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N. Chakraborty

Publications and source records attributed to N. Chakraborty.

At least 19 recordsLinked to original sources

Ramsey interferometry of non-Hermitian quantum impurities

We introduce a Ramsey pulse scheme which extracts the non-Hermitian Hamiltonian associated to an arbitrary Lindblad dynamics. We propose a realted protocol to measure via interferometry a generalised Loschmidt echo of a generic state evolving in time with the non-Hermitian Hamiltonian itself, and we apply the scheme to a one-dimensional weakly interacting Bose gas coupled to a stochastic atomic impurity. The Loschmidt echo is mapped into a functional integral from which we calculate the long-time decohering dynamics at arbitrary impurity strengths. For strong dissipation we uncover the phenomenology of a quantum many-body Zeno effect: corrections to the decoherence exponent resulting from the impurity self-energy becomes purely imaginary, in contrast to the regime of small dissipation where they instead enhance the decay of quantum coherences. Our results illustrate the prospects for experiments employing Ramsey interferometry to study dissipative quantum impurities in condensed matter and cold atoms systems.

cond-mat.quant-gas

Resolving the Crab pulsar wind nebula at teraelectronvolt energies

The Crab nebula is one of the most studied cosmic particle accelerators, shining brightly across the entire electromagnetic spectrum up to very high-energy gamma rays. It is known from radio to gamma-ray observations that the nebula is powered by a pulsar, which converts most of its rotational energy losses into a highly relativistic outflow. This outflow powers a pulsar wind nebula (PWN), a region of up to 10~light-years across, filled with relativistic electrons and positrons. These particles emit synchrotron photons in the ambient magnetic field and produce very high-energy gamma rays by Compton up-scattering of ambient low-energy photons. While the synchrotron morphology of the nebula is well established, it was up to now not known in which region the very high-energy gamma rays are emitted. Here we report that the Crab nebula has an angular extension at gamma-ray energies of 52 arcseconds (assuming a Gaussian source width), significantly larger than at X-ray energies. This result closes a gap in the multi-wavelength coverage of the nebula, revealing the emission region of the highest energy gamma rays. These gamma rays are a new probe of a previously inaccessible electron and positron energy range. We find that simulations of the electromagnetic emission reproduce our new measurement, providing a non-trivial test of our understanding of particle acceleration in the Crab nebula.

astro-ph.HE

Upper Limits on Very-High-Energy Gamma-ray Emission from Core-Collapse Supernovae Observed with H.E.S.S

Young core-collapse supernovae with dense-wind progenitors may be able to accelerate cosmic-ray hadrons beyond the knee of the cosmic-ray spectrum, and this may result in measurable gamma-ray emission. We searched for gamma-ray emission from ten supernovae observed with the High Energy Stereoscopic System (H.E.S.S.) within a year of the supernova event. Nine supernovae were observed serendipitously in the H.E.S.S. data collected between December 2003 and December 2014, with exposure times ranging from 1.4 hours to 53 hours. In addition we observed SN 2016adj as a target of opportunity in February 2016 for 13 hours. No significant gamma-ray emission has been detected for any of the objects, and upper limits on the $>1$ TeV gamma-ray flux of the order of $\sim$10$^{-13}$ cm$^{-2}$s$^{-1}$ are established, corresponding to upper limits on the luminosities in the range $\sim$2 $\times$ 10$^{39}$ erg s$^{-1}$ to $\sim$1 $\times$ 10$^{42}$ erg s$^{-1}$. These values are used to place model-dependent constraints on the mass-loss rates of the progenitor stars, implying upper limits between $\sim$2 $\times 10^{-5}$ and $\sim$2 $\times 10^{-3}$M$_{\odot}$yr$^{-1}$ under reasonable assumptions on the particle acceleration parameters.

astro-ph.HE

H.E.S.S. observations of the flaring gravitationally lensed galaxy PKS 1830-211

PKS 1830-211 is a known macrolensed quasar located at a redshift of z=2.5. Its high-energy gamma-ray emission has been detected with the Fermi-LAT instrument and evidence for lensing was obtained by several authors from its high-energy data. Observations of PKS 1830-211 were taken with the H.E.S.S. array of Imaging Atmospheric Cherenkov Telescopes in August 2014, following a flare alert by the Fermi- LAT collaboration. The H.E.S.S observations were aimed at detecting a gamma-ray flare delayed by 20-27 days from the alert flare, as expected from observations at other wavelengths. More than twelve hours of good quality data were taken with an analysis threshold of $\sim67$ GeV. The significance of a potential signal is computed as a function of the date as well as the average significance over the whole period. Data are compared to simultaneous observations by Fermi-LAT. No photon excess or significant signal is detected. An upper limit on PKS 1830-211 flux above 67 GeV is computed and compared to the extrapolation of the Fermi-LAT flare spectrum.

astro-ph.HE

Gauge phonon dominated resistivity in twisted bilayer graphene near magic angle

Recent experiments on twisted bilayer graphene (tBG) close to magic angle show that a small relative rotation in a van der Waals heterostructure greatly alters its electronic properties. We consider various scattering mechanisms and show that the carrier transport in tBG is dominated by a combination of charged impurities and acoustic gauge phonons. Charged impurities still dominate at low temperature and densities because of the inability of Dirac fermions to screen long-range Coulomb potentials at charge neutrality; however, the gauge phonons dominate for most of the experimental regime because although they couple to current, they do not induce charge and are therefore unscreened by the large density of states close to magic angle. We show that the resistivity has a strong monotonically decreasing carrier density dependence at low temperature due to charged impurity scattering, and weak density dependence at high temperature due to gauge phonons. Away from charge neutrality, the resistivity increases with temperature, while it does the opposite close to the Dirac point. A non-monotonic temperature dependence observed only at low temperature and carrier density is a signature of our theory that can be tested in experimentally available samples.

cond-mat.mes-hall

Evaluating Quasi-Periodic Variations in the $γ$-ray Lightcurves of Fermi-LAT Blazars

The detection of periodicities in light curves of active galacticnuclei (AGN) could have profound consequences for our understanding of the nature and radiation physics of these objects. At high energies (HE; E>100 MeV) 5 blazars (PG 1553+113,PKS 2155-304, 0426-380, 0537-441, 0301-243) have been reported to show year-like quasi-periodic variations (QPVs) with significance >3 sig. As these findings are based on few cycles only, care needs to be taken to properly account for random variations which can produce intervals of seemingly periodic behaviour. We present results of an updated timing analysis for 6 blazars (adding PKS 0447-439), utilizing suitable methods to evaluate their long term variability properties and to search for QPVs in their light curves. We generate gamma-ray light curves covering almost 10 years, study their timing properties and search for QPVs using the Lomb-Scargle Periodogram and the Wavelet Z-transform. Extended Monte Carlo simulations are used to evaluate the statistical significance. Comparing their probability density functions (PDFs), all sources (except PG 1553+113) exhibit a clear deviation from a Gaussian distribution, but are consistent with being log-normal, suggesting that the underlying variability is of a non-linear, multiplicative nature. Apart from PKS 0301-243 the power spectral density for all investigated blazars is close to flicker noise (PL slope -1). Possible QPVs with a local significance ~ 3 sig. are found in all light curves (apart from PKS 0426-380 and 0537-441), with observed periods between (1.7-2.8) yr. The evidence is strongly reduced, however, if evaluated in terms of a global significance. Our results advise caution as to the significance of reported year-like HE QPVs in blazars. Somewhat surprisingly, the putative, redshift-corrected periods are all clustering around 1.6 yr. We speculate on possible implications for QPV generation.

astro-ph.HE

The 2014 TeV Gamma-ray Flare of Mrk 501 Seen with H.E.S.S.: Temporal and Spectral Constraints on Lorentz Invariance Violation

The blazar Mrk 501 (z=0.034) was observed at very-high-energy (VHE, $E\gtrsim 100$~GeV) gamma-ray wavelengths during a bright flare on the night of 2014 June 23-24 (MJD 56832) with the H.E.S.S. phase-II array of Cherenkov telescopes. Data taken that night by H.E.S.S. at large zenith angle reveal an exceptional number of gamma-ray photons at multi-TeV energies, with rapid flux variability and an energy coverage extending significantly up to 20 TeV. This data set is used to constrain Lorentz invariance violation (LIV) using two independent channels: a temporal approach considers the possibility of an energy dependence in the arrival time of gamma rays, whereas a spectral approach considers the possibility of modifications to the interaction of VHE gamma rays with extragalactic background light (EBL) photons. The non-detection of energy-dependent time delays and the non-observation of deviations between the measured spectrum and that of a supposed power-law intrinsic spectrum with standard EBL attenuation are used independently to derive strong constraints on the energy scale of LIV ($E_{\rm{QG}}$) in the subluminal scenario for linear and quadratic perturbations in the dispersion relation of photons. For the case of linear perturbations, the 95% confidence level limits obtained are $E_{\rm{QG},1} > 3.6 \times 10^{17} \ \rm{GeV} $ using the temporal approach and $E_{\rm{QG},1} > 2.6 \times 10^{19} \ \rm{GeV}$ using the spectral approach. For the case of quadratic perturbations, the limits obtained are $E_{\rm{QG},2} > 8.5 \times 10^{10} \ \rm{GeV} $ using the temporal approach and $E_{\rm{QG},2} > 7.8 \times 10^{11} \rm{ GeV}$ using the spectral approach.

astro-ph.HE

Particle Transport within the Pulsar Wind Nebula HESS J1825-137

Aims: We present a detailed view of the pulsar wind nebula (PWN) HESS J1825-137. We aim to constrain the mechanisms dominating the particle transport within the nebula, accounting for its anomalously large size and spectral characteristics. Methods: The nebula is studied using a deep exposure from over 12 years of H.E.S.S. I operation, together with data from H.E.S.S. II improving the low energy sensitivity. Enhanced energy-dependent morphological and spatially-resolved spectral analyses probe the Very High Energy (VHE, E > 0.1 TeV) gamma-ray properties of the nebula. Results: The nebula emission is revealed to extend out to 1.5 degrees from the pulsar, ~1.5 times further than previously seen, making HESS J1825--137, with an intrinsic diameter of ~100 pc, potentially the largest gamma-ray PWN currently known. Characterisation of the nebula's strongly energy-dependent morphology enables the particle transport mechanisms to be constrained. A dependence of the nebula extent with energy of R $\propto$ E^αwith α= -0.29 +/- 0.04 (stat) +/- 0.05 (sys) disfavours a pure diffusion scenario for particle transport within the nebula. The total gamma-ray flux of the nebula above 1~TeV is found to be (1.12 +/- 0.03 (stat) +/- 0.25 (sys)) $\times 10^{-11}$ cm$^{-2}$ s$^{-1}$, corresponding to ~64% of the flux of the Crab Nebula. Conclusions: HESS J1825-137 is a PWN with clear energy-dependent morphology at VHE gamma-ray energies. This source is used as a laboratory to investigate particle transport within middle-aged PWNe. Deep observations of this highly spatially-extended PWN enable a spectral map of the region to be produced, providing insights into the spectral variation within the nebula.

astro-ph.HE

VHE $γ$-ray discovery and multi-wavelength study of the blazar 1ES 2322-409

A hotspot at a position compatible with the BL Lac object 1ES 2322-409 was serendipitously detected with H.E.S.S. during observations performed in 2004 and 2006 on the blazar PKS 2316-423. Additional data on 1ES 2322-409 were taken in 2011 and 2012, leading to a total live-time of 22.3h. Point-like very-high-energy (VHE; E>100GeV) $γ$-ray emission is detected from a source centred on the 1ES 2322-409 position, with an excess of 116.7 events at a significance of 6.0$σ$. The average VHE $γ$-ray spectrum is well described with a power law with a photon index $Γ=3.40\pm0.66_{\text{stat}}\pm0.20_{\text{sys}}$ and an integral flux $Φ(E>200GeV) = (3.11\pm0.71_{\rm stat}\pm0.62_{\rm sys})\times10^{-12} cm^{-2} s^{-1}$, which corresponds to 1.1$\%$ of the Crab nebula flux above 200 GeV. Multi-wavelength data obtained with Fermi LAT, Swift XRT and UVOT, RXTE PCA, ATOM, and additional data from WISE, GROND and Catalina, are also used to characterise the broad-band non-thermal emission of 1ES 2322-409. The multi-wavelength behaviour indicates day-scale variability. Swift UVOT and XRT data show strong variability at longer scales. A spectral energy distribution (SED) is built from contemporaneous observations obtained around a high state identified in Swift data. A modelling of the SED is performed with a stationary homogeneous one-zone synchrotron-self-Compton (SSC) leptonic model. The redshift of the source being unknown, two plausible values were tested for the modelling. A systematic scan of the model parameters space is performed, resulting in a well-constrained combination of values providing a good description of the broad-band behaviour of 1ES 2322-409.

astro-ph.HE

Searches for gamma-ray lines and `pure WIMP' spectra from Dark Matter annihilations in dwarf galaxies with H.E.S.S

Dwarf spheroidal galaxies are among the most promising targets for detecting signals of Dark Matter (DM) annihilations. The H.E.S.S. experiment has observed five of these systems for a total of about 130 hours. The data are re-analyzed here, and, in the absence of any detected signals, are interpreted in terms of limits on the DM annihilation cross section. Two scenarios are considered: i) DM annihilation into mono-energetic gamma-rays and ii) DM in the form of pure WIMP multiplets that, annihilating into all electroweak bosons, produce a distinctive gamma-ray spectral shape with a high-energy peak at the DM mass and a lower-energy continuum. For case i), upper limits at 95\% confidence level of about $\langle σv \rangle \lesssim 3 \times 10^{-25}$ cm$^3$ s$^{-1}$ are obtained in the mass range of 400 GeV to 1 TeV. For case ii), the full spectral shape of the models is used and several excluded regions are identified, but the thermal masses of the candidates are not robustly ruled out.

astro-ph.HE

First Ground-based Measurement of Sub-20 GeV to 100 GeV $γ$-rays from the Vela Pulsar with H.E.S.S. II

We report on the measurement and investigation of pulsed high-energy $γ$-ray emission from the Vela pulsar, PSR B0833$-$45, based on 40.3 hours of observations with the largest telescope of H.E.S.S., CT5, in monoscopic mode, and on 8 years of data obtained with the Fermi-LAT. A dedicated very-low-threshold event reconstruction and analysis pipeline was developed and, together with the CT5 telescope response model, was validated using the Fermi-LAT data as reference. A pulsed $γ$-ray signal at a significance level of more than $15σ$ is detected from the P2 peak of the Vela pulsar light curve. Of a total of 15835 events, more than 6000 lie at an energy below 20 GeV, implying a significant overlap between H.E.S.S. II-CT5 and the Fermi-LAT. While the investigation of the pulsar light curve with the LAT confirms characteristics previously known up to 20 GeV, in the tens of GeV energy range, CT5 data show a change in the pulse morphology of P2, i.e., an extreme sharpening of its trailing edge, together with the possible onset of a new component at 3.4$σ$ significance level. Assuming a power-law model for the P2 spectrum, an excellent agreement is found for the photon indices ($Γ\simeq$ 4.1) obtained with the two telescopes above 10 GeV and an upper bound of 8% is derived on the relative offset between their energy scales. Using both instruments data, it is however shown that the spectrum of P2 in the 10-100 GeV has a pronounced curvature, i.e. a confirmation of the sub-exponential cutoff form found at lower energies with the LAT. This is further supported by the weak evidence for an emission above 100 GeV obtained with CT5. In contrast, converging indications are found from both CT5 and LAT data for the emergence of a hard component above 50 GeV in the leading wing (LW2) of P2, which possibly extends beyond 100 GeV.

astro-ph.HE

The $γ$-ray spectrum of the core of Centaurus A as observed with H.E.S.S. and Fermi-LAT

Centaurus A (Cen A) is the nearest radio galaxy discovered as a very-high-energy (VHE; 100 GeV-100 TeV) $γ$-ray source by the High Energy Stereoscopic System (H.E.S.S.). It is a faint VHE $γ$-ray emitter, though its VHE flux exceeds both the extrapolation from early Fermi-LAT observations as well as expectations from a (misaligned) single-zone synchrotron-self Compton (SSC) description. The latter satisfactorily reproduces the emission from Cen A at lower energies up to a few GeV. New observations with H.E.S.S., comparable in exposure time to those previously reported, were performed and eight years of Fermi-LAT data were accumulated to clarify the spectral characteristics of the $γ$-ray emission from the core of Cen A. The results allow us for the first time to achieve the goal of constructing a representative, contemporaneous $γ$-ray core spectrum of Cen A over almost five orders of magnitude in energy. Advanced analysis methods, including the template fitting method, allow detection in the VHE range of the core with a statistical significance of 12$σ$ on the basis of 213 hours of total exposure time. The spectrum in the energy range of 250 GeV-6 TeV is compatible with a power-law function with a photon index $Γ=2.52\pm0.13_{\mathrm{stat}}\pm0.20_{\mathrm{sys}}$. An updated Fermi-LAT analysis provides evidence for spectral hardening by $ΔΓ\simeq0.4\pm0.1$ at $γ$-ray energies above $2.8^{+1.0}_{-0.6}$ GeV at a level of $4.0σ$. The fact that the spectrum hardens at GeV energies and extends into the VHE regime disfavour a single-zone SSC interpretation for the overall spectral energy distribution (SED) of the core and is suggestive of a new $γ$-ray emitting component connecting the high-energy emission above the break energy to the one observed at VHE energies.

astro-ph.HE

The starburst galaxy NGC 253 revisited by H.E.S.S. and Fermi-LAT

(Abridged) Context. NGC 253 is one of only two starburst galaxies found to emit $γ$-rays from hundreds of MeV to multi-TeV energies. Accurate measurements of the very-high-energy (VHE) (E $>$ 100 GeV) and high-energy (HE) (E $>$ 60 MeV) spectra are crucial to study the underlying particle accelerators and cosmic-ray interaction and transport. Aims. The measurement of the VHE $γ$-ray emission of NGC 253 published in 2012 by H.E.S.S. was limited by large systematic uncertainties. Here, a measurement of the $γ$-ray spectrum of NGC 253 is investigated in both HE and VHE $γ$-rays. Methods. The data of H.E.S.S. observations are reanalysed using an updated calibration and analysis chain. The $Fermi$-LAT analysis employs more than 8 years of data processed using pass 8. The cosmic-ray particle population is evaluated from the combined HE--VHE $γ$-ray spectrum using NAIMA. Results. The VHE $γ$-ray energy spectrum is best fit by a power-law with a flux normalisation of $(1.34\,\pm\,0.14^{\mathrm{stat}}\,\pm\,0.27^{\mathrm{sys}}) \times 10^{-13} \mathrm{cm^{-2} s^{-1} TeV^{-1}}$ at 1 TeV -- about 40 \% above, but compatible with the value obtained in Abramowski et al. (2012). The spectral index $Γ= 2.39 \pm 0.14^{\mathrm{stat}} \pm 0.25^{\mathrm{sys}}$ is slightly softer than but consistent with the previous measurement. At energies above $\sim$3 GeV the HE spectrum is consistent with a power-law ranging into the VHE part of the spectrum measured by H.E.S.S. Conclusions. Two scenarios for the starburst nucleus are tested, in which the gas in the starburst nucleus acts as a target for hadronic cosmic rays. In these two models, the level to which NGC\,253 acts as a calorimeter is estimated to a range of $f_{\rm cal} = 0.1$ to $1$ while accounting for the measurement uncertainties.

astro-ph.HE

Search for $γ$-ray line signals from dark matter annihilations in the inner Galactic halo from ten years of observations with H.E.S.S

Spectral lines are among the most powerful signatures for dark matter (DM) annihilation searches in very-high-energy $γ$-rays. The central region of the Milky Way halo is one of the most promising targets given its large amount of DM and proximity to Earth. We report on a search for a monoenergetic spectral line from self-annihilations of DM particles in the energy range from 300 GeV to 70 TeV using a two-dimensional maximum likelihood method taking advantage of both the spectral and spatial features of signal versus background. The analysis makes use of Galactic Center (GC) observations accumulated over ten years (2004 - 2014) with the H.E.S.S. array of ground-based Cherenkov telescopes. No significant $γ$-ray excess above the background is found. We derive upper limits on the annihilation cross section $\langleσv\rangle$ for monoenergetic DM lines at the level of $\sim4\times10^{-28}$ cm$^{3}$s$^{-1}$ at 1 TeV, assuming an Einasto DM profile for the Milky Way halo. For a DM mass of 1 TeV, they improve over the previous ones by a factor of six. The present constraints are the strongest obtained so far for DM particles in the mass range 300 GeV - 70 TeV. Ground-based $γ$-ray observations have reached sufficient sensitivity to explore relevant velocity-averaged cross sections for DM annihilation into two $γ$-ray photons at the level expected from the thermal relic density for TeV DM particles.

astro-ph.HE

A search for new supernova remnant shells in the Galactic plane with H.E.S.S

A search for new supernova remnants (SNRs) has been conducted using TeV gamma-ray data from the H.E.S.S. Galactic plane survey. As an identification criterion, shell morphologies that are characteristic for known resolved TeV SNRs have been used. Three new SNR candidates were identified in the H.E.S.S. data set with this method. Extensive multiwavelength searches for counterparts were conducted. A radio SNR candidate has been identified to be a counterpart to HESS J1534-571. The TeV source is therefore classified as a SNR. For the other two sources, HESS J1614-518 and HESS J1912+101, no identifying counterparts have been found, thus they remain SNR candidates for the time being. TeV-emitting SNRs are key objects in the context of identifying the accelerators of Galactic cosmic rays. The TeV emission of the relativistic particles in the new sources is examined in view of possible leptonic and hadronic emission scenarios, taking the current multiwavelength knowledge into account.

astro-ph.HE

Deeper H.E.S.S. observations of Vela Junior (RX J0852.0$-$4622): Morphology studies and resolved spectroscopy

Aims. We study gamma-ray emission from the shell-type supernova remnant (SNR) RX J0852.0$-$4622 to better characterize its spectral properties and its distribution over the SNR. Methods. The analysis of an extended High Energy Spectroscopic System (H.E.S.S.) data set at very high energies (E > 100 GeV) permits detailed studies, as well as spatially resolved spectroscopy, of the morphology and spectrum of the whole RX J0852.0$-$4622 region. The H.E.S.S. data are combined with archival data from other wavebands and interpreted in the framework of leptonic and hadronic models. The joint Fermi-LAT-H.E.S.S. spectrum allows the direct determination of the spectral characteristics of the parent particle population in leptonic and hadronic scenarios using only GeV-TeV data. Results. An updated analysis of the H.E.S.S. data shows that the spectrum of the entire SNR connects smoothly to the high-energy spectrum measured by Fermi-LAT. The increased data set makes it possible to demonstrate that the H.E.S.S. spectrum deviates significantly from a power law and is well described by both a curved power law and a power law with an exponential cutoff at an energy of $E_\mathrm{cut} = (6.7 \pm 1.2_\mathrm{stat} \pm 1.2_\mathrm{syst})$ TeV. The joint Fermi-LAT-H.E.S.S. spectrum allows the unambiguous identification of the spectral shape as a power law with an exponential cutoff. No significant evidence is found for a variation of the spectral parameters across the SNR, suggesting similar conditions of particle acceleration across the remnant. A simple modeling using one particle population to model the SNR emission demonstrates that both leptonic and hadronic emission scenarios remain plausible. It is also shown that at least a part of the shell emission is likely due to the presence of a pulsar wind nebula around PSR J0855$-$4644.

astro-ph.HE

H.E.S.S. discovery of very high energy gamma-ray emission from PKS 0625-354

PKS 0625-354 (z=0.055) was observed with the four H.E.S.S. telescopes in 2012 during 5.5 hours. The source was detected above an energy threshold of 200 GeV at a significance level of 6.1$σ$. No significant variability is found in these observations. The source is well described with a power-law spectrum with photon index $Γ =2.84 \pm 0.50_{stat} \pm 0.10_{syst}$ and normalization (at $E_0$=1.0 TeV) $N_0(E_0)=(0.58 \pm 0.22_{stat} \pm 0.12_{syst})\times10^{-12}$ TeV$^{-1}$cm$^{-2}$s$^{-1}$. Multi-wavelength data collected with Fermi-LAT, Swift-XRT, Swift-UVOT, ATOM and WISE are also analysed. Significant variability is observed only in the Fermi-LAT $γ$-ray and Swift-XRT X-ray energy bands. Having a good multi-wavelength coverage from radio to very high energy, we performed a broadband modelling from two types of emission scenarios. The results from a one zone lepto-hadronic, and a multi-zone leptonic models are compared and discussed. On the grounds of energetics, our analysis favours a leptonic multi-zone model. Models associated to the X-ray variability constraint supports previous results suggesting a BL Lac nature of PKS 0625-354, with, however, a large-scale jet structure typical of a radio galaxy.

astro-ph.HE

Population study of Galactic supernova remnants at very high $γ$-ray energies with H.E.S.S.

Shell-type supernova remnants (SNRs) are considered prime candidates for the acceleration of Galactic cosmic rays (CRs) up to the knee of the CR spectrum at $\mathrm{E} \approx \mathrm{3}\times \mathrm{10}^\mathrm{15}$ eV. Our Milky Way galaxy hosts more than 350 SNRs discovered at radio wavelengths and at high energies, of which 220 fall into the H.E.S.S. Galactic Plane Survey (HGPS) region. Of those, only 50 SNRs are coincident with a H.E.S.S source and in 8 cases the very high-energy (VHE) emission is firmly identified as an SNR. The H.E.S.S. GPS provides us with a legacy for SNR population study in VHE $γ$-rays and we use this rich data set to extract VHE flux upper limits from all undetected SNRs. Overall, the derived flux upper limits are not in contradiction with the canonical CR paradigm. Assuming this paradigm holds true, we can constrain typical ambient density values around shell-type SNRs to $n\leq 7~\textrm{cm}^\textrm{-3}$ and electron-to-proton energy fractions above 10~TeV to $ε_\textrm{ep} \leq 5\times 10^{-3}$. Furthermore, comparisons of VHE with radio luminosities in non-interacting SNRs reveal a behaviour that is in agreement with the theory of magnetic field amplification at shell-type SNRs.

astro-ph.HE