arXiv subjects

F. Brun

Publications and source records attributed to F. Brun.

At least 19 recordsLinked to original sources

arXiv2026

Evidence for a spectral steepening of the gamma-ray emission from the Galactic Center ridge

Very-high-energy (VHE) $\gamma$-ray emission detected from the central molecular zone (CMZ) hints at diffusive propagation of cosmic rays (CRs) injected continuously near the Galactic center (GC). Using H.E.S.S. VHE $\gamma$-ray observations, we aim to construct a multi-component description of the region in order to derive the spatial and spectral distributions of CRs and discuss their potential origin. We rely on a spectro-morphological analysis, in which spectral and spatial parameters of different components are fit simultaneously, and on a three-dimensional description of the CMZ and CR distributions. The GC ridge emission is well reproduced with the assumed gas distribution model weighted by a $1/r^{\alpha}$ CR density profile with $\alpha = 1.10 \pm 0.05_{\rm{stat}} \pm 0.10_{\rm{syst}}$. We detect no significant spectral variations across the CMZ, which supports a continuous injection from the GC. We report a significant (> 3 $\sigma$) curvature in the GC ridge $\gamma$-ray spectrum, implying a parent proton break (or cutoff energy) of $E_b \sim 15-50$ TeV ($E_{\rm{cut}} \sim 60-160$ TeV). We also derive the best-fit spectral parameters of the other sources in the region and report a significant cutoff at $E \sim 5$ TeV in the spectrum of the pulsar wind nebula G0.9+0.1. Finally we constrain the position of the injection site to be close to the GC (ruling out the Arches and Quintuplet clusters as major contributors to the emission). We discuss possible origins for the GC ridge emission, potential mechanisms for causing the observed curvature, a possible contribution of the gas content to the emission of HESS J1745-290 and derive qualitative constraints on the line-of-sight positions of the clouds shaping the CMZ.

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arXiv2026

Search for gamma-ray spectral lines from dark matter annihilation with the H.E.S.S. Inner Galaxy Survey

Spectral gamma-ray line features are expected as key signatures from dark matter (DM) annihilations of TeV-scale particle DM. Observations of the Galactic Centre with atmospheric Cherenkov telescopes are unique to probe thermal-relic TeV particle DM, well beyond the reach of direct detection and collider searches. We report here on the search for line signals in very-high-energy gamma rays using data from the Inner Galaxy Survey, consisting of 546 hours of H.E.S.S. observations of the inner few degrees of the Galactic Centre. No significant signal is detected. We then compute the exclusion limits on the annihilation line cross section $\langle \sigma v \rangle_{\rm line}$, with a two-dimensional log-likelihood ratio test statistics, exploiting spectral and spatial features of the DM signal. Assuming an Einasto DM density profile for the Milky Way, our results provide the most constraining limits so far, reaching $\langle \sigma v \rangle_{\rm line} = 2.3$ $\times$ $10^{-28}$ and $2.4 \times$ $10^{-27}$ cm$^3$s$^{-1}$ for DM masses of 1 and 10 TeV, respectively. The present limits are used to constrain the widely searched Wino, Higgsino and Quintuplet models. For the first time, thermal Higgsino DM is probed for DM Milky Way models.

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arXiv2026

Gamma-Ray Constraints on Heavy Axion-Like-Particle Decays from Fermi-LAT and H.E.S.S. Blazar Spectra

The propagation of very-high-energy (VHE; $E_{\gamma} \geq 100$ GeV) gamma rays from extragalactic sources is affected by interactions with photons of the extragalactic background light (EBL), resulting in pair production that attenuates the intrinsic gamma-ray flux. This interaction renders the Universe increasingly opaque to VHE photons at high energies and redshifts. New physics scenarios involving axion-like particles (ALPs) could modify this expected optical depth. In particular, ALPs with masses $m_a \sim 10$ eV can decay into two photons over cosmological timescales, thereby contributing to the diffuse EBL. If such ALPs constitute a significant fraction of the dark matter density, their decay would enhance the EBL intensity and consequently increase the gamma-ray optical depth. In this study, we investigate this scenario using a large sample of gamma-ray spectra observed with the High Energy Stereoscopic System (H.E.S.S.) and the Fermi Large Area Telescope. We model the contribution of decaying ALPs to the EBL and assess their impact on the spectra of blazars across redshifts. By comparing these observations with standard EBL models, we place constraints on the properties of heavy ALPs, specifically their mass and photon coupling, and evaluate their viability as a dark matter candidate capable of modifying the gamma-ray transparency of the Universe. From the combined analysis, and under the assumption that ALPs constitute the entire dark matter density, we derive 95% confidence exclusion limits on the photon-ALP coupling down to $g_{a\gamma} \sim 7 \times 10^{-12}$ GeV$^{-1}$ for masses $m_a\sim 15$ eV. These constraints are competitive with existing astrophysical bounds and provide complementary sensitivity to other techniques, closing a previously unconstrained region of parameter space in the $m_a \sim 2.5$-$20$ eV range.

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arXiv2026

Search for long-term variability of HESS J1745-290

At the center of our Galaxy lies the bright {\gamma}-ray point-like source HESS J1745-290, which is compatible in position with Sgr A star, although an association between the two remains uncertain. Using data obtained between 2004 and 2019 with the High Energy Stereoscopic System (H.E.S.S.) on the Galactic center region, we studied the variability of HESS J1745-290 over 353 hours of observations collected over 16 years, representing the largest dataset gathered yet on this region at TeV energies. We performed a 3D maximum-likelihood analysis of the central source and the diffuse {\gamma}-ray emission in the Galactic center region. This analysis allowed us to extract the spectral and morphological intrinsic behavior of the two components. By performing this analysis on an annual basis, we derived the light curve of HESS J1745-290 and the diffuse emission over the past 16 years. The 3D maximum-likelihood analysis method allowed us to separate the central source from the overlapping diffuse emission, enabling a recalibration of the former by the latter and alleviating some of the systematic effects. We find no long-term or yearly variability. We also provide an estimate of the sensitivity of H.E.S.S. to variation of this specific source over 16 years. We rule out any yearly gamma-ray flux variation of this source larger than 30 percent, as well as any linear flux variation exceeding 30% over this time period.

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arXiv2026

H.E.S.S. observations of composite Seyfert-starburst galaxies

Context: Composite galaxies that contain both Seyfert and starburst components may produce very high-energy (VHE; >100 GeV) gamma-ray emission at a wide range of spatial scales, from a few Schwarzschild radii of a supermassive black hole to dimensions of kiloparsec-size jet-driven outflows. In addition to supernova remnants, various sources have been suggested to explain data collected on composite galaxies, including multi-messenger neutrino and ultra-high-energy cosmic-ray data. Aims: The closest composite Seyfert-starburst galaxies (NGC 1068, the Circinus galaxy, and NGC 4945) are observed with the High Energy Stereoscopic System (H.E.S.S.) to provide constraints on cosmic-ray populations in these systems. Methods: Data obtained in H.E.S.S. observations have been analyzed to search for VHE gamma-ray counterparts to the GeV gamma-ray signals detected with Fermi-LAT and for potential spectral components in the VHE range. Results: No significant signals have been found in these H.E.S.S. data. Upper limits on the VHE gamma-ray fluxes were applied to constrain theoretical models involving different spectral components.

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arXiv2026

The second H.E.S.S. gamma-ray burst catalogue: 15 years of observations with the H.E.S.S. telescopes

Recent observational efforts using imaging atmospheric Cherenkov telescopes (IACTs) have led to firm detections of very-high-energy (VHE) signals from bright gamma-ray bursts (GRBs), often at moderate redshifts. This work presents 15 years of H.E.S.S. GRB observations and examines their implications through population comparisons and selected modelling cases. GRBs are a key science target of the High Energy Stereoscopic System (H.E.S.S.). With a low-energy threshold ($\lesssim$100 GeV) and rapid repointing capabilities, H.E.S.S. can begin follow-up observations within tens of seconds after a GRB trigger, covering the late prompt or early afterglow phases. We report GRB follow-up observations with H.E.S.S. from 2004 to 2019, which resulted in no significant VHE signals (aside from the detections of GRB~180720B and GRB~190829A). The resulting upper limits comprise the largest set available for GRBs at VHE. A subset of bursts with favourable conditions were selected for X-ray analysis and emission modelling. Population studies were performed to compare detected and non-detected GRBs. The results indicate that VHE-detected GRBs are not a distinct population, but tend to feature luminous X-ray emission and favourable redshift and observing conditions. This highlights the potential of next-generation IACTs such as the Cherenkov Telescope Array Observatory (CTAO), whose lower energy threshold will enhance the detection of fainter and more distant GRBs.

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arXiv2026

Scrutinizing the 2020 multiwavelength outburst of PKS 0903-57 through observations with H.E.S.S

The blazar PKS 0903-57 has recently been classified as a flat spectrum radio quasar at a redshift of $z=0.2621$. In March and April 2020, Fermi-LAT and AGILE reported tremendous activity in high-energy $\gamma$ rays with the flux increasing by $\sim$2 orders of magnitude compared to quiescence. The flare was observed with H.E.S.S. in very-high-energy $\gamma$ rays for six nights with a total observation time of 13.1 h, resulting in the discovery of PKS 0903-57 in this energy band with an average flux of $1.5\times 10^{-10}$ ph cm$^{-2}$s$^{-1}$ above an energy threshold of $\sim 180$ GeV corresponding to $60\%$ of the Crab Nebula flux above the same threshold. The very-high-energy $\gamma$-ray flux was strongly variable. X-ray and optical data were collected with Swift and ATOM, and also indicate significant variability. The observed multiwavelength flux and spectral variability during the H.E.S.S. observation window suggest variability time scales on the order of a few hours and reveal complex correlation patterns. The lack of absorption beyond that of the extragalactic background light in the $\gamma$-ray domain suggests that the emission region was located outside of the broad-line region. A leptonic one-zone modeling of the six H.E.S.S. observation nights using the dusty torus as seed photons for the inverse-Compton scattering, results in a low magnetization of the emission region. This implies that shock acceleration is likely the main driver during the event.

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arXiv2026

H.E.S.S. detection of the PSR J0855-4644 nebula

HESS J0852-463 is a TeV {\gamma}-ray source located in the Galactic plane. The region consists of a supernova remnant (SNR, RX J0852.0-4622) with a shell-like morphology, commonly referred to as Vela Junior, and a pulsar denoted PSR J0855-4644. Pulsars are among the most efficient leptonic accelerators in our Galaxy, making this region particularly interesting to study. We utilise the most recent data taken by the High Energy Stereoscopic System (H.E.S.S.), to investigate any {\gamma}-ray emission associated with the pulsar in this region, PSR J0855-4644. We applied a full forward folding method on the H.E.S.S. data. Utilising 3D modelling techniques, we evaluated the TeV {\gamma}-ray emission towards the various components of this complex system. The distinct energy-dependent morphology observed in our data motivates further investigation of this source. We resolved the emission in the Vela Junior region into various components, several of which correspond to the SNR itself. In particular, we find a new extended component which is coincident with the position of PSR J0855-4644. The spectrum follows a power-law distribution with a best-fit index of {\Gamma}E = 1.81 \pm 0.07stat which differs from the properties of the surrounding {\gamma}-ray emission of the Vela Junior SNR. A one-zone leptonic joint fit between the X-rays (from XMM-Newton) and {\gamma}-rays (from H.E.S.S.) leads to a lower limit on the magnetic field of 1.6{\mu}G and a spectral index of {\alpha} = 1.88 \pm 0.01, in line with expectations of pulsar wind nebulae (PWNe). In this paper, we report the first detection of the PWN of PSR J0855-4644 at TeV energies with the H.E.S.S. experiment at a significance of 12.2{\sigma}. This is attributed to the advanced techniques of the 3D analysis. Based on the pulsar's characteristics, its PWN is consistent with the known TeV PWNe population in the Galaxy.

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arXiv2025

Prompt Searches for Very-High-Energy {\gamma}-Ray Counterparts to IceCube Astrophysical Neutrino Alerts

The search for sources of high-energy astrophysical neutrinos can be significantly advanced through a multi-messenger approach, which seeks to detect the gamma rays that accompany neutrinos as they are produced at their sources. Multi-messenger observations have so far provided the first evidence for a neutrino source, illustrated by the joint detection of the flaring blazar TXS 0506+056 in highenergy (HE, E > 1 GeV) and very-high-energy (VHE, E > 100 GeV) gamma rays in coincidence with the high-energy neutrino IceCube-170922A, identified by IceCube. Imaging atmospheric Cherenkov telescopes (IACTs), namely FACT, H.E.S.S., MAGIC, and VERITAS, continue to conduct extensive neutrino target-of-opportunity follow-up programs. These programs have two components: followup observations of single astrophysical neutrino candidate events (such as IceCube-170922A), and observation of known gamma-ray sources after the identification of a cluster of neutrino events by IceCube. Here we present a comprehensive analysis of follow-up observations of high-energy neutrino events observed by the four IACTs between September 2017 (after the IceCube-170922A event) and January 2021. Our study found no associations between gamma-ray sources and the observed neutrino events. We provide a detailed overview of each neutrino event and its potential counterparts. Furthermore, a joint analysis of all IACT data is included, yielding combined upper limits on the VHE gamma-ray flux.

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arXiv2025

Constraining the nature of the most extreme Galactic particle accelerator. H.E.S.S. observations of the microquasar V4641 Sgr

Microquasars have emerged as promising candidates to explain the cosmic-ray flux at petaelectronvolt energies. LHAASO observations revealed V4641~Sgr as the most extreme example so far. Using $\approx$100~h of H.E.S.S. data, we performed a spectro-morphological study of the gamma-ray emission around V4641~Sgr. We employed HI and dedicated CO observations of the region to infer the target material for cosmic-ray interactions. We detected multi-TeV emission around V4641~Sgr with a high significance. The emission region is elongated. We found a power-law spectrum with an index $\approx$1.8, and together with results from other gamma-ray instruments, this reveals a spectral energy distribution that peaks at energies of $\approx$100~TeV for the first time. We found indications (3$\sigma$) of a two-component morphology, with indistinguishable spectral properties. The position of V4641~Sgr is inconsistent with the best-fit position of the single-component model and with the dip between the two components. We found no significant evidence of an energy-dependent morphology. No dense gas was found at any distance towards V4641~Sgr. The peak of the SED at $\approx$100~TeV identifies V4641~Sgr as a candidate cosmic-ray accelerator beyond the so-called knee. The absence of dense target gas places stringent energetic constraints on hadronic interpretations, however. The H.E.S.S. measurement requires an unusually hard ($\approx 1.5$) spectral index for the protons. A leptonic scenario faces fewer obstacles if the particle transport is fast enough to avoid losses and to reproduce the observed energy-independent morphology. The absence of bright \xray emission across the gamma-ray emission region requires a magnetic field strength $\lesssim3$~$\mu$G, however. Our findings favour a leptonic origin of the gamma-ray emission. This conclusion does not exclude hadron acceleration in the V4641~Sgr system.

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arXiv2025

H.E.S.S. programme searching for VHE gamma rays associated with FRBs

Fast Radio Bursts (FRBs) are highly energetic, extremely short-lived bursts of radio flashes. Despite extensive research, the exact cause of these outbursts remains speculative. The high luminosity, short duration, and high dispersion measure of these events suggest they result from extreme, high-energy extragalactic sources, such as highly magnetized and rapidly spinning neutron stars known as magnetars. The number of detected FRBs, including repeating ones, has grown rapidly in recent years. Except for FRB 20200428D, and FRB-like radio burst that is associated to Galactic magnetar SGR 1935+2154, no multi-wavelength counterpart to any FRB has been detected yet. The High Energy Stereoscopic System (H.E.S.S.) telescope has developed a {program} to follow up FRBs searching for their gamma-ray counterparts, helping to uncover the nature of FRBs and FRB sources. This paper provides an overview of the searches for FRB sources conducted by H.E.S.S., including follow-up observations and simultaneous multi-wavelength campaigns with radio and X-ray observatories. Among the FRB sources observed by H.E.S.S., nine are localized with redshifts ranging between 0.11 and 0.492 from 2015 to 2022. No significant very high energy (VHE) emission was detected during these observations. We report constraints on the VHE luminosity ranging from $10^{44}$ erg s$^{-1}$ and $10^{48}$ erg s$^{-1}$, placing limits on the FRB's region persistent VHE emission and potential FRB afterglow emission across timescales from hours to years.

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arXiv2025

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.

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arXiv2025

Detection of very-high-energy gamma-ray emission from Eta Carinae during its 2020 periastron passage

The colliding-wind binary system $\eta$ Carinae has been identified as a source of high-energy (HE, below $\sim$100\,GeV) and very-high-energy (VHE, above $\sim$100\,GeV) gamma rays in the last decade, making it unique among these systems. With its eccentric 5.5-year-long orbit, the periastron passage, during which the stars are separated by only $1-2$\,au, is an intriguing time interval to probe particle acceleration processes within the system. In this work, we report on an extensive VHE observation campaign that for the first time covers the full periastron passage carried out with the High Energy Stereoscopic System (H.E.S.S.) in its 5-telescope configuration with upgraded cameras. VHE gamma-ray emission from $\eta$ Carinae was detected during the periastron passage with a steep spectrum with spectral index $\Gamma= 3.3 \pm 0.2_{\mathrm{stat}} \, \pm 0.1_{\mathrm{syst}}$. Together with previous and follow-up observations, we derive a long-term light curve sampling one full orbit, showing hints of an increase of the VHE flux towards periastron, but no hint of variability during the passage itself. An analysis of contemporaneous Fermi-LAT data shows that the VHE spectrum represents a smooth continuation of the HE spectrum. From modelling the combined spectrum we conclude that the gamma-ray emission region is located at distances of ${\sim}10 - 20$\,au from the centre of mass of the system and that protons are accelerated up to energies of at least several TeV inside the system in this phase.

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arXiv2024

High-Statistics Measurement of the Cosmic-Ray Electron Spectrum with H.E.S.S

Owing to their rapid cooling rate and hence loss-limited propagation distance, cosmic-ray electrons and positrons (CRe) at very high energies probe local cosmic-ray accelerators and provide constraints on exotic production mechanisms such as annihilation of dark matter particles. We present a high-statistics measurement of the spectrum of CRe candidate events from 0.3 to 40 TeV with the High Energy Stereoscopic System (H.E.S.S.), covering two orders of magnitude in energy and reaching a proton rejection power of better than $10^{4}$. The measured spectrum is well described by a broken power law, with a break around 1 TeV, where the spectral index increases from $\Gamma_1 = 3.25$ $\pm$ 0.02 (stat) $\pm$ 0.2 (sys) to $\Gamma_2 = 4.49$ $\pm$ 0.04 (stat) $\pm$ 0.2 (sys). Apart from the break, the spectrum is featureless. The absence of distinct signatures at multi-TeV energies imposes constraints on the presence of nearby CRe accelerators and the local CRe propagation mechanisms.

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arXiv2024

Very-high-energy $\gamma$-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 $\gamma$-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 $\gamma$-ray emission from 30 Dor C, the only superbubble detected at TeV energies presently. The $\gamma$-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 $\gamma$-ray emission from each source is extended with a significance of $>3\sigma$ and a Gaussian width of about $30\,\mathrm{pc}$. For 30 Dor C, a connection between the $\gamma$-ray emission and the nonthermal X-ray emission appears likely. Different interpretations of the $\gamma$-ray signal from R136 are discussed.

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arXiv2024

H.E.S.S. observations of the 2021 periastron passage of PSR B1259-63/LS 2883

PSR B1259-63 is a gamma-ray binary system that hosts a pulsar in an eccentric orbit, with a 3.4 year period, around an O9.5Ve star. At orbital phases close to periastron passages, the system radiates bright and variable non-thermal emission. We report on an extensive VHE observation campaign conducted with the High Energy Stereoscopic System, comprised of ~100 hours of data taken from $t_p-24$ days to $t_p+127$ days around the system's 2021 periastron passage. We also present the timing and spectral analyses of the source. The VHE light curve in 2021 is consistent with the stacked light curve of all previous observations. Within the light curve, we report a VHE maximum at times coincident with the third X-ray peak first detected in the 2021 X-ray light curve. In the light curve -- although sparsely sampled in this time period -- we see no VHE enhancement during the second disc crossing. In addition, we see no correspondence to the 2021 GeV flare in the VHE light curve. The VHE spectrum obtained from the analysis of the 2021 dataset is best described by a power law of spectral index $\Gamma = 2.65 \pm 0.04_{\text{stat}}$ $\pm 0.04_{\text{sys}}$, a value consistent with the previous H.E.S.S. observations of the source. We report spectral variability with a difference of $\Delta \Gamma = 0.56 ~\pm~ 0.18_{\text{stat}}$ $~\pm~0.10_{\text{sys}}$ at 95% c.l., between sub-periods of the 2021 dataset. We also find a linear correlation between contemporaneous flux values of X-ray and TeV datasets, detected mainly after $t_p+25$ days, suggesting a change in the available energy for non-thermal radiation processes. We detect no significant correlation between GeV and TeV flux points, within the uncertainties of the measurements, from $\sim t_p-23$ days to $\sim t_p+126$ days. This suggests that the GeV and TeV emission originate from different electron populations.

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arXiv2024

Unveiling extended gamma-ray emission around HESS J1813-178

HESS J1813$-$178 is a very-high-energy $\gamma$-ray source spatially coincident with the young and energetic pulsar PSR J1813$-$1749 and thought to be associated with its pulsar wind nebula (PWN). Recently, evidence for extended high-energy emission in the vicinity of the pulsar has been revealed in the Fermi Large Area Telescope (LAT) data. This motivates revisiting the HESS J1813$-$178 region, taking advantage of improved analysis methods and an extended data set. Using data taken by the High Energy Stereoscopic System (H.E.S.S.) experiment and the Fermi-LAT, we aim to describe the $\gamma$-ray emission in the region with a consistent model, to provide insights into its origin. We performed a likelihood-based analysis on 32 hours of H.E.S.S. data and 12 years of Fermi-LAT data and fit a spectro-morphological model to the combined datasets. These results allowed us to develop a physical model for the origin of the observed $\gamma$-ray emission in the region. In addition to the compact very-high-energy $\gamma$-ray emission centered on the pulsar, we find a significant yet previously undetected component along the Galactic plane. With Fermi-LAT data, we confirm extended high-energy emission consistent with the position and elongation of the extended emission observed with H.E.S.S. These results establish a consistent description of the emission in the region from GeV energies to several tens of TeV. This study suggests that HESS J1813$-$178 is associated with a $\gamma$-ray PWN powered by PSR J1813$-$1749. A possible origin of the extended emission component is inverse Compton emission from electrons and positrons that have escaped the confines of the pulsar and form a halo around the PWN.

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arXiv2024

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 $\gamma$ 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 $\gamma$-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 $\gamma$-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.

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