Discrete versions of some Dirac type equations and plane wave solutions

A discrete version of the plane wave solution to some discrete Dirac type equations in the spacetime algebra is established. The conditions under which a discrete analogue of the plane wave solution satisfies the discrete Hestenes equation are briefly discussed.Comment: 12 pages. arXiv admin note: text overlap with arXiv:1609.0459

Chiral properties of discrete Joyce and Hestenes equations

This paper concerns the question of how chirality is realized for discrete counterparts of the Dirac-K\"{a}hler equation in the Hestenes and Joyce forms. It is shown that left and right chiral states for these discrete equations can be described with the aid of some projectors on a space of discrete forms. The proposed discrete model admits a chiral symmetry. We construct discrete analogues of spin operators, describe spin eigenstates for a discrete Joyce equation, and also discuss chirality.Comment: 14 pages, conference pape

H.E.S.S. observations of PSR B1259-63 during its 2014 periastron passage

An extended observation campaign of the gamma-ray binary system PSR B1259$-$63 has been conducted with the H.E.S.S. (High Energy Stereoscopic System) II 5-telescope array during the system's periastron passage in 2014. We report on the outcome of this campaign, which consists of more than 85 h of data covering both pre- and post-periastron orbital phases. The lower energy threshold of the H.E.S.S. II array allows very-high-energy (VHE; $E \gtrsim 100$ GeV) gamma-ray emission from PSR B1259$-$63 to be studied for the first time down to 200 GeV. The new dataset partly overlaps with and extends in phase previous H.E.S.S. campaigns on this source in 2004, 2007 and 2011, allowing for a detailed long-term characterisation of the flux level at VHEs. In addition, the 2014 campaign reported here includes VHE observations during the exact periastron time, $t_{\rm per}$, as well as data taken simultaneously to the gamma-ray flare detected with the Fermi-LAT. Our results will be discussed in a multiwavelength context, thanks to the dense broad-band monitoring campaign conducted on the system during this last periastron passage.Comment: 8 pages, 5 figures. In Proceedings of the 34th International Cosmic Ray Conference (ICRC2015), The Hague, The Netherland

Multi-wavelength observations of the binary system PSR B1259-63/LS 2883 around the 2010-2011 periastron passage

We report on broad multi-wavelength observations of the 2010-2011 periastron passage of the gamma-ray loud binary system PSR B1259-63. High resolution interferometric radio observations establish extended radio emission trailing the position of the pulsar. Observations with the Fermi Gamma-ray Space Telescope reveal GeV gamma-ray flaring activity of the system, reaching the spin-down luminosity of the pulsar, around 30 days after periastron. There are no clear signatures of variability at radio, X-ray and TeV energies at the time of the GeV flare. Variability around periastron in the H$\alpha$ emission line, can be interpreted as the gravitational interaction between the pulsar and the circumstellar disk. The equivalent width of the H$\alpha$ grows from a few days before periastron until a few days later, and decreases again between 18 and 46 days after periastron. In near infrared we observe the similar decrease of the equivalent width of Br$\gamma$ line between the 40th and 117th day after the periastron. For the idealized disk, the variability of the H$\alpha$ line represents the variability of the mass and size of the disk. We discuss possible physical relations between the state of the disk and GeV emission under assumption that GeV flare is directly related to the decrease of the disk size.Comment: accepted to MNRA

Essential self-adjointness of magnetic Schr\"odinger operators on locally finite graphs

We give sufficient conditions for essential self-adjointness of magnetic Schr\"odinger operators on locally finite graphs. Two of the main theorems of the present paper generalize recent results of Torki-Hamza.Comment: 14 pages; The present version differs from the original version as follows: the ordering of presentation has been modified in several places, more details have been provided in several places, some notations have been changed, two examples have been added, and several new references have been inserted. The final version of this preprint will appear in Integral Equations and Operator Theor

Evidence for proton acceleration up to TeV energies based on VERITAS and Fermi-LAT observations of the Cas A SNR

We present a study of $\gamma$-ray emission from the core-collapse supernova remnant Cas~A in the energy range from 0.1GeV to 10TeV. We used 65 hours of VERITAS data to cover 200 GeV - 10 TeV, and 10.8 years of \textit{Fermi}-LAT data to cover 0.1-500 GeV. The spectral analysis of \textit{Fermi}-LAT data shows a significant spectral curvature around $1.3 \pm 0.4_{stat}$ GeV that is consistent with the expected spectrum from pion decay. Above this energy, the joint spectrum from \textit{Fermi}-LAT and VERITAS deviates significantly from a simple power-law, and is best described by a power-law with spectral index of $2.17\pm 0.02_{stat}$ with a cut-off energy of $2.3 \pm 0.5_{stat}$ TeV. These results, along with radio, X-ray and $\gamma$-ray data, are interpreted in the context of leptonic and hadronic models. Assuming a one-zone model, we exclude a purely leptonic scenario and conclude that proton acceleration up to at least 6 TeV is required to explain the observed $\gamma$-ray spectrum. From modeling of the entire multi-wavelength spectrum, a minimum magnetic field inside the remnant of $B_{\mathrm{min}}\approx150\,\mathrm{\mu G}$ is deduced.Comment: 33 pages, 9 Figures, 6 Table

Measurement of Cosmic-ray Electrons at TeV Energies by VERITAS

Cosmic-ray electrons and positrons (CREs) at GeV-TeV energies are a unique probe of our local Galactic neighborhood. CREs lose energy rapidly via synchrotron radiation and inverse-Compton scattering processes while propagating within the Galaxy and these losses limit their propagation distance. For electrons with TeV energies, the limit is on the order of a kiloparsec. Within that distance there are only a few known astrophysical objects capable of accelerating electrons to such high energies. It is also possible that the CREs are the products of the annihilation or decay of heavy dark matter (DM) particles. VERITAS, an array of imaging air Cherenkov telescopes in southern Arizona, USA, is primarily utilized for gamma-ray astronomy, but also simultaneously collects CREs during all observations. We describe our methods of identifying CREs in VERITAS data and present an energy spectrum, extending from 300 GeV to 5 TeV, obtained from approximately 300 hours of observations. A single power-law fit is ruled out in VERITAS data. We find that the spectrum of CREs is consistent with a broken power law, with a break energy at 710 $\pm$ 40$_{stat}$ $\pm$ 140$_{syst}$ GeV.Comment: 17 pages, 2 figures, accepted for publication in PR

Detailed spectral and morphological analysis of the shell type SNR RCW 86

Aims: We aim for an understanding of the morphological and spectral properties of the supernova remnant RCW~86 and for insights into the production mechanism leading to the RCW~86 very high-energy gamma-ray emission. Methods: We analyzed High Energy Spectroscopic System data that had increased sensitivity compared to the observations presented in the RCW~86 H.E.S.S. discovery publication. Studies of the morphological correlation between the 0.5-1~keV X-ray band, the 2-5~keV X-ray band, radio, and gamma-ray emissions have been performed as well as broadband modeling of the spectral energy distribution with two different emission models. Results:We present the first conclusive evidence that the TeV gamma-ray emission region is shell-like based on our morphological studies. The comparison with 2-5~keV X-ray data reveals a correlation with the 0.4-50~TeV gamma-ray emission.The spectrum of RCW~86 is best described by a power law with an exponential cutoff at $E_{cut}=(3.5\pm 1.2_{stat})$ TeV and a spectral index of $\Gamma$~$1.6\pm 0.2$. A static leptonic one-zone model adequately describes the measured spectral energy distribution of RCW~86, with the resultant total kinetic energy of the electrons above 1 GeV being equivalent to $\sim$0.1\% of the initial kinetic energy of a Type I a supernova explosion. When using a hadronic model, a magnetic field of $B$~100$\mu$G is needed to represent the measured data. Although this is comparable to formerly published estimates, a standard E$^{-2}$ spectrum for the proton distribution cannot describe the gamma-ray data. Instead, a spectral index of $\Gamma_p$~1.7 would be required, which implies that ~$7\times 10^{49}/n_{cm^{-3}}$erg has been transferred into high-energy protons with the effective density $n_{cm^{-3}}=n/ 1$ cm^-3. This is about 10\% of the kinetic energy of a typical Type Ia supernova under the assumption of a density of 1~cm^-3.Comment: accepted for publication by A&

The exceptionally powerful TeV gamma-ray emitters in the Large Magellanic Cloud

The Large Magellanic Cloud, a satellite galaxy of the Milky Way, has been observed with the High Energy Stereoscopic System (H.E.S.S.) above an energy of 100 billion electron volts for a deep exposure of 210 hours. Three sources of different types were detected: the pulsar wind nebula of the most energetic pulsar known N 157B, the radio-loud supernova remnant N 132D and the largest non-thermal X-ray shell - the superbubble 30 Dor C. The unique object SN 1987A is, surprisingly, not detected, which constrains the theoretical framework of particle acceleration in very young supernova remnants. These detections reveal the most energetic tip of a gamma-ray source population in an external galaxy, and provide via 30 Dor C the unambiguous detection of gamma-ray emission from a superbubble.Comment: Published in Science Magazine (Jan. 23, 2015). This ArXiv version has the supplementary online material incorporated as an appendix to the main pape

Characterizing the gamma-ray long-term variability of PKS 2155-304 with H.E.S.S. and Fermi-LAT

Studying the temporal variability of BL Lac objects at the highest energies provides unique insights into the extreme physical processes occurring in relativistic jets and in the vicinity of super-massive black holes. To this end, the long-term variability of the BL Lac object PKS 2155-304 is analyzed in the high (HE, 100 MeV 200 GeV) gamma-ray domain. Over the course of ~9 yr of H.E.S.S observations the VHE light curve in the quiescent state is consistent with a log-normal behavior. The VHE variability in this state is well described by flicker noise (power-spectral-density index {\ss}_VHE = 1.10 +0.10 -0.13) on time scales larger than one day. An analysis of 5.5 yr of HE Fermi LAT data gives consistent results ({\ss}_HE = 1.20 +0.21 -0.23, on time scales larger than 10 days) compatible with the VHE findings. The HE and VHE power spectral densities show a scale invariance across the probed time ranges. A direct linear correlation between the VHE and HE fluxes could neither be excluded nor firmly established. These long-term-variability properties are discussed and compared to the red noise behavior ({\ss} ~ 2) seen on shorter time scales during VHE-flaring states. The difference in power spectral noise behavior at VHE energies during quiescent and flaring states provides evidence that these states are influenced by different physical processes, while the compatibility of the HE and VHE long-term results is suggestive of a common physical link as it might be introduced by an underlying jet-disk connection.Comment: 11 pages, 16 figure