2 Experimental set-up and method

The measurements reported here have been made with the prototype telescope #1 of the HEGRA collaboration. This telescope has a two-axis equatorial drive head and a 5 m² segmented mirror plane. In the focal plane, at approximately 5 m distance, an imaging Cherenkov camera is located. The camera consists of 127 closely packed EMI9083-photomultiplier tubes coupled to light collecting aluminum cones forming a hexagon. The signal at the anode of the photomultiplier tubes is read out by independent electronic circuits, one for direct current (dc-branch) and one for pulse measurements (ac-branch): The output of the dc-branch is equivalent to the dc-anode current with a resolution of 8 bit corresponding to a value of $I_{\mathrm{LSB}}=0.195~\mu\mathrm{A}$. The output of the ac-branch corresponds to the pulse charges at the anode integrated over 30 ns and amplified with a factor of $16\pm0.5$. The resolution is 12 bit corresponding to Q_LSB=0.25 pC. Hence the errors of the current and charge measurements $\Delta I_{\rm Q}$ and $\Delta Q_{\rm Q}$ due to the ADC quantization are given by $\Delta I_{\rm Q}= I_{\mathrm{LSB}}/2=\pm 0.097~\mu\mathrm{A}$ and $\Delta Q_{\rm Q}= Q_{\mathrm{LSB}}/2=\pm 0.125~\mathrm{pQ}$ (Tietze & Schenk [1991]). Other uncertainties such as temperature drifts have been found to be negligible compared to these figures in careful laboratory tests. More details can be found in Mirzoyan ([1995]) and Njoo ([1995]).

The most important consideration of the method is, what kind of stellar types have to be selected in order to obtain an emission spectrum and detection sensitivity similar to Cherenkov light. Telescope #1 is especially sensitive in the wavelength range of approximately 260 nm to 650 nm. The observed energy spectrum of photons hitting the telescope is determined by the primary photon spectrum corrected for the extinction in the atmosphere. A simulation of Cherenkov light production by cosmic rays and its extinction was performed by Akhperjanian & Wiedner ([1993]) and their results have been adopted for the present study. Since the Cherenkov light of an air shower induced by a VHE $\gamma$ ray does not traverse the entire atmosphere, owing to the fact that most of it is emitted below the ozone layer, the extinction is less than for starlight. Nevertheless, the spectrum of detected Cherenkov light is very steep, as can be seen in Fig. 1.

Figure 1: Spectra of Cherenkov light ("Ch'') and of $\tau$ Scorpius ("Sco'', approximately 30000 K) with extinction in the atmosphere (index "Ext'') and without. As an example of a spectrum not to be used for this method, the spectrum of Vega ("Vega Ext'', approximately 9500 K) is also plotted. All spectra are normalized at $\lambda=0.55~\mu\mathrm{m}$

For comparison, different stellar spectra are plotted in Fig. 1 as well. These spectra are calculated by using simulations for stellar atmospheres performed by Kurucz (Kurucz [1979], [1993]; Kurucz et al. [1974]), which gave very realistic results when compared to actual measured spectra (Malagnini [1983]; Longo et al. [1989]). The flux at the top of the Earth's atmosphere is calculated in terms of UBV photometry (Hagen & Boksenberg [1995]). The atmospheric extinction on La Palma was calculated within reasonable models based on the most important effects such as Rayleigh and Mie scattering as well as molecular Ozone absorption. These model calculations were adjusted to measurements of the (close by) Carlsberg Observatory.

Although no stellar spectrum observed at the Earth fits the Cherenkov light spectrum perfectly, very hot stars which do not show distinct absorption bands in the relevant wavelength range do approximate it quite well. Using the Pogson formula (Budding [1993]) the calculation of color indices of stellar spectra that do so is easy. Stars with color indices of about $B-V=-0.\!\!^{\mathrm{m}}105$ and $U-B=-1.\!\!^{\mathrm{m}}730$ would fit the plotted spectrum of Cherenkov light in Fig. 1 (Karschnick [1996]).

Two other points have to be considered when the various stars are selected. First, the stars have to be bright enough and second, the stars have to be visible under small zenith angles in order to keep the fluctuation of the atmospheric extinction negligible.

A number of stars, that approximately meet the above criteria, have been selected for the calibration and are given in Table 1. Better candidates were not available for La Palma at that observation time. Since detailed spectral information is not available for most of the stars and in order to treat all stars on equal footings calculated energy and photon fluxes, respectively, based on the simulations of Kurucz ([1979], [1993]) have been used.

The calculated spectra have been normalized in such a way that the energy flux at $\lambda_{u}=550~\mathrm{nm}$ corresponds to the visual magnitude, thus neglecting the interstellar extinction. The atmospheric extinction, also measured by the Carlsberg Observatory at $\lambda_{u}=550~\mathrm{nm}$ in the same night when the starlight measurements were made, have been extrapolated to the sensitive wavelength region of the telescope ( 260 nm-650 nm) by the method described above.