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Astron. Astrophys. 342, 69-86 (1999)

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4. The 1997 Mkn 501 light curve

Between March 16th and October 1st, 1997, 110 h of Mkn 501 data, satisfying the conditions described above, were acquired. The excess of about [FORMULA] photons is shown in Fig. 10 in equatorial coordinates (hardware threshold, no cuts). Note, that the figure shows the number of excess events as function of declination and right ascension and not a likelihood contour. The mean location of the excess photons coincides with the Mkn 501 location with an accuracy of [FORMULA] (Pühlhofer et al. 1997), corresponding to an angular resolution of the IACT system of better than 40 arc sec when limited by systematic uncertainties and not by statistics.

[FIGURE] Fig. 10. All events reconstructed in the [FORMULA] solid-angle region centered on the Mkn 501 direction. The prominent [FORMULA]-ray excess can be seen above the approximately flat background (hardware threshold, no cuts).

Fig. 11 shows the differential spectra obtained for 8 exemplary individual nights. For each of the four data periods March/April, April/May, May/June, and June/July 1997 a night of weak emission and a night of strong emission has been chosen. As can be seen, the stereoscopic IACT system, due to its high signal to noise ratio and due to an energy resolution of [FORMULA], permits a detailed spectral analysis on a diurnal basis. The spectra can approximately be described by power law models, although above 5 TeV the spectra apparently steepen (see also Aharonian et al. 1997c; Samuelson et al. 1998).

[FIGURE] Fig. 11. The differential [FORMULA]-ray spectra of eight individual nights. For each of the four data periods March/April, April/May, May/June, and June/July, 1997 a night of weak emission and a night of strong emission has been chosen. Statistical errors only; see text for systematic errors; the upper limit has 2[FORMULA] confidence level (MJD 50550 corresponds to April 12th, 1997).

In a first analysis, we fit the data with power laws in the energy region from 1 to 5 TeV. The lower bound of the fit region is determined by the requirement of the bound being higher than the energy threshold of the IACT system in the zenith angle interval from [FORMULA] to [FORMULA]. The upper bound of 5 TeV has been chosen to minimize systematic correlations between the emission intensity and the fitted spectral index which could be caused by the combined effect of a curvature of the Mkn 501 spectrum and the effective maximum fit range. The latter actually is smaller for nights of low Mkn 501 activity, since for these nights the higher energy channels above [FORMULA]5 TeV are frequently not populated and do not contribute to the fit result.

In order to minimize the correlations between the fitted flux amplitude and the spectral index due to the fitting procedure, the model [FORMULA] is used, where [FORMULA] is the differential flux at 2 TeV and [FORMULA] is the spectral index. The energy 2 TeV approximately equals the median energy of the Mkn 501 [FORMULA]-rays recorded with the IACT system.

We estimate the systematic error on the flux amplitude to be [FORMULA]20%. This error is dominated by the 15% uncertainty of the energy scale. The systematic error on the spectral index is currently estimated to be 0.1 and derives from the Monte Carlo-dependence of the results. The systematic errors as well as more detailed studies of the differential Mkn 501 spectra, especially in the energy range below 1 TeV and above 10 TeV, will extensively be discussed in a forthcoming paper. Note, that all errors shown in the following plots are statistical only.

The differential fluxes at 2 TeV and the spectral indices determined on a daily basis are shown in Fig. 12. In Table 3 the results are summarized. The gaps in the light curve are caused by the moon, since the IACT system is only operated during nights without moon. The emission amplitude is dramatically variable, the measured daily averages range from a fraction of the Crab emission to [FORMULA]10 Crab, the average flux being 3 Crab. The largest flare was observed in June 1997 and peaked at June 26th/27th.

[FIGURE] Fig. 12. Daily flux amplitudes [FORMULA] and differential spectral indices (1-5 TeV) for the 1997 Mkn 501 data. For clearness, spectral indices are shown only for the days with sufficient statistics, i.e. with errors on the spectral index smaller than 0.5. Statistical errors only; see text for systematic errors (MJD 50550 corresponds to April 12th, 1997).


Table 3. Results on diurnal basis . Statistical Errors only; see text for systematic errors.

In contrast, the spectral indices are rather constant. A constant model of [FORMULA] fits all spectral indices with a chance probability for a larger [FORMULA] of 11%. The largest deviations have been found for the nights MJD 50550/50551 where the spectral index of -1.87 +0.13 -0.14 deviates by 2.7 [FORMULA] from the mean value and for MJD 50694/50695 where the spectral index -1.05 +0.30 -0.38 deviates by 3.2 [FORMULA] from the mean value. Henceforth, although the IACT system makes it possible to determine the daily spectral index [FORMULA] with an accuracy of [FORMULA] [FORMULA] 0.1 for 15% of the nights, with an accuracy of [FORMULA] [FORMULA] 0.2 for 45% of the nights, and with an accuracy of [FORMULA] [FORMULA] 0.35 for 75% of the nights the evidence for a change in the spectrum is marginal.

In order to study the correlation between flux intensity and differential spectrum, we divided the IACT system data into five groups according to the diurnal emission intensity, i.e. a [FORMULA]-value in units of [FORMULA] of below 7 (group i), 7-10 (group ii), 10-20 (group iii), 20-30 (group iv), and above 30 (group v), respectively. In Fig. 13 the differential spectra determined with the data of each group are shown. Within statistical errors the shapes of the five spectra are the same. This is exemplified in Fig. 14, where the four lower flux differential spectra (group i - iv) have been divided by the highest flux differential spectrum (group v). For all four cases the ratio of the differential fluxes as a function of primary energy can be described by a constant model. The largest reduced [FORMULA]-values of a constant fit is 1.21 for 9 degrees of freedom, which corresponds to a chance probability for larger deviation from the hypothesis of a constant ratio spectrum of 28%. In Table 4 the power law spectral indices (1 to 5 TeV) of the five groups are listed. Within the statistical errors the first five indices are consistent with the mean value of -2.25.

[FIGURE] Fig. 13. The Mkn 501 data has been divided into 5 groups according to the activity of the source as determined on a night to night basis. For each of the 5 groups a time averaged spectrum has been determined. The five groups have (from bottom to upwards) [FORMULA] [FORMULA] of below 7, 7-10, 10-20, 20-30, and above 30, respectively. Statistical errors only; see text for systematic errors.

[FIGURE] Fig. 14a-d. The results of dividing the differential spectra of the four lower flux intensity groups (a -d corresponding to group i-iv) by the differential spectrum of the highest flux intensity group (group v). The lines show the results of constant model fits to the ratio spectra.


Table 4. Fit parameters of differential spectra of 7 data groups. Statistical Errors only; see text for systematic errors.

We studied whether the TeV spectra during the rising epochs of the light curves systematically differ from the TeV spectra during the falling epochs of the light curves. For this purpose we selected two subsets of the data, consisting of the accumulated data where the flux increased (group vi) or decreased (group vii) by at least 25% in comparison to the preceding night. Also in this case, the ratio spectrum can well be fitted with a constant model. The reduced [FORMULA]-value of the constant model fit is 0.72 for 9 degrees of freedom, corresponding to a chance probability for larger [FORMULA]-values of 69%.

In Table 4 the power law spectral indices (1 to 5 TeV) of these two groups are given. There is only a weak indication that group vi ("rising" days) with a spectral index of -2.19[FORMULA]0.03 might have a flatter spectrum than group vii ("falling" days) with a spectral index of -2.29[FORMULA]0.05.

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© European Southern Observatory (ESO) 1999

Online publication: December 22, 1998