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Astron. Astrophys. 343, L65-L69 (1999)

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3. Analysis and results

3.1. Detection and photometry

Source catalogs from our field in LW2 and LW3 were constructed using the SExtractor package (Bertin & Arnouts, 1996). The detection algorithm searches for 15 contiguous pixels, each having a surface brightness exceeding a threshold (chosen as 1.5 [FORMULA] of the sky noise), after subtracting a smooth background signal and convolving the image with a gaussian filter of the same width as the 7 and 15 µm image PSF. We performed [FORMULA] aperture photometry. Aussel et al. (1998) showed that aperture photometry is very linear above 100 µJy, though at the faintest fluxes the remnants of cosmic rays pollute the sources with a positive bias. The photometry was corrected for loss of flux in the PSF wings, by using measurements of calibration stars under similar conditions (microscanning & rastering): 60% of the signal is found within a [FORMULA] diameter at 7 µm and 48% at 15 µm .

To assess the contribution of noise to our catalogs we ran the detection algorithm on the negative fluctuations in the maps, concluding that we have no false detections above 60 µJy in the central [FORMULA][FORMULA][FORMULA] area of the maps in both filter bands.

Finally, to determine the completeness of the sample we added a template faint source (scaled-down version of a calibration star) to the maps repeatedly at different positions in the map and estimated the efficiency of detecting this source as a function of its flux density. This provided a reliable estimate of the visibility of a faint compact source in the maps. The estimated 80% and 50% completeness limits of the catalogs derived from these simulations are listed in Table 1. These numbers refer to apparent source brightness before lensing correction. They are similar to the deepest observations published to date at 7 µm on the Lockman Hole (Taniguchi et al. (1997) report faintest detections around 30µJy) and at 15 µm on the HDF (where the faintest sources are around 50 µJy). However, thanks to the gravitational magnification of a factor [FORMULA]2 to 10, the sources are intrisically the faintest MIR sources detected to date.


[TABLE]

Table 1. MIR source counts in the image plane, N: number of detected sources, Nneg: number of detected sources on the inverted image


3.2. Cluster contamination

Thanks to our high-resolution images we have been able to unambiguously identify more than 90% of the sources with counterparts in deep NIR and optical (HST/WFPC2 and ground-based) images. The relative astrometric accuracy is found to be better than [FORMULA] in both filters. In only a few cases we do suspect that two sources are blended. There is one obvious case in the 7 µm map, where the straight arc (Pelló et al. 1991) is blended with the nearby elliptical galaxy. Unambiguous cross-identification was possible with detections at other wavelengths thanks to a large density of sources and a good sampling of the PSF, see Fig. 1 (right).

At 7 µm 30 sources are detected. 2 stars and 14 easily identified cluster-member galaxies (Pelló et al. 1991, Leborgne et al. 1992, Abraham et al. 1996). The 5-8.5 [FORMULA]m emission of the cluster galaxies corresponds to 4.5-6.9 [FORMULA]m rest-frame emission. For E/S0 galaxies it corresponds mostly to the Rayleigh-Jeans tail of their old stellar population, as in the Virgo cluster (Boselli et al. 1998). Eleven sources are identified as lensed galaxies. These lensed sources are all detected at 15 µm .

At 15 µm, 34 sources are detected in the central [FORMULA][FORMULA][FORMULA] field. Only three sources are identified as cluster members: the cD galaxy (Lémonon et al. 1998, Edge et al. 1998) and 2 other galaxies. Based upon spectroscopic or photometric redshifts, all the other sources are identified as faint lensed galaxies. All sources for which we have spectroscopic redshifts are background objects. Although we can not rule out some of the other targets being in the cluster, the probability is very small. The detection of almost exclusively background sources in the cluster images demonstrates that at 15 µm the cluster-core becomes transparent, as in Sub-mm bands (Blain et al. 1997). Therefore the key feature is that the cluster-core acts as a natural gravitational telescope amplifying the flux of background sources, typically by a factor of 2.

3.3. Source counts

The number density of sources is high with respect to the size of the FWHM ([FORMULA] diameter at 15 µm). But the PSF is well sampled on the final maps and its shape can be used to separate the sources. With 25 beams per source, confusion should not be too severe. Only two 15 µm sources lie at the location of pairs of suspected high-z galaxies. The occasional blending of the sources has not been taken into account, but the surface area occupied by bright sources is subtracted for the computation of the surface density of the fainter ones (because other faint sources could be hidden by brighter ones). We used the completeness of the detections at 15 µm given in Table 1. This correction is negligible for the 7 µm counts and was not applied.

Due to the non-uniform sensitivity of our maps, because of the combined effects of observation strategy and the lensing, the object density per flux bin was computed using magnification-dependant surface areas derived from the lensing model so dividing the maps into sub-maps. Only the central [FORMULA][FORMULA][FORMULA] area was taken into account for the faintest fluxes.

A detailed lensing model of A2390 has been produced by Kneib et al. (1999). The lensing acts in two ways on the background population of galaxies. It causes:

  • i) an amplification of the source brightness, typically by a factor of 2, but up to 10 in the higher gain regions.
  • ii) a surface dilation effect of the area probed, which itself depends on the redshift; the space dilation is stronger towards the centre (core of the cluster) and increases with source-plane redshift.

To estimate these factors we used the spectroscopic redshift for 7 objects (Pelló et al. 1991, Bézecourt & Soucail 1997), and for the rest we use the best redshift estimate obtained with photometric redshift techniques (Pelló, private communication), and/or lensing inversion techniques (Kneib et al. 1999). By analysing the case with all background galaxies at a mean redshift [FORMULA], we checked the dependence of the results on redshift uncertainties.

By correcting for the lens magnification and surface dilution effects, contamination by cluster galaxies, and non-uniform sensitivity of our maps, we can derive number counts at 15 µm to compare with blank sky counts (e.g. in the Hubble Deep field and Lockman Hole). The 7 µm number counts are more difficult to derive due to the larger contamination by the cluster and because of the small number statistics.

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© European Southern Observatory (ESO) 1999

Online publication: March 1, 1999
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