## 6. ResultsIn this Sect. the methods explained in Sect. 5 are applied to the data set discussed in Sect. 4. ## 6.1. and spectraFig. 5 shows the and spectra. These spectra display a relatively sharp knee at values consistent with a primary energy for the knee as determined below. ## 6.2. Energy spectraFig. 6 displays the integral energy spectra uncorrected for an A dependent bias obtained with the four reconstruction methods. The differences in absolute normalisation and spectral slope originate from the different mass dependent biases. After the correction of the chemical bias the integral spectra are similar (Fig. 7). This nontrivial fact is in favour of the internal consistency of data analysed here; a longitudinal shower development different from the one predicted by the Monte Carlo or errors in the calibration of and could have spoiled the agreement of spectra obtained with different energy reconstructions. The differential energy spectrum is shown in Fig. 8. A steepening of the energy spectrum is visible around an energy of 4 PeV. There seems to be no "fine structure" in the energy spectrum around the knee in excess of 20 . Apparent structure with smaller amplitudes that appears in the spectrum reconstructed with a given energy-reconstruction method is not reproduced with other methods. This is expected due to the A dependent bias of our energy-reconstruction methods (see Fig. 2). Note that with these methods, a potential structure in the energy spectrum consisting of different nuclei is smeared out. If two different power laws, smoothly connected at the knee (corresponding to a "sharp" knee), are fitted to the differential spectra we obtain: -
a "knee" position of *E*(Knee) = PeV, -
a spectral index of below and above the knee.
The reduced values of the fits to the differential spectrum (12 d.o.f.) were 6.75, 4.03, 3.53 and 1.47 with energy reconstruction methods 1 to 4 respectively. Some of these values are much larger than one. It is then difficult to specify a statistical error; we specify the statistical errors for method 4 that has a marginally acceptable reduced value. The large values for the analysis with energy-reconstruction methods 1-3 can be interpreted as an argument in favour of a knee not absolutely sharp in energy. However, the fact that one of the fits is acceptable on the 90 confidence level means that we cannot reject the hypothesis of a "sharp" knee (two power laws with no transition region) within our systematic errors. The large statistical error on the knee position further indicates that we cannot reject the hypothesis of a spectrum without a knee in the limited energy range of this analysis with high significance. The spectral index for the spectrum below the knee is consistent with direct measurements at lower energies (Wiebel-Sooth et al. 1998) and a recent Cherenkov-light based determination of the spectral index in the TeV range (Aharonian et al. 1999); there is therefore no evidence for any change in spectral index from the TeV range right up to the knee. ## 6.3. Composition of CR
The fraction of light nuclei as a function of reconstructed energy -
obtained from the fits to the measured penetration-depth distributions
(see Sect. 5.2)- is presented in Fig. 10. At energies below the knee
the composition is mixed and consistent with direct measurements
around 100 TeV, namely ()/all = 0.54
0.08 (Watson 1997). The data points
seem to indicate a gradual enrichment of heavy elements above about 1
PeV though the error bars are large (remember that there are only six
## 6.4. Elongation rateFig. 11 shows the corrected mean shower maximum depth as a function of energy. A least-squares fit to the values as a function of energy, using only the statistical errors, yields an elongation rate ER=78.3
1.0 (stat) 6.2 (syst)
g/cm These results are not in contradiction with previous measurements
in this energy range (Wdowczyk 1994; Turver 1992). This elongation
rate, and also the absolute , is
consistent with data at higher energies, obtained mainly by the
Yakutsk and Fly's Eye collaboration (Watson 1997). A constant
elongation rate of 73
g/cm ## 6.5. Fluctuation of shower penetration depth
The RMS of the penetration depth distributions - calculated in
reconstructed-energy bins, i.e. biased in favour of the light
component of CR especially at low energies - is shown in Table 3.
It does not show any obvious trend towards a heavy composition.
Therefore the fact that the composition at the highest energy seems to
be heavy with all energy reconstruction methods (Fig. 10) is mainly
determined by the fact that the in
the highest energy bin lies about 20 g/cm
© European Southern Observatory (ESO) 2000 Online publication: July 7, 2000 |