5 Photometric data reductions

The main part of the photometric reductions are carried out by the same calibration programme described in Sect. 4.2. The photometric data used as the standards are the $B_{\rm T}$ and $V_{\rm T}$ values from the Tycho 2 catalogue. Although there are catalogues with higher accuracies at the faint end, Tycho 2 is uniquely homogeneous and dense. However, not all Tycho 2 stars were used. In order to make the photometric reductions more robust, stars identified as variable were excluded from the calibration. Due to the nature of the reduction process used to create Tycho 2, variability information is not available in that catalogue. For this, the original Tycho data (ESA 1997) must be used.

The intensities determined from the images (see Sect. 4.1) are first converted into magnitudes ( $m=-2.5\log_{10}i$) and are then corrected in order to take into account the difference between isophotal and total magnitudes (see Sect. 5.1). Following this, the calibration then simply consists of determining the zero point of the magnitude scale.

Figure 5: This colour-colour diagram shows the relationship between the Tycho 2 magnitudes and the CMT instrumental magnitude, $r'_{\rm CMT}$. Only stars brighter than $V_{\rm T}<10$ were used in the determination. The green line is a least-squares linear fit to the data.

Figure 6: The results of synthetic colour calculations are shown in this plot. The various symbols stand for different types of star. The line drawn is the same as that in Fig. 5.

Since the CMT only observes in one passband, photometry from the telescope cannot be placed on a standard photometric system without additional colour information. However, using the colour data in the Tycho 2 catalogue, it is possible to calibrate onto the instrumental magnitude system. Figure 5 shows the least-squares solution used to determine the linear colour term. This was found to be $0.435\times(B-V)_{\rm T}$.

By using this a priori colour term, the $V_{\rm T}$ of the Tycho 2 standards can be converted into the natural system of the CCD and filter combination. This is close to the Sloan r' passband, but will be on the Vega scale rather than the spectrophotometric AB$_\nu$ magnitude system (Fukugita et al. 1996).

To test that this colour term was reasonable, synthetic colours were generated in a manner similar to that in Evans (1989). Again, the difference being the use of data from Pickles (1998) rather than from Gunn & Stryker (1983). The resulting colour-colour diagram is shown in Fig. 6 along with a line representing the colour term that was determined from the CMT data. At the red end, the line lies close to the giant stars rather than the main sequence stars. This agrees with the expectation that for V<10, almost all red stars are giants (Besançon Galaxy Model, Robin & Crézé 1986).

When determining the zero point, a weighted least-squares solution is used along with a rejection filter to identify outliers. A number of diagnostics are determined in this solution. The main ones are the scatter of the residuals from the calibration and the magnitude limit. The former gives an indication of the quality of the photometric conditions, while the latter will show the presence of cloud. In addition to this, a median filter is applied to the photometric residuals as a function of time in order to determine if an exposure was interrupted by cloud. Depending on the level of the cloud opacity, parts of a data frame can be flagged as non-photometric or not suitable for the survey. In the latter case, this is when the effective magnitude limit of a part of an exposure is brighter than $r'_{\rm CMT}=16$. This information is then passed to the selection programme so that another observation can be rescheduled. Non-photometric observations are accepted into the survey, since the primary purpose of the survey is astrometry.

  
5.1 Linearized photometry scale

Checks have been carried out using timed exposures to confirm the linearity of the CCD. These show that the CCD is linear to at least the 1% level all the way up to when the CCD saturates at about 60 000 counts. This corresponds to an $r'_{\rm CMT}$ magnitude of 8-9 for typical observing conditions.

Since the photometry is derived from isophotal intensities a correction is required to obtain total magnitudes. Since the image profiles have been found to be exponential, the appropriate correction from Irwin & Hall (1983) has been applied. Investigations into an alternative method of linearizing the photometry scale using a variant of the algorithm developed by Bunclark & Irwin (1983) have also been carried out.

  
5.2 Photometric extinction

With the photoelectric micrometer, the photometric solution that was carried out each night followed a more classical solution (Carlsberg Consortium 1999), with the extinction in V being calculated as part of the photometric solution. This data was published regularly on the Internet and covered the years 1984-1998.

From June 1998, since a CCD was being used, the observing strategy and the part of the sky being observed, prevented a classical solution of the extinction being made since there was not a large enough range in sec z. However, by assuming that the zero point of the photometric solution only changes gradually over time and that the lowest measurable extinction would correspond to the dust-free value for $r'_{\rm CMT}$ (0.09), it is possible to derive an extinction value for each relatively stable night.

To do this, the zero point determined from the photometry is first corrected for exposure time ($\equiv$ $\cos\delta$) and then a simple linear model is applied to account for the change in sensitivity of the system. Finally, a correction for sec z is applied in order to produce an extinction value. Although this is only for the $r'_{\rm CMT}$ passband, it is possible to generate extinction values for other passbands using the data contained in King (1985).

Since March 1999, extinction values for $r'_{\rm CMT}$ have been published on the Internet, cf. the earlier data. In these tables the mean for each night is given using only those CCD frames that were considered photometric. On average, each data frame has 30-40 calibrating stars in it.

Even though this is not a customized extinction monitor, such as Hogg et al. (2001), the CMT extinction data is currently the only source of regular extinction measurement available on the La Palma site and thus provides a valuable service.