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Astron. Astrophys. 353, 479-486 (2000)

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2. Data analysis

Coma galaxy counts and LF have been computed from the photometry presented in Andreon et al. (1999), to which we defer for details (hereafter Paper I). In summary, a [FORMULA] arcmin region of the Coma cluster, located [FORMULA] arcmin from the centre, have been imaged with the Moicam camera at the 2.0m Bernard Lyot telescope at Pic du Midi. Images were taken in the H band under moderate to good seeing conditions (i.e. [FORMULA] arcsec), with average exposure time of [FORMULA] sec. About 300 objects have been detected and classified by Sextractor version 2 (Bertin & Arnouts 1996) in the best exposed part of our mosaic ([FORMULA] arcmin2).

Different magnitudes are presented in Paper I. We adopt here the Kron magnitudes (see Kron 1980 for the exact definition, and Bertin & Arnouts 1996 for the software implementation). They are defined as the flux measured in a region which area is adapted to each galaxy. Unfortunately, they depend sensibly on the determination of the object size, in particular for faint objects, and therefore, for faint objects we prefer aperture magnitudes. More precisely, we adopt, as a measure of the magnitude for a galaxy, the magnitude computed within 2.5 Kron radii for galaxies brighter than [FORMULA] mag, and aperture magnitudes (within 10 arcsec aperture) for fainter galaxies. The two quantities are identical, within the errors, for galaxies in a large magnitude range including [FORMULA] mag (Paper I). The catalog is complete, in the 10 arcsec aperture magnitude, down to [FORMULA]-17.2 mag 1. To be safe and for easy computation, we cut the catalog at [FORMULA] mag. Given the galaxy catalog and the knowledge of the surveyed area, galaxy counts in the Coma direction are computed straightforwardly. They are presented in Fig. 1 (open dots), as derived for objects identified as galaxies (see Paper I for details).

[FIGURE] Fig. 1. Galaxy counts as a function of the apparent H magnitude. Open dots are the counts in the Coma cluster direction, solid triangles are counts in the HDF South 1 & 2 directions. The center of the strip marks the average K counts converted in H assuming [FORMULA]. The strip width corresponds to a background variance of [FORMULA], the typical value for the area surveyed in Coma. The solid line histogram gives for comparison the expected counts from our model. See text for details. Error bars are computed according to Gehrels (1986). Bins are 1 magnitude wide. The abscissa is given by Kron magnitudes for bright galaxies and aperture magnitudes for faint galaxies.

The Coma cluster LF is computed as the statistical excess of galaxies in the Coma cluster direction with respect to other directions. In order to estimate the fore and background contribution of the field, we use when possible observed values measured by different authors, as well as a simple standard model for number counts, based on pure luminosity evolution for galaxies (see Rocca-Volmerange & Guiderdoni, 1990, Pozzetti et al. 1996 and Pozzetti et al. 1998) and computed through the Bruzual & Charlot evolutionary code (1993, updated as GISSEL98). The parameters of the counts model have been set up in order to roughly reproduce the observed number counts to B = 28 mag (Williams et al. 1996), and normalized to the observed counts at [FORMULA] mag. This model is only used in order to derive the mean redshift of the dominant population at a given magnitude, when comparing with other LF estimates, computed with other filters.

Field counts have been measured on the H band images of the Hubble Deep Field South 1 & 2 (hereafter HDFS1+S2), presented in Da Costa et al. (1999). These images were taken at the NTT and they are much deeper (several magnitudes) than our Coma images, but extending to a smaller region and exposed in a non uniform way. We have used their uniformly exposed part, a central region [FORMULA] pixel wide (i.e. [FORMULA] arcmin2 large, thus more than 10 times smaller than the Coma area studied in this paper). We have detected and classified objects in this HDFS1+S2 area by means of Sextractor (Bertin & Arnouts 1996), using the same parameters as in Paper I. Fig. 1 presents the resulting counts (closed triangles). At [FORMULA] mag, field counts have large errors because the HDFS1+S2 is not tailored for measuring galaxy counts at such bright magnitudes, but for going deep on a small region. This fact prompts us to look for a H band survey more adapted to our aims, i.e. shallower and wider. Since it does not exist, we get a different estimate of the H band galaxy counts using K band galaxy counts and assuming a mean [FORMULA] color for galaxies in the relevant magnitude range. The observed color of [FORMULA] mag galaxies is [FORMULA] mag (Stanford et al. 1995). This value is also in fairly good agreement with the mean [FORMULA] expected from the counts model ([FORMULA] mag to [FORMULA] mag, where the population is dominated by galaxies with [FORMULA] at [FORMULA] mag, and with [FORMULA] at [FORMULA] mag). We apply the mean [FORMULA] value to the Bershady et al. (1998) compilation of K band surveys. These counts are presented in Fig. 1 as a strip with center given by the average counts presented in their paper. There are also presented in Fig. 1 the expected number counts derived from our model (solid line histogram). In spite of unavoidable differences between the types of magnitude used by the different authors, and also the approximations involved in the conversions between photometric systems, the agreement between the galaxy counts in the HDFS1+S2 direction and the H counts estimated from K counts is very good. They are also in good agreement with the counts derived from our simple model. We adopt these counts as average background counts in the Coma direction.

An expected and important source of error in the LF determination is the background variance from field to field, in addition to Poissonian fluctuations: if the background variance is high, then the background in the Coma direction could be significatively different from the average computed above. Among the K band shallow surveys, two of them are adapted to roughly compute the order of magnitude of this variance. Gardner et al. (1993) presented galaxy counts for the HMDS (Hawaii Medium Deep Survey) extending over an area which is only half of that sampled for Coma, and also for the HMWS (Hawaii Medium Wide Survey), extending over a much wider area than the present one. The counts in the two surveys show a [FORMULA]% scatter, and we adopt this value as a typical fluctuation for the background (to be added quadratically to Poissonian fluctuations). The amplitude of the strip in Fig. 1 shows this scatter. This background variance seems plausible for two reasons: first, counts in the HDFS1+S2, which extend on an area [FORMULA] times smaller than our one, and [FORMULA] times smaller than the HDMS survey, are well within the strip, showing that background fluctuations are unlikely to be larger than our derived variance. Secondly, the expected field to field fluctuations are [FORMULA]%, according to the formulas (and the hypothesis) in Huang et al. (1997).

Fig. 1 shows that at all magnitudes considered here, the Coma cluster counts have small errors and stand out with respect to the field counts, down to [FORMULA] mag. Therefore, errors on the Coma LF will be small and only slightly affected by the background subtraction. In order to judge on the progress achieved in this paper with respect to previous investigations, the reader can compare our magnitude-counts diagram with the analogous one in Mobasher & Trentham (1998) for a much smaller (and denser) region of Coma. These authors took an observational strategy quite different from ours: given the available telescope time, they went as deep as possible on a very small area, which resulted in a large field to field background variance.

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© European Southern Observatory (ESO) 2000

Online publication: December 17, 1999
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