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Astron. Astrophys. 320, L5-L8 (1997)

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4. Spectral Index and Flux calculations

The procedure to examine the spectral behaviour of the source and subsequently determine the integral photon flux follows largely the one described in Paper I. Again, Monte Carlo (MC) data was produced using the code described by Konopelko et al. (1996 ).

The effective collection area of CT1 for our given set of cuts was calculated taking into account the dependence of the cut efficiencies on primary energy and impact parameter. The main sources of systematic errors in the flux calculation are the energy calibration, i.e. the conversion from Cherenkov photons to ADC counts which our measurements suggest is uncertain by [FORMULA] 20 %, and the determination of the shape of the primary photon energy spectrum.

Spectral shape is estimated from analysis of the differential distribution of the parameter SIZE which is defined as the total light content of the shower image in the camera. Our MC simulations show that here SIZE is in first order proportional to the energy of the primary [FORMULA] -ray, but fluctuates for individual showers by up to 50 % (2 [FORMULA]).

The measured distributions for Mkn 501 and the Crab Nebula are shown in Figure 2a. The signal in each SIZE bin was derived in the same way as the total signal (see Section 2). From MC simulations of [FORMULA] -showers and the detector, the shape of the SIZE distribution can be predicted for a given night sky background noise, average zenith angle and shape of the primary energy spectrum. Figure 2b shows examples for power law spectra with differential spectral index [FORMULA] = 1.5, 2.5, 3.5 and 4.5.

[FIGURE] Fig. 2. a (upper left) the measured differential SIZE distribution for Mkn 501 and the Crab Nebula. The integrals of all distributions are normalized to 1. The SIZE parameter is measured in units of photoelectrons (ph.e.). The errorbars are the combined statistical and systematic error. b (lower left) four examples of simulated SIZE spectra for different shapes of the primary energy spectrum. [FORMULA] is the differential spectral index of the power law. c (right) the reduced [FORMULA] from the comparison of the measured with the simulated SIZE spectra as a function of [FORMULA].

By varying [FORMULA] between 1.25 and 4.5 in steps of 0.25 and calculating the reduced [FORMULA] of the comparison of the simulated with the measured SIZE distribution, we find that the spectrum of the Crab Nebula is compatible with an index

[FORMULA] (Crab Nebula) = [FORMULA]

The minimum reduced [FORMULA] reached is 0.1 independent of whether only the first three, four or all five points are used. In order to test the robustness of the procedure we varied the photon to ADC count conversion factor by [FORMULA] 20 %. The most probable index changed by less than 0.1.

Assuming a spectral index of [FORMULA], we determine the integral flux of the Crab Nebula above 1.5 TeV from the 1995/96 CT1 data to be

[FORMULA] cm-2 s-1

where the systematic error combines the uncertainties in the spectral index and the energy calibration.

The same method applied to Mkn 501 results in a similar spectral index:

[FORMULA] (Mkn 501) = [FORMULA]

The minimum [FORMULA] reached is 1.4.

Given this uncertainty in the spectral shape, we cannot make strong statements about modifications to the power law spectrum such as cutoffs. We find that the impact of a possible cutoff on our calculated integral flux would be negligible if it was at energies [FORMULA] 6 TeV. We assume for the calculation of the flux a spectral index of 2.6 [FORMULA]. Based on the total Mkn 501 dataset at [FORMULA] [FORMULA] we thus find an integral flux above 1.5 TeV of

[FORMULA] cm-2 s-1

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© European Southern Observatory (ESO) 1997

Online publication: June 30, 1998
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