Energy Spectrum of Cosmic-Ray Electrons at TeV Energies

The very large collection area of ground-based $\gamma$-ray telescopes gives them a substantial advantage over balloon or satellite based instruments in the detection of very-high-energy ($>600\mathrm{GeV}$) cosmic-ray electrons. Here we present the electron spectrum derived from data taken with the High Energy Stereoscopic System (H.E.S.S.) of imaging atmospheric Cherenkov telescopes. In this measurement, the first of this type, we are able to extend the measurement of the electron spectrum beyond the range accessible to direct measurements. We find evidence for a substantial steepening in the energy spectrum above 600 GeV compared to lower energies.

Figure 1

The measured distribution of the parameter $\zeta$, compared with distributions for simulated protons and electrons, for showers with reconstructed energy between 1 and 4 TeV. The best fit model combination of electrons and protons is shown as a shaded band. The proton simulations use the SIBYLL hadronic interaction event generator. The left inset shows the complete distribution from zero to one with entries on a log scale; the data are shown as points, the filled histogram shows a mixed composition (proton, He, N, Si & Fe) cosmic-ray model. To demonstrate the match between simulation and data in electromagnetic showers, the right inset shows background subtracted $\gamma$-ray data as points and $\gamma$-ray simulations as filled histogram.

Figure 2

The distribution of reconstructed shower maximum ($X_{\max }$) for H.E.S.S. data, compared to simulations. For each shower the measured $X_{\max }$ is corrected for the energy-dependent shower elongation ($93\mathrm{g}{\mathrm{cm}}^{-2}/\mathrm{\text{decade}}$ is the reconstructed elongation rate expected for electron primaries). Showers with reconstructed energies between 1 and 4 TeV are included. The bands show the combination of electrons and protons (simulated using SIBYLL) and of $\gamma$ rays and protons, with a ratio determined by a fit to the $\zeta$ distribution of the data in this energy range. The distributions of electrons and $\gamma$ rays are shown for comparison. The inset contains a comparison of this data (black) with a $\gamma$-ray rich data set taken from regions $<0.15°$ from $\gamma$-ray sources (gray).

Figure 3

The energy spectrum $E^3$ $\mathrm{dN}/\mathrm{dE}$ of CR electrons as measured by H.E.S.S. in comparison with previous measurements. The H.E.S.S. data are shown as solid points. The two fit functions ($A$ and $B$) are described in the main text. The shaded band indicates the approximate systematic error arising from uncertainties in the modeling of hadronic interactions and in the atmospheric model. The double arrow indicates the effect of an energy scale shift of 15%, the approximate systematic uncertainty on the H.E.S.S. points. Previous data are reproduced from AMS [18], HEAT [19], HEAT 94-95 [20], BETS [21], PPB-BETS [22], Kobayashi [2], and ATIC [23].