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Astron. Astrophys. 353, 847-852 (2000)

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3. Upper limits in Crab units and in flux units

In the following analysis, measured fluxes or flux upper limits are first determined in Crab units and are only subsequently converted into absolute flux values or flux upper limits. Results in Crab units have the advantage of relying exclusively on measured data and of being free from systematic errors due to the Monte Carlo simulations of the air showers and the detector response. Moreover, as several Bl Lac objects have been observed with only three telescopes in the CT-system, we can directly compare their observations to Crab data taken under the same conditions, at the same epoch, avoiding thus specific simulations. The trigger rate is constant within 5% for a given zenith angle (Aharonian et al. 1999a), thus no strictly simultaneous data can be compared safely. For each source and each zenith angle interval [FORMULA] the number of events in the ON-source region ([FORMULA]), the number of events in the OFF-source region ([FORMULA]), and the observation time [FORMULA] is determined. To maximize the statistics the analysis is based on "loose" cuts: the mean scaled width of the showers (Konopelko 1995; Daum et al. 1997) has to be smaller than 1.2 (to retain [FORMULA] 80% of photon induced showers) and the squared angular distance of the reconstructed shower direction from the source direction has to be smaller than 0.05 deg2. For each time period of fixed experimental conditions, a reference Crab data sample was analyzed (compare Table 2) and the numbers [FORMULA], [FORMULA], and [FORMULA] were determined for all zenith angle intervals. As Crab observations with three telescopes have been performed only for several days, the flux upper limits derived with this reference data are considerably higher than for the data with 4 telescopes in the system.


[TABLE]

Table 2. Information about the observations of the Crab Nebula used for computing flux upper limits in Crab units.


Using the probability density function of the number of source events, we compute the upper limit of the number of counts [FORMULA] from [FORMULA] hours of source observations at 99% confidence level (Helene 1983). Similarly, we calculate the lower limit [FORMULA] of the number of counts for [FORMULA] hours of Crab observations. We compute the upper limit in Crab units [FORMULA] from: [FORMULA].

The energy threshold [FORMULA] is computed by Monte-Carlo for each source as a function of the mean zenith angle of the object during the observations. For the CT-system, the energy threshold scales with zenith angle [FORMULA] roughly as [FORMULA] (Konopelko et al. 1998). Only data with good weather conditions are used and phototube voltage fluctuations are corrected.

Assuming a source energy spectrum, the conversion of upper limits in Crab units into upper limits in absolute flux units is straightforward. In the following we use two slopes for observed source spectrum: dN/dE [FORMULA], as measured for the Crab nebulae around 1 TeV (Konopelko et al. 1998) and a steeper one dN/dE [FORMULA]. Above 0.5 TeV, the integral Crab flux is [FORMULA]= [FORMULA] cm-2s-1. In the other case, we normalise the flux in order to get the same integral flux in this range.
The upper limits on the integral flux are then computed from:
[FORMULA], and
[FORMULA].

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© European Southern Observatory (ESO) 2000

Online publication: January 18, 2000
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