S.S.) are presented. The survey comprises 2720 hours of very high-energy gamma-ray observations of the extragalactic sky, recorded with H.E.S.S. from 2004 up to the end of 2012. These data have been re-analysed using a common consistent set of up-to-date data calibration and analysis tools. From this analysis, a list of 23 detected objects, predominantly blazars, was obtained. This catalogue was assessed in terms of the source class populations that it contains. The level of source parameter bias for the blazar sources, probed by this observational dataset, was evaluated using Monte-Carlo simulations. Spectral results obtained with the H.E.S.S. data were compared with the \textit{Fermi}-LAT catalogues to present the full gamma-ray picture of the detected objects. Lastly, this unique dataset was used to assess the contribution of BL Lacertae objects and flat-spectrum radio quasars to the extragalactic gamma-ray background light at several hundreds of giga-electronvolts. These results are accompanied by the release of the high-level data to the astrophysical community.

astro-ph.HE

Hunting Star-Forming Galaxies in the Gamma-Ray Domain

Context. Star-forming galaxies emit γrays with relatively low luminosity, but the study of their emission is no less captivating. While it is known that their γ-ray luminosity in the GeV band is strongly linked to their star formation, the origin of their emission at higher energies remains uncertain due to limited observations. Aims. Our aim is to assemble the largest possible sample of star-forming galaxies with potential detectability by the new-generation of Cherenkov telescopes. Methods. To achieve this, we compile a comprehensive sample of galaxies, including those previously detected by Fermi-LAT in the GeV energy range as well as a larger sample of star-forming galaxies in the Local Volume that have been cataloged in the near-infrared band. We estimate their γ-ray flux assuming a proportional relationship with their star formation rate, and then select the brightest candidates. The predicted spectra in the TeV band are derived using a simple empirical model normalized to the star formation rate and a model based on extrapolating the latest Fermi-LAT data to higher energies. The ground-based detectability of γ-ray emission from these sources is assessed through a comparison to the most recent instrument response functions. Results. Our investigation reveals that almost a dozen star-forming galaxies may be detectable by upcoming γ-ray telescopes. Conclusions. The observation of numerous star-forming galaxies in the TeV band is a fundamental piece of the panchromatic puzzle for understanding the physics inside these galaxies. The significant increase in the number of galaxies that can be studied in detail in the near future, particularly with the Cherenkov Telescope Array Observatory, promises a major step forward in the study of the conditions of acceleration and transport of cosmic rays in nearby extragalactic environments.

astro-ph.HE

The transition from Galactic to extragalactic cosmic rays: the high-energy end of the Galactic spectrum

Understanding the transition from Galactic to extragalactic cosmic rays (CRs) is essential to make sense of the Local cosmic ray spectrum. Several models have been proposed to account for this transition in the 0.1 - 10 $\times 10^{18}$ eV range. For instance: ankle models, where the change from a steep Galactic component to a hard extragalactic spectrum occurs in the $4-10 \times 10^{18}$ eV region, dip models, where the interactions of CR protons with the CMB producing electron-positron pairs shape the ankle, or mixed composition models, in which extragalactic CRs are composed of nuclei of various types. In all these scenarios, the low-energy part of the transition involves the high-energy part of the Galactic component. Therefore, any information on the Galactic component, such as maximum energy, chemical composition, and spectrum after propagation, is crucial to understanding the Galactic-extragalactic transition. We briefly review the high-energy part of the CR spectrum expected from the best potential sources of Galactic CRs.

astro-ph.HE

Diffusive shock acceleration of dust grains at supernova remnants

Diffusive shock acceleration (DSA) is a prominent mechanism for energizing charged particles up to very large rigidities at astrophysical collisionless shocks. In addition to ions and electrons, it has been proposed that interstellar dust grains could also be accelerated through diffusive shock acceleration, for instance, at supernova remnants (SNRs). Considering interstellar dust grains of various size and composition, we investigate the possibility of grain acceleration at young SNR shocks (throughout the free expansion and Sedov-Taylor phases) and the maximum energies reached by the accelerated grains. We investigate the potential implications on the abundance of refractory species relative to volatile elements in the cosmic-ray composition. We rely on semi-analytical descriptions of particle acceleration at strong shocks, and on self-similar solutions for the dynamics of SNR shock waves. For simplicity, type Ia thermonuclear SNRs expanding in uniform interstellar medium are considered. We find that the acceleration of dust grains at relativistic speed is possible, up to Lorentz factor of $\sim 10^{2}$, kinetic energy $E_{\rm k}/\text{nuc}\sim 10^2$ GeV/nuc for the smaller grains of size $a\sim 5 \times 10^{-7}$ cm. We find that the subsequent sputtering of grains can produce nuclei with a rigidity sufficient to be injected in the process of diffusive shock acceleration. Such scenario can help naturally account for the overabundance of refractory elements in the Galactic cosmic-ray composition, provided that a fraction $η\sim 10^{-3}-10^{-2}$ of dust grains swept up by a SNR are energized through DSA.

astro-ph.HE

Very-high-energy $γ$-ray emission from young massive star clusters in the Large Magellanic Cloud

The Tarantula Nebula in the Large Magellanic Cloud is known for its high star formation activity. At its center lies the young massive star cluster R136, providing a significant amount of the energy that makes the nebula shine so brightly at many wavelengths. Recently, young massive star clusters have been suggested to also efficiently produce high-energy cosmic rays, potentially beyond PeV energies. Here, we report the detection of very-high-energy $γ$-ray emission from the direction of R136 with the High Energy Stereoscopic System, achieved through a multicomponent, likelihood-based modeling of the data. This supports the hypothesis that R136 is indeed a very powerful cosmic-ray accelerator. Moreover, from the same analysis, we provide an updated measurement of the $γ$-ray emission from 30 Dor C, the only superbubble detected at TeV energies presently. The $γ$-ray luminosity above $0.5\,\mathrm{TeV}$ of both sources is $(2-3)\times 10^{35}\,\mathrm{erg}\,\mathrm{s}^{-1}$. This exceeds by more than a factor of 2 the luminosity of HESS J1646$-$458, which is associated with the most massive young star cluster in the Milky Way, Westerlund 1. Furthermore, the $γ$-ray emission from each source is extended with a significance of $>3σ$ and a Gaussian width of about $30\,\mathrm{pc}$. For 30 Dor C, a connection between the $γ$-ray emission and the nonthermal X-ray emission appears likely. Different interpretations of the $γ$-ray signal from R136 are discussed.

astro-ph.HE

Evidence for gamma-ray emission from the remnant of Kepler's supernova based on deep H.E.S.S. observations

Observations with imaging atmospheric Cherenkov telescopes (IACTs) have enhanced our knowledge of nearby supernova (SN) remnants with ages younger than 500 years by establishing Cassiopeia A and the remnant of Tycho's SN as very-high-energy (VHE) gamma-ray sources. The remnant of Kepler's SN, which is the product of the most recent naked-eye supernova in our Galaxy, is comparable in age to the other two, but is significantly more distant. If the gamma-ray luminosities of the remnants of Tycho's and Kepler's SNe are similar, then the latter is expected to be one of the faintest gamma-ray sources within reach of the current generation IACT arrays. Here we report evidence at a statistical level of 4.6 sigma for a VHE signal from the remnant of Kepler's SN based on deep observations by the High Energy Stereoscopic System (H.E.S.S.) with an exposure of 152 hours. The measured integral flux above an energy of 226 GeV is ~0.3% of the flux of the Crab Nebula. The spectral energy distribution (SED) reveals a gamma-ray emitting component connecting the VHE emission observed with H.E.S.S. to the emission observed at GeV energies with Fermi-LAT. The overall SED is similar to that of the remnant of Tycho's SN, possibly indicating the same non-thermal emission processes acting in both these young remnants of thermonuclear SNe.

astro-ph.HE

Spectrum and extension of the inverse-Compton emission of the Crab Nebula from a combined Fermi-LAT and H.E.S.S. analysis

The Crab Nebula is a unique laboratory for studying the acceleration of electrons and positrons through their non-thermal radiation. Observations of very-high-energy $γ$ rays from the Crab Nebula have provided important constraints for modelling its broadband emission. We present the first fully self-consistent analysis of the Crab Nebula's $γ$-ray emission between 1 GeV and $\sim$100 TeV, that is, over five orders of magnitude in energy. Using the open-source software package Gammapy, we combined 11.4 yr of data from the Fermi Large Area Telescope and 80 h of High Energy Stereoscopic System (H.E.S.S.) data at the event level and provide a measurement of the spatial extension of the nebula and its energy spectrum. We find evidence for a shrinking of the nebula with increasing $γ$-ray energy. Furthermore, we fitted several phenomenological models to the measured data, finding that none of them can fully describe the spatial extension and the spectral energy distribution at the same time. Especially the extension measured at TeV energies appears too large when compared to the X-ray emission. Our measurements probe the structure of the magnetic field between the pulsar wind termination shock and the dust torus, and we conclude that the magnetic field strength decreases with increasing distance from the pulsar. We complement our study with a careful assessment of systematic uncertainties.

astro-ph.HE

The galactic bubbles of starburst galaxies The influence of galactic large-scale magnetic fields

Context. The galactic winds of starburst galaxies (SBGs) give rise to remarkable structures on kiloparsec scales. However, the evolution and shape of these giant wind bubbles, as well as the properties of the shocks they develop, are not yet fully understood. Aims. We aim to understand what shapes the galactic winds of SBGs, with a particular focus on the role of large-scale magnetic fields in the dynamical evolution of galactic wind-inflated bubbles. In addition, we aim to explore where the conditions for efficient particle acceleration are met in these systems. Methods. We performed magnetohydrodynamic simulations with the AMRVAC code (Adaptive Mesh Refinement Versatile Advection Code) with various configurations of the galactic medium density profile and magnetization. Results. We observe that the large-scale magnetic field, in which galactic winds expand, can impact the structure and evolution of inflated bubbles. However, the typical structures observed in starburst galaxies, such as M82, cannot be solely explained by the magnetic field structures that have been considered. This highlights the importance of other factors, such as the galactic disk, in shaping the galactic bubble. Furthermore, in all the magnetized cases we investigated, the forward wave resulting from the expanding bubbles only results in compression waves, whereas the wind termination shock features high Mach numbers, making it a promising site for diffusive shock acceleration up to $\sim 10^{2}$ PeV. The synthetic X-ray images generated from our models reveal an envelope surrounding the bubbles that extends up to 2 kpc, which could correspond to the polarized emission observed from planar geometry in M82, as well as a large structure inside the bubble corresponding to the shocked galactic wind.

astro-ph.GA

First light of VLT/HiRISE: High-resolution spectroscopy of young giant exoplanets

A major endeavor of this decade is the direct characterization of young giant exoplanets at high spectral resolution to determine the composition of their atmosphere and infer their formation processes and evolution. Such a goal represents a major challenge owing to their small angular separation and luminosity contrast with respect to their parent stars. Instead of designing and implementing completely new facilities, it has been proposed to leverage the capabilities of existing instruments that offer either high contrast imaging or high dispersion spectroscopy, by coupling them using optical fibers. In this work we present the implementation and first on-sky results of the HiRISE instrument at the very large telescope (VLT), which combines the exoplanet imager SPHERE with the recently upgraded high resolution spectrograph CRIRES using single-mode fibers. The goal of HiRISE is to enable the characterization of known companions in the $H$ band, at a spectral resolution of the order of $R = λ/Δλ= 100\,000$, in a few hours of observing time. We present the main design choices and the technical implementation of the system, which is constituted of three major parts: the fiber injection module inside of SPHERE, the fiber bundle around the telescope, and the fiber extraction module at the entrance of CRIRES. We also detail the specific calibrations required for HiRISE and the operations of the instrument for science observations. Finally, we detail the performance of the system in terms of astrometry, temporal stability, optical aberrations, and transmission, for which we report a peak value of $\sim$3.9% based on sky measurements in median observing conditions. Finally, we report on the first astrophysical detection of HiRISE to illustrate its potential.

astro-ph.IM

Sensitivity of the Cherenkov Telescope Array to spectral signatures of hadronic PeVatrons with application to Galactic Supernova Remnants

The local Cosmic Ray (CR) energy spectrum exhibits a spectral softening at energies around 3~PeV. Sources which are capable of accelerating hadrons to such energies are called hadronic PeVatrons. However, hadronic PeVatrons have not yet been firmly identified within the Galaxy. Several source classes, including Galactic Supernova Remnants (SNRs), have been proposed as PeVatron candidates. The potential to search for hadronic PeVatrons with the Cherenkov Telescope Array (CTA) is assessed. The focus is on the usage of very high energy $γ$-ray spectral signatures for the identification of PeVatrons. Assuming that SNRs can accelerate CRs up to knee energies, the number of Galactic SNRs which can be identified as PeVatrons with CTA is estimated within a model for the evolution of SNRs. Additionally, the potential of a follow-up observation strategy under moonlight conditions for PeVatron searches is investigated. Statistical methods for the identification of PeVatrons are introduced, and realistic Monte--Carlo simulations of the response of the CTA observatory to the emission spectra from hadronic PeVatrons are performed. Based on simulations of a simplified model for the evolution for SNRs, the detection of a $γ$-ray signal from in average 9 Galactic PeVatron SNRs is expected to result from the scan of the Galactic plane with CTA after 10 hours of exposure. CTA is also shown to have excellent potential to confirm these sources as PeVatrons in deep observations with $\mathcal{O}(100)$ hours of exposure per source.

astro-ph.HE

A deep spectromorphological study of the $γ$-ray emission surrounding the young massive stellar cluster Westerlund 1

Young massive stellar clusters are extreme environments and potentially provide the means for efficient particle acceleration. Indeed, they are increasingly considered as being responsible for a significant fraction of cosmic rays (CRs) accelerated within the Milky Way. Westerlund 1, the most massive known young stellar cluster in our Galaxy is a prime candidate for studying this hypothesis. While the very-high-energy $γ$-ray source HESS J1646-458 has been detected in the vicinity of Westerlund 1 in the past, its association could not be firmly identified. We aim to identify the physical processes responsible for the $γ$-ray emission around Westerlund 1 and thus to better understand the role of massive stellar clusters in the acceleration of Galactic CRs. Using 164 hours of data recorded with the High Energy Stereoscopic System (H.E.S.S.), we carried out a deep spectromorphological study of the $γ$-ray emission of HESS J1646-458. We furthermore employed H I and CO observations of the region to infer the presence of gas that could serve as target material for interactions of accelerated CRs. We detected large-scale ($\sim 2^\circ$ diameter) $γ$-ray emission with a complex morphology, exhibiting a shell-like structure and showing no significant variation with $γ$-ray energy. The combined energy spectrum of the emission extends to several tens of TeV, and is uniform across the entire source region. We did not find a clear correlation of the $γ$-ray emission with gas clouds as identified through H I and CO observations. We conclude that, of the known objects within the region, only Westerlund 1 can explain the bulk of the $γ$-ray emission. Several CR acceleration sites and mechanisms are conceivable, and discussed in detail. (abridged)

astro-ph.HE

TOI-1759 b: a transiting sub-Neptune around a low mass star characterized with SPIRou and TESS

We report the detection and characterization of the transiting sub-Neptune TOI-1759 b, using photometric time-series from TESS and near infrared spectropolarimetric data from SPIRou on the CFHT. TOI-1759 b orbits a moderately active M0V star with an orbital period of $18.849975\pm0.000006$ d, and we measure a planetary radius and mass of $3.06\pm0.22$ R$_\oplus$ and $6.8\pm2.0$ M$_\oplus$. Radial velocities were extracted from the SPIRou spectra using both the CCF and the LBL methods, optimizing the velocity measurements in the near infrared domain. We analyzed the broadband SED of the star and the high-resolution SPIRou spectra to constrain the stellar parameters and thus improve the accuracy of the derived planet parameters. A LSD analysis of the SPIRou Stokes $V$ polarized spectra detects Zeeman signatures in TOI-1759. We model the rotational modulation of the magnetic stellar activity using a GP regression with a quasi-periodic covariance function, and find a rotation period of $35.65^{+0.17}_{-0.15}$ d. We reconstruct the large-scale surface magnetic field of the star using ZDI, which gives a predominantly poloidal field with a mean strength of $18\pm4$ G. Finally, we perform a joint Bayesian MCMC analysis of the TESS photometry and SPIRou RVs to optimally constrain the system parameters. At $0.1176\pm0.0013$ au from the star, the planet receives $6.4$ times the bolometric flux incident on Earth, and its equilibrium temperature is estimated at $433\pm14$ K. TOI-1759 b is a likely gas-dominated sub-Neptune with an expected high rate of photoevaporation. Therefore, it is an interesting target to search for neutral hydrogen escape, which may provide important constraints on the planetary formation mechanisms responsible for the observed sub-Neptune radius desert.

astro-ph.EP

The first days of type II-P core collapse supernovae in the gamma-ray range

Type II-P supernovæ~(SNe), the most common core-collapse SNe type, result from the explosions of red supergiant stars. Their detection in the radio domain testifies of the presence of relativistic electrons, and shows that they are potentially efficient energetic particle accelerators. If hadrons can also be accelerated, these energetic particles are expected to interact with the surrounding medium to produce a gamma-ray signal even in the multi--TeV range. The intensity of this signal depends on various factors, but an essential one is the density of the circumstellar medium. Such a signal should however be limited by electron-positron pair production arising from the interaction of the gamma-ray photons with optical photons emitted by the supernova photosphere, which can potentially degrade the gamma-ray signal by over ten orders of magnitude in the first days/weeks following the explosion. We calculate the gamma-gamma opacity from a detailed modelling of the time evolution of the forward shock and supernova photosphere, taking a full account of the non-isotropy of the photon interactions. We discuss the time-dependent gamma-ray TeV emission from type II-P SNe as a function of the stellar progenitor radius and mass-loss rate, as well as the explosion energy and mass of the ejected material. We evaluate the detectability of the SNe with the next generation of Cherenkov telescopes. We find that, while most extragalactic events may be undetectable, type II-P SNe exploding in our Galaxy or in the Magellanic Clouds should be detected by gamma-ray observatories such as the upcoming Cherenkov Telescope Array.

astro-ph.HE