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Astron. Astrophys. 349, 11-28 (1999)

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5. Experimental results

In this section we first present the 1997 Mkn 501 time averaged energy spectrum. As discussed already in the introduction the derivation of a time averaged spectrum is meaningful since the changes in the spectral shape during the HEGRA observations were rather small, i.e. they were too small to be assessed with an accuracy of typically between 0.1 and 0.3 in the diurnal spectral indices. Moreover, as described in Paper 1, dividing the data into groups according to the absolute flux level or according to the rising or falling behavior of the source activity yielded mean spectra which did not differ significantly from each other in the one to ten TeV energy range. The weakness of the correlation between the absolute flux and the spectral shape will further be substantiated below over the energy region from 500 GeV to 15 TeV. Nevertheless, the importance of the spectral constancy should not be overestimated. If the spectral variability is not tightly correlated with the absolute flux, diurnal spectral variability characterized by a change of the spectral index at several TeV by approximately [FORMULA]0.1 is surely consistent with the HEGRA data. The time-averaged energy spectrum is shown in Fig. 9. For the determination of the spectrum also at energies below 800 GeV, only the data from zenith angles smaller 30o have been used (80 h observation time). The measurements extend from 500 GeV to 24 TeV. The hatched region in Fig. 9 ff. gives our estimate of the systematic errors on the shape of the spectrum, except the 15% uncertainty on the absolute energy scale. The spectrum shows a gradual steepening over the entire energy range. A fit of the data from 500 GeV to 24 TeV with a power law model with an exponential cut off gives:


[FORMULA], [FORMULA], and [FORMULA] TeV. The systematic errors on the fit parameters result from worst case assumptions concerning the systematic errors of the data points, and their correlations and include the error caused by the 15% uncertainty in the energy scale. The errors on the fit parameters, especially on [FORMULA] and [FORMULA], are strongly correlated. The variation of only one of the parameters within the quoted error range yields spectra which are inconsistent with the measured spectrum. The data points and their errors are summarized in Table 1.

[FIGURE] Fig. 9. Time-averaged energy spectrum of Mkn 501 for the 1997 observation period. Vertical errors bars indicate statistical errors. The hatched area gives the estimated systematic errors, except the 15% uncertainty on the absolute energy scale. The lines shows the fit discussed in the text.


Table 1. The time-averaged differential spectrum of Mkn 501.
a) energy in TeV
b) in (cm-2 s-1 TeV-1)
c) statistical error in (cm-2 s-1 TeV-1)
d) systematic error on the shape of the spectrum in (cm-2 s-1 TeV-1) e) upper limits in (cm-2 s-1 TeV-1) at 2 [FORMULA] confidence level

In the highest energy bin (19 TeV to 24 TeV) 40 excess events are found above a background of 13 events, corresponding to a nominal significance of S = ([FORMULA] - [FORMULA]) / [FORMULA] of 3.7 [FORMULA]. However, due to the steep spectrum in this energy range, a part of these events may represent a spill-over from lower energies. To provide an absolutely reliable lower limit on the highest energies in the sample, the spectrum was fit to the form of Eq. 6, but with a sharp cutoff at [FORMULA]: [FORMULA] [FORMULA] [FORMULA] [FORMULA]. The best fit is achieved with [FORMULA] TeV; the [FORMULA] lower limit is [FORMULA] TeV.

Fig. 10 illustrates the spectral energy distribution, [FORMULA] as determined from the small zenith angle data ([FORMULA]30o, energy threshold 500 GeV) and the large zenith angle data (30o to 45o, 32 h observation time, energy threshold 1 TeV). Note that the large zenith angle data has mainly been acquired during the second half of the 1997 data taking period. Nevertheless the shape of both spectra agrees within the statistical and systematic errors. The combined small and large zenith angle data set yields the same lower limit on [FORMULA] of 16 TeV as derived from the small zenith angle data alone. It can be recognized that the spectral energy distribution is essentially flat from 500 GeV up to [FORMULA] 2 TeV.

[FIGURE] Fig. 10. The spectral energy distribution [FORMULA], for the data set of low zenith angles ([FORMULA], full circles) and for the data set of large zenith angles ([FORMULA] between [FORMULA] and 45o, 32 h observation time, open symbols). Since the observation periods do not overlap for the variable source, the spectra are normalized at the energy 2 TeV. The hatched band indicates the systematic error on the shape of the spectrum for the low zenith angle data. The systematic error on the high zenith angle spectrum at energy E approximately equals the systematic error on the low zenith angle spectrum at energy E/2.

Fig. 11 (upper panel) shows the spectral energy distribution for the overall data sample and for periods of high and low flux separately: dN/dE(2 TeV) determined on diurnal basis above 3 and below 1.6 [FORMULA], with a ratio of the mean fluxes close to 5. The high and low flux spectra agree within statistical errors, as shown by the ratio of both spectra, presented in Fig. 11 (lower panel). The systematic error is to good approximation the same for both data samples and cancels out in the ratio. The result thus confirms our previous conclusion about the flux-independence of the spectrum of Mkn 501 in 1997 between 1 and 10 TeV (Paper 1). Now the statement is extended to the broader energy region, from 500 GeV to 15 TeV. From 1 TeV to several TeV the slope of the spectrum is determined with high statistical accuracy, e.g. a power law fit in the energy region from 1 TeV to 5 TeV gives a differential index of -2.23 [FORMULA] and [FORMULA] for the high and the low flux spectrum respectively. In the narrow energy range from 500 GeV to 1 TeV the statistical uncertainty on the spectral index is considerably larger, we compute 0.2 for the high flux sample and 0.4 for the low flux sample. Therefore, our 1997 Mkn 501 data would not contradict a correlation of emission strength and spectral shape below 1 TeV as tentatively reported by the CAT-group (Djannati-Atai et al. 1999).

[FIGURE] Fig. 11. The upper panel illustrates the spectral energy distribution [FORMULA], for the full data set (full circles), for periods of low flux (open circles), and for periods of high flux (triangles) (dN/dE(2 TeV) above 30 and below 16 times [FORMULA]). Only the statistical errors are given here; the systematic errors enter the three spectra in the same way and can be neglected comparing the three spectra. The dashed lines indicate the shape of the mean spectrum (fit from Eq. 6) overlaid over all three spectra to simplify the comparison of the shape of the three spectra. In the lower panel the ratio of the low flux spectrum divided by the high flux spectrum is shown. The dashed line gives the fit to a constant. The [FORMULA]-value is 12.3 for 15 degrees of freedom.

For completeness, the HEGRA IACT system data are plotted in Fig. 12 jointly with the HEGRA CT1 (Aharonian et al. 1999c), the CAT (Barrau 1998), the Telescope Array (Hayashida et al. 1998), and the Whipple (Samuelson et al. 1998) results concerning the Mrk 501 energy spectrum during the 1997 outburst. Generally a good agreement can be recognized in the overlapping energy regions, except for a steeper Telescope Array spectrum.

[FIGURE] Fig. 12. The Time-averaged spectrum of Mrk 501 during 1997, compared with published results from other experiments (Aharonian et al. 1999c, Hayashida et al. 1998, Samuelson et al. 1998, Barrau 1998). Since the observation periods do not completely overlap for the variable source, the spectra are normalized at the energy 2 TeV. For the HEGRA system the hatched area shows the systematic errors on the shape of the spectrum as described in the text. For the other experiments only statistical errors are shown. Only data points with a signal to noise ratio larger than one have been used.

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© European Southern Observatory (ESO) 1999

Online publication: August 25, 1999