4 Discussion

   
4.1 Comparison with other VHE detections

The energy spectrum of Mkn 421 has been measured in the same energy range by the Whipple Observatory (Zweerink et al. 1997; Krennrich et al. 1999a,1999b) and by the HEGRA experiment (Aharonian et al. 1999; Horns 2001). All these experiments have fitted a power law to the spectrum and given the values of $\phi_0^{\rm pl}$ and of $\gamma^{\rm pl}$ in several observation periods corresponding to different levels of activity of the source. Our results for the periods 1998 and 2000 are plotted in Fig. 6 together with their results. This figure includes both statistical and systematic errors for all measurements. Although CAT data tend to indicate some spectral curvature in 2000, we used the values of $\gamma^{\rm pl}$ for this comparison, given that this parameter is in any case clearly indicative of the energy dependence of the spectrum ( $\gamma^{\rm cs}_0\simeq\gamma^{\rm pl}$, see end of Sect. 3.2). In this figure we also added the result obtained during the single night between 4 and 5 February, 2000, for which the high source intensity (see Sect. 3.1) allowed us to extract a spectrum. Since the corresponding errors are larger (see Table 1), this single result is fully compatible with the other two.

Some caution is necessary when comparing results from experiments with different systematic errors. As an example, in the case of a curved spectrum, the value of the energy $E^{\rm cs}_0$(see Table 1) corresponding to the minimal error on the spectral exponent $\gamma^{\rm cs}_l$is not necessarily the same for experiments with different energy thresholds. Possible systematic effects could be responsible for the dispersion of results shown in Fig. 6, since, if one excepts a recent preliminary result from HEGRA (Horns 2001), HEGRA and CAT data favour higher values of $\gamma^{\rm pl}$, whereas data from the Whipple Observatory yield a rather low spectral index. However, experiments showing the largest difference in spectral indices in the figure (Whipple Observatory and HEGRA) are in good agreement on the spectrum of the Crab nebula (Hillas et al. 1998; Aharonian et al. 2000). Furthermore, some evidence for a spectral variability has been already suggested on the basis of the Whipple 1995-96 low-flux data (Zweerink et al. 1997), with a spectral index $\gamma^{\rm pl}=2.96 \pm 0.22$, but no flux value is quoted in the latter reference, precluding any comparison with the results discussed here.

Data from all experiments with the source in both low and high states would be desirable in order to exclude that experimental effects are responsible for the dispersion seen in Fig. 6. Besides, as different flares may be intrinsically different from each other, the spectral index-flux correlation may not provide us with complete information, thus stressing again the need for more numerous observations.

Figure 6: Compilation of spectral measurements on Mkn 421, obtained by the HEGRA (Aharonian et al. 1999; Horns 2001), CAT (this work) and Whipple (Zweerink et al. 1997; Krennrich et al. 1999a,1999b) experiments between 1995 and 2000. The results are given in the $\{\phi _0^{\rm pl},\gamma ^{\rm pl}\}$ plane of spectral parameters in the power-law hypothesis. While the dashed lines around CAT points show only the 68% confidence level contour (statistical error), the error bars take account, for all measurements, of both statistical and systematic errors, the latter being conservative if unknown: $(\Delta \phi _0^{\rm pl}/\phi _0^{\rm pl})^{\rm syst}=\pm 30$% and $(\Delta \gamma ^{\rm pl})^{\rm syst}=\pm 0.10$ were used where these values are not quoted directly. The $\chi ^2$ per d.o.f corresponding to the absence of any dependence of the spectral index with flux is 3.5.

4.2 Comparison with results on Mkn 501

The second ${\rm TeV}$ blazar, Mkn 501, underwent a series of intense flares in 1997 observed by all Cherenkov telescopes in the Northern Hemisphere (Djannati-Ataï et al. 1999 and references therein). Figure 7 shows two spectral energy distributions (SEDs) of Mkn 501, as measured by CAT. The first one is the 1997 time-averaged spectrum and the second one corresponds to the single night of April 16th, 1997, during which the source reached its highest intensity. The spectral variability observed by CAT on the basis of a hardness ratio (Djannati-Ataï et al. 1999) is illustrated here by the shift in the peak energy of the SED: $0.56\pm 0.10~{\rm TeV}$ for the average spectrum and $0.94\pm 0.16~{\rm TeV}$ for the highest flare. Figure 7 also shows the SEDs of Mkn 421 for the two observation periods 1998 and 2000: both are obtained with the assumption of a curved spectrum (see Sect. 3.2).

In the framework of the phenomenological unification scheme of blazars established by Fossati et al. (1998), the broad-band SED of such a source consists of two components, respectively a low-energy component attributed to synchrotron radiation and a high-energy component peaking in the $\gamma$-ray range. Peak energies of the preceding components are correlated and Mkn 501, as observed in 1997, appears to be the most extreme blazar, with the synchrotron part of the SED spectrum peaking in the hard X-ray range and the $\gamma$-ray component peaking around or above $500\:{\rm GeV}$.

Figure 7: Comparison of the Mkn 421 spectral energy distributions derived in this paper (unfilled areas) with that obtained by CAT for Mkn 501 in 1997 (hatched areas) (Djannati-Ataï et al. 1999; Piron 2000). All areas show the 68% confidence level contour given by the likelihood method in the curved shape hypothesis.

In the case of Mkn 421, the CAT 1998 and 2000 data, and the weakness of its detection by EGRET, when interpreted within the preceding unification scheme, indicate that the peak energy of the high-energy component of the SED lies in the $50\:{\rm GeV}$ region, while its synchrotron peak is known to lie in the UV-soft X-ray band. A shift of both components towards higher energies during an intense flare, similar to that observed by CAT for Mkn 501 in 1997, would result in a harder spectrum in the energy region covered by Cherenkov telescopes and thus account for the trend shown in Fig. 6. In fact, the spectral hardening of Mkn 421 at ${\rm TeV}$ energies during flares, if clearly proven, should not be a surprise, since a similar effect has been already observed at a few ${\rm keV}$ from this source by the ASCA and Beppo-SAX satellites (Takahashi et al. 1999; Malizia et al. 2000), and since X-ray and $\gamma$-ray integrated emissions of Mkn 421 have proven to be correlated on many occasions (see, e.g., Maraschi et al. 1999; Takahashi et al. 1999,2000).