2. Observations and data analysis
Between March and August 1996 Mkn 501 was observed in tracking mode (rather than taking interleaved ON- and OFF-source runs) to obtain maximum exposure time. 147 hours of good quality data were obtained at zenith angles between and . Atmospheric extinction measurements from the Carlsberg Automatic Meridian Circle near the HEGRA site were used as a guide to data quality. Analysis proceeded in three steps: (1) flat-fielding and calibration, (2) filtering to obtain a dataset of showers with well determined image parameters (for a definition see e.g. Reynolds et al. 1993 ), (3) selection of candidates using cuts on the image parameters. For a more detailed description of our image analysis methods see Paper I and references therein.
1. Calibration and flat fielding are based on regular measurements of the pedestals and the relative photomultiplier gains.
2. CT1 carries a 127 photomultiplier camera faced with hollow hexagonal light guides of diameter. In addition to a hardware trigger condition of any 2 out of 127 pixels fired, a software trigger condition of any 2 out of 91 pixels above 16 photoelectrons was applied to the calibrated signals to exclude camera-edge events with incomplete images. Events recorded under poor telescope positioning were rejected leaving a mean absolute pointing error of .
3. A series of image parameter cuts was applied which reject events of probable hadronic origin leaving a sample of -shower candidates. For our detection of Mkn 421 (Paper I), neither observations of the Crab Nebula nor all parameters for the Monte Carlo optimization of the cuts were available for the new camera, therefore we used the set of cuts developed for a 91 pixel camera with similar resolution as described in Reynolds et al. (1993 ):
In addition, a cut CONC was applied. We continued to use these previously successful cuts for our analysis of Mkn 501. Monte Carlo data now being available, we can calculate the flux from Mkn 501 by comparison with this simulated data which has not also been used in optimisation of the cuts (see Section 4).
The determination of the background follows an approach different to our earlier publications and will be described in more detail in Petry et al. (1997 ). In order to maximise our exposure time at small zenith angles the data were recorded in consecutive ON-source runs. OFF-source observations required for background determination were made when Mkn 501 was not observable. Observations of 9 different "empty-sky" regions made before, during and after the Mkn 501 observing season were available, forming a combined OFF-source dataset of 86.3 h at . From these data the background was determined, both for the Crab Nebula and for Mkn 501, as follows.
From Monte Carlo studies we expect less than 1% of source events in our camera to fulfill the condition ALPHA . The number of events which pass all other cuts and lie in this ALPHA region is therefore used to normalise the ALPHA-distribution of the OFF data to that of the ON data. Since the characteristics of the shower images are zenith angle () dependent, we adjust the distribution of the OFF data to that of the ON data, by performing the normalization in n separate bins. The normalisation constants are calculated using
where is the number of ON-source events with ALPHA in bin i and is the corresponding number for the OFF data. The width of the bins was a compromise between the accuracy of a small bin width and sufficient events per bin for a low statistical error. For both Mkn 501 and the Crab Nebula n = 3 approximately equidistant bins between and were used.
The number of expected background events in the signal region of ALPHA , B, is then obtained from
where is the number of OFF-source candidates (after all cuts including ALPHA ) in bin i. By standard error propagation, the statistical error on B is
We calculate the significance S of the signal as the excess divided by the statistical error on the excess:
where is the number of events in the ON-source dataset after all cuts including ALPHA .
This conservative approach takes into account both the dependency of the image parameters on and the statistical error in our knowledge of this dependency.
© European Southern Observatory (ESO) 1997
Online publication: June 30, 1998