Astron. Astrophys. 318, 729-740 (1997)

4. Image detection and photometry

Image detection was accomplished with a connected-pixel algorithm, using the IMAGES program of the RGASP galaxy photometry software package (Cawson 1983). For classification as a genuine image, a group of ten or more adjacent pixels ( arcsec diameter) had to have R band intensities above a threshold of above the sky background (where represents the pixel-to-pixel standard deviation of the sky background). This minimum number of pixels corresponds to the expected minimum area of any reliably detected image due to the size of the seeing disc; given the image scale of 0.3 arcsec/pixel, this corresponds to the area within the half-maximum intensity isophote of a star under good seeing. The threshold was chosen to exclude a significant chance contribution of background pixels to the area of detected images (Driver 1994). A conservative estimate of the background standard deviation was taken, based on adopting the largest value from either: the measured background variation; a theoretical prediction of the noise in the background assuming Poisson statistics; or a value of of the background level (based on the expectation of a limiting accuracy of the flatfielding process on large scales). In practice, the Poissonian prediction of the background standard deviation was adopted for all four fields. To safeguard against spurious detections of random groups of sky background pixels, a signal-to-noise ratio test was used to reject low confidence detections. Monte-Carlo tests were performed on simulated data frames constructed using Poissonian noise distributions in order to assess the number of false detections retained after imposing different signal-to-noise ratio limits. Further simulations were carried out using twilight sky frames subjected to the same data reduction procedure as the night sky data. On the basis of these tests, a signal-to-noise ratio limit of 6.0 for the isophotal data was adopted. This value was found to give as few as one or two false detections per frame for the random noise simulations.

Once R band catalogues of images on the data frames had been compiled, magnitudes were determined using (variable) aperture photometry. In contrast to isophotal photometry, this technique should measure all the flux from a detected object when used with a large enough aperture size. Ideally the radius of the aperture should be chosen for a particular galaxy to include essentially all the signal from the galaxy, but not so large that it includes unnecessary noise from the sky background or nearby sources. Tyson (1988) noted that, as expected, isophotal magnitudes are close to the total magnitudes for bright objects, while Metcalfe et al. (1991) showed that aperture photometry using Kron radii (Kron, 1980) results in fixed aperture sizes for faint objects (effectively the Kron radius for a star). We therefore chose a variable circular aperture radius computed from the isophotal radius as,

where and n are constants. was calculated from the number of pixels having intensities above the threshold of the RGASP detection process, being the radius of a circular region containing that number. is set to 3 arcsec, about twice the typical seeing width (and in keeping with Metcalfe et al., 1991, and Lilly et al. 1991). The aperture radius therefore reduces to 3 arcsec for the faintest objects while approaching the isophotal radius for the brightest. The optimal value of the exponent n was selected on the basis of simulations of the measurement of images of face-on exponential disc galaxies; being circular and lacking bulge or nuclear components, these provide the most extended and flattest profiles among the conventional galaxy population. The values of for different values of n were calculated for different magnitudes and compared with the isophotal radius, the Kron radius and the radius containing of the light. Using an exponent of was found to be close to the light radius over a wide range of total magnitudes, even at the faintest limits, and close to 2.5 Kron radii; we therefore chose to adopt Fig. 2 shows the dependence of the total detected magnitude within a circular aperture for different aperture radii for the case of face-on, exponential light profile, galaxies. The various curves in the figure represent different methods for defining the aperture radius.

Fig. 2. A comparison of radii of variously defined photometric apertures as a function of total galaxy magnitude. The curves represent the sizes of circular apertures defined in six different ways for simulated face-on exponential disc galaxies. The locus for radii chosen to contain 90% of the light is shown, as is that corresponding to detection at the 26.0 mag. (arcsec)-2 isophote. Radii set at 2.5 times the Kron (1980) radius are presented. The results of Eq. (1) are given for indices and 2.0. An index was selected for the photometry of Sect. 4

A local measurement of the sky background surface brightness was used to remove the sky background contribution from the total signal within the aperture for each image. This was defined as the median of the pixel intensities in a 15-pixel wide circular annulus centred on the image, having an inner radius of excluding pixels which themselves lay within the inner radius of the equivalent annuli used to determine the background level around other images. In this way, an estimate of the background level was obtained which was essentially free of the contributions of detected images.

To avoid problems associated with incomplete data at the edges of the frames, only object images whose centres lie further than 30 pixels from the edges are considered. Fuller details of the image detection and photometric techniques are presented by Driver (1994).

The determination of the observed properties of galaxies is complicated by the overlapping of images through chance alignments. The reliable decoupling of blended images is a difficult process, complicated by factors such as the uncertainty in deciding how to assign the signal in the merged regions between the images, and the dependence of the efficiency of the process on the brightness of the image. For this analysis, if the isophotes of the two objects overlapped we simply considered the system as merged and counted it as a single image. The effects of the overlapping of images in detecting and parameterising faint galaxies in the vicinity of brighter ones are discussed in Sect. 5.3, where it is shown that overlapping images do not significantly affect the clustering statistics of interest here.

Once these principles had been used to provide R-band magnitudes for each detected image, B magnitudes were computed using the same (R band) image catalogue and the R band apertures. This method ensures that each image is treated identically in each of the two wavebands in an effort to minimise photometric errors in the colour index.

The photometric results for all four fields are displayed as a colour-magnitude diagram in Fig. 3, showing all images, both stars and galaxies. The broad distribution is similar to that found by other authors (e.g. Tyson, 1988, and Metcalfe et al., 1991). The faint blue excess, however, is encountered about one magnitude brighter at any given colour than in many other studies. This effect is found to be pronounced among the 1993 field data, but not those from 1991. That this is not a calibration problem affecting the 1993 data is confirmed by an inspection of the against colour-colour diagram for brighter () images; a majority of the images, which at these magnitudes are expected to contain a significant fraction of stars (50-60%), conform closely (within ) to standard (Bessell 1979, and Bell & Gustafsson 1979, 1989) stellar loci. The problem therefore affects only fainter images - if indeed it is a problem rather than some statistical fluke. While it is expected that random photometric errors will be greater for the 1993 observations due to their shorter integration times, the origin of the difference remains unclear. However, for the purposes of the present study, where colours and magnitudes need to be measured only sufficiently accurately to enable a broad classification, the excess blue tail to the colour distribution at faint magnitudes is unimportant.

Fig. 3. The - B colour-magnitude diagram for the detected images of all fields, showing the candidate the faint blue and the faint red galaxy samples. The solid curve is the locus corresponding to the no-evolution model of Sa-type giants. The dotted curve is the Sa giant locus displaced by an amount corresponding to Bruzual's (1983) models. The dashed line illustrates the predicted completeness limit for the deepest field; all galaxies beyond this limit are rejected from the samples

© European Southern Observatory (ESO) 1997

Online publication: July 3, 1998
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