5. Flux and spectral index
The stereoscopic HEGRA IACT system with its energy resolution of about 20% allows detailed studies of the spectrum of -ray sources. To derive the flux , the rate at a given reconstructed energy E is divided by the selection efficiency and the (energy-dependent) effective detection area. Only events where at least three telescopes triggered are used, to guarantee good stereoscopic reconstruction. Events are counted within a radius of from the source, and the background determined from the average yield of events around a virtual source on the opposite side of the camera is subtracted. To avoid significant Monte-Carlo based corrections, the loose shape cuts were used, with a -ray efficiency above 90%. A similarly conservative approach is followed for the effective detection area. We impose an energy-dependent limit on the maximum distance between the shower core and the central telescope, such that the trigger probability according to simulations is at least 80%, and also require at least one active telescope within 140 m from the core. Between 1 TeV and 4 TeV, rises from about 100 m to 200 m. After this selection, the effective area is determined by simple geometry, up to a small correction. Below about 0.8 TeV, trigger probabilities do not safely saturate and data are not used. In the determination of spectra, only runs with zenith angles below were included, with a median zenith angle of .
The resulting differential energy spectrum of Mkn 501 is shown for energies up to 10 TeV in Fig. 4, together with the spectrum of the Crab Nebula analyzed in the identical fashion, based on 9.7 h of earlier observations at small zenith angles. The width of the energy bins corresponds roughly to the rms energy resolution of about 20%. Both spectra are compatible with pure power laws, with a differential spectral index of (stat. error only) in case of the Crab Nebula, and for Mkn 501; the integral fluxes above 1 TeV are /cm2 s (stat. error only) and /cm2 s, respectively. We note that this procedure has also been applied on a night by night basis and that the shape of the spectrum does not change within the statistical errors of about 0.2. Also it is found that the spectrum of Mkn 501 shows no indication for a cutoff in the energy range from 1 TeV to 10 TeV.
To estimate the systematic errors on the flux and the spectral slopes, the cuts and reconstruction procedures were varied over a wide range. E.g., the width cut was omitted entirely, or the angular cut increased to , or the maximum core radius was limited to 100 m. Different weights and radial dependencies were used in the energy determination. The fit range was varied. From these studies, we estimate a systematic error of % in the flux and in the spectral slope. An additional error of 36% on the flux arises from the 20% uncertainty in the absolute energy calibration, increasing the total systematic error on the flux to 45%. It is likely that these errors can be reduced as our experience in the analysis of IACT system data increases. In the comparison of the characteristics of -ray emission from the Crab Nebula and from Mkn 501, the systematic errors should cancel to a large extent.
We note, that within the statistical and systematic errors, the measurements of the -ray flux from the Crab Nebula are consistent with earlier HEGRA measurements using the single telescopes CT1 and CT2 (Konopelko et al. 1996, Petry et al. 1996, Bradbury et al. 1997).
© European Southern Observatory (ESO) 1997
Online publication: April 6, 1998