The number of flags in finite vector spaces: Asymptotic normality and Mahonian statistics

We study the generalized Galois numbers which count flags of length r in N-dimensional vector spaces over finite fields. We prove that the coefficients of those polynomials are asymptotically Gaussian normally distributed as N becomes large. Furthermore, we interpret the generalized Galois numbers as weighted inversion statistics on the descent classes of the symmetric group on N elements and identify their asymptotic limit as the Mahonian inversion statistic when r approaches infinity. Finally, we apply our statements to derive further statistical aspects of generalized Rogers-Szegoe polynomials, re-interpret the asymptotic behavior of linear q-ary codes and characters of the symmetric group acting on subspaces over finite fields, and discuss implications for affine Demazure modules and joint probability generating functions of descent-inversion statistics.Comment: 19 pages. Corrected proof of asymptotic normality (Theorem 3.5). Previous Proposition 3.3 is fals

HESS J1809−-193: a halo of escaped electrons around a pulsar wind nebula?

Context. HESS J1809$-$193 is an unassociated very-high-energy $\gamma$-ray source located on the Galactic plane. While it has been connected to the nebula of the energetic pulsar PSR J1809$-$1917, supernova remnants and molecular clouds present in the vicinity also constitute possible associations. Recently, the detection of $\gamma$-ray emission up to energies of $\sim$100 TeV with the HAWC observatory has led to renewed interest in HESS J1809$-$193. Aims. We aim to understand the origin of the $\gamma$-ray emission of HESS J1809$-$193. Methods. We analysed 93.2 h of data taken on HESS J1809$-$193 above 0.27 TeV with the High Energy Stereoscopic System (H.E.S.S.), using a multi-component, three-dimensional likelihood analysis. In addition, we provide a new analysis of 12.5 yr of Fermi-LAT data above 1 GeV within the region of HESS J1809$-$193. The obtained results are interpreted in a time-dependent modelling framework. Results. For the first time, we were able to resolve the emission detected with H.E.S.S. into two components: an extended component that exhibits a spectral cut-off at $\sim$13 TeV, and a compact component that is located close to PSR J1809$-$1917 and shows no clear spectral cut-off. The Fermi-LAT analysis also revealed extended $\gamma$-ray emission, on scales similar to that of the extended H.E.S.S. component. Conclusions. Our modelling indicates that based on its spectrum and spatial extent, the extended H.E.S.S. component is likely caused by inverse Compton emission from old electrons that form a halo around the pulsar wind nebula. The compact component could be connected to either the pulsar wind nebula or the supernova remnant and molecular clouds. Due to its comparatively steep spectrum, modelling the Fermi-LAT emission together with the H.E.S.S. components is not straightforward. (abridged)Comment: 14 pages, 10 figures. Accepted for publication in A&A. Corresponding authors: Vikas Joshi, Lars Mohrman

A deep spectromorphological study of the γ\gamma-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 $\gamma$-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 $\gamma$-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 $\gamma$-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) $\gamma$-ray emission with a complex morphology, exhibiting a shell-like structure and showing no significant variation with $\gamma$-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 $\gamma$-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 $\gamma$-ray emission. Several CR acceleration sites and mechanisms are conceivable, and discussed in detail. (abridged)Comment: 15 pages, 9 figures. Corresponding authors: L. Mohrmann, S. Ohm, R. Rauth, A. Specoviu

Detection of extended gamma-ray emission around the Geminga pulsar with H.E.S.S

Geminga is an enigmatic radio-quiet gamma-ray pulsar located at a mere 250 pc distance from Earth. Extended very-high-energy gamma-ray emission around the pulsar was discovered by Milagro and later confirmed by HAWC, which are both water Cherenkov detector-based experiments. However, evidence for the Geminga pulsar wind nebula in gamma rays has long evaded detection by imaging atmospheric Cherenkov telescopes (IACTs) despite targeted observations. The detection of gamma-ray emission on angular scales > 2 deg poses a considerable challenge for the background estimation in IACT data analysis. With recent developments in understanding the complementary background estimation techniques of water Cherenkov and atmospheric Cherenkov instruments, the H.E.S.S. IACT array can now confirm the detection of highly extended gamma-ray emission around the Geminga pulsar with a radius of at least 3 deg in the energy range 0.5-40 TeV. We find no indications for statistically significant asymmetries or energy-dependent morphology. A flux normalisation of $(2.8\pm0.7)\times10^{-12}$ cm$^{-2}$s$^{-1}$TeV$^{-1}$ at 1 TeV is obtained within a 1 deg radius region around the pulsar. To investigate the particle transport within the halo of energetic leptons around the pulsar, we fitted an electron diffusion model to the data. The normalisation of the diffusion coefficient obtained of $D_0 = 7.6^{+1.5}_{-1.2} \times 10^{27}$ cm$^2$s$^{-1}$, at an electron energy of 100 TeV, is compatible with values previously reported for the pulsar halo around Geminga, which is considerably below the Galactic average.Comment: 16 pages, 15 figures, 7 tables. Accepted for publication in Astronomy & Astrophysic

Constraints on the intergalactic magnetic field using Fermi-LAT and H.E.S.S. blazar observations

Magnetic fields in galaxies and galaxy clusters are believed to be the result of the amplification of intergalactic seed fields during the formation of large-scale structures in the universe. However, the origin, strength, and morphology of this intergalactic magnetic field (IGMF) remain unknown. Lower limits on (or indirect detection of) the IGMF can be obtained from observations of high-energy gamma rays from distant blazars. Gamma rays interact with the extragalactic background light to produce electron-positron pairs, which can subsequently initiate electromagnetic cascades. The $\gamma$-ray signature of the cascade depends on the IGMF since it deflects the pairs. Here we report on a new search for this cascade emission using a combined data set from the Fermi Large Area Telescope and the High Energy Stereoscopic System. Using state-of-the-art Monte Carlo predictions for the cascade signal, our results place a lower limit on the IGMF of $B > 7.1\times10^{-16}$ G for a coherence length of 1 Mpc even when blazar duty cycles as short as 10 yr are assumed. This improves on previous lower limits by a factor of 2. For longer duty cycles of $10^4$ ($10^7$) yr, IGMF strengths below $1.8\times10^{-14}$ G ($3.9\times10^{-14}$ G) are excluded, which rules out specific models for IGMF generation in the early universe.Comment: 20 pages, 7 figures, 4 tables. Accepted for publication in ApJ Letters. Auxiliary data is provided in electronic format at https://zenodo.org/record/801431

Search for enhanced TeV gamma ray emission from Giant Molecular Clouds using H.E.S.S.

Cosmic Ray (CR) interactions with the dense gas inside Giant Molecular Clouds (GMCs) produce neutral pions, which in turn decay into gamma rays. Thus, the gamma ray emission from GMCs is a direct tracer of the cosmic ray density and the matter density inside the clouds. Detection of enhanced TeV emission from GMCs, i.e., an emission significantly larger than what is expected from the average Galactic cosmic rays illuminating the cloud, can imply a variation in the local cosmic ray density, due to, for example, the presence of a recent accelerator in proximity to the cloud. Such gamma-ray observations can be crucial in probing the cosmic ray distribution across our Galaxy, but are complicated to perform with present generation Imaging Atmospheric Cherenkov Telescopes (IACTs). These studies require differentiating between the strong cosmic-ray induced background, the large scale diffuse emission, and the emission from the clouds, which is difficult to the small field of view of present generation IACTs. In this contribution, we use H.E.S.S. data collected over 16 years to search for TeV emission from GMCs in the inner molecular galacto-centric ring of our Galaxy. We implement a 3D FoV likelihood technique, and simultaneously model the hadronic background, the galactic diffuse emission and the emission expected from known VHE sources to probe for excess TeV gamma ray emission from GMCs

Is PKS 0625-354 another variable TeV active galactic nucleus?

The majority of the active galactic nuclei (AGN) detected at very-high-energies above 100 GeV belong to the class of blazars with a small angle between the jet-axis and the line-of-sight. Only about 10 percent of the gamma-ray AGN are objects with a larger viewing angle resulting in a smaller Doppler boosting of the emission. Originally, it was believed that gamma-ray emission can only be observed from blazars and those are variable in its brightness. Instead, the last years have shown that non-blazar active galaxies also show a fascinating variability behaviour which provide important new insights into the physical processes responsible for the gamma-ray production and especially for flaring events. Here, we report on the observation of gamma-ray variability of the active galaxy PKS 0625−354 detected with the H.E.S.S. telescopes in November 2018. The classification of PKS 0625−354 is a still matter of debate. The H.E.S.S. measurements were performed as part of a flux observing program and showed in the first night of the observation a detection of the object with > 5σ. A denser observation campaign followed for the next nine nights resulting in a decrease of the gamma-ray flux. Those observations were accompanied with Swift in the X-ray and UV/optical band allowing for the reconstruction of a multi-band broad-band spectral energy distribution. We will discuss the implications of the gamma-ray variability of the object

Evidence of 100 TeV γ-ray emission from HESS J1702-420 : a new PeVatron candidate

The identification of active PeVatrons, hadronic particle accelerators reaching the knee of the cosmic-ray spectrum (at the energy of few PeV), is crucial to understand the origin of cosmic rays in the Galaxy. In this context, we report on new H.E.S.S. observations of the PeVatron candidate HESS J1702-420, which bring evidence for the presence of γ-rays up to 100 TeV. This is the first time in the history of H.E.S.S. that photons with such high energy are observed. Remarkably, the new deep observations allowed the discovery of a new γ-ray source component, called HESS J1702-420A, that was previously hidden under the bulk emission traditionally associated with HESS J1702-420. This new object has a power-law spectral slope < 2 and a γ-ray spectrum that, extending with no sign of curvature up to 100 TeV, makes it an excellent candidate site for the presence of PeV-energy cosmic rays. This discovery brings new information to the ongoing debate on the nature of the unidentified source HESSJ1702-420, and on the origin of Galactic cosmic rays

Search for dark matter annihilation signals from unidentified Fermi-LAT objects with H.E.S.S.

Cosmological N-body simulations show that Milky-Way-sized galaxies harbor a population of unmerged dark matter subhalos. These subhalos could shine in gamma rays and be eventually detected in gamma-ray surveys as unidentified sources. We search for very-high-energy (VHE, E $\geq$ 100~GeV) gamma-ray emission using H.E.S.S. observations carried out from a thorough selection of unidentified Fermi-LAT Objects (UFOs) as dark matter subhalo candidates. Provided that the dark matter mass is higher than a few hundred GeV, the emission of the UFOs can be well described by dark matter annihilation models. No significant VHE gamma-ray emission is detected in any UFO dataset nor in their combination. We, therefore, derive constraints on the product of the velocity-weighted annihilation cross-section \left by the J-factor on dark matter models describing the UFO emissions. Upper limits at 95% confidence level are derived on \left J in W$^{+}$W$^{-}$ and τ$^{+}$τ$^{-}$ annihilation channels for the TeV dark matter particles. Focusing on thermal WIMPs, strong constraints on the J-factors are obtained from H.E.S.S. observations. Adopting model-dependent predictions from cosmological N-body simulations on the J-factor distribution function for Milky Way (MW)-sized galaxies, only $\lesssim$ 0.3 ~TeV mass dark matter models marginally allow to explain observed UFO emission