4 Selection of the catalogue

Our low detection threshold led to a large number of detections (more than 4500 on less than 5 arcmin²): it is therefore necessary to evaluate the number of spurious sources. The depth and coverage for each filter is not homogeneous in the field of view, due to the variety of pointings that were combined together. The image depth fades towards the edges of the area covered, as well as in a cross-shaped area between detectors which received much lower coverage than the central region of each chip. As a consequence of the decreased image quality, the outer regions of each image are less reliable: in fact sky RMS is higher than the average one and some sources near the edges revealed at inspection to be spurious. We selected reliable sources by means of criteria based on S/N ratio and comparisons with simulations.

The "Drizzle'' algorithm (Variable-Pixel Linear Reconstruction) used to combine the various pointings preserves photometry and resolution and removes the effects of geometric distortion, but it causes adjacent pixels to be correlated. The pixel-to-pixel noise ( $\sigma_{{\rm sky}}$)therefore underestimates the true noise of a larger area by a factor 1.9. The noise measured on PC field is greater by a factor $\approx2$ than that measured on the WF area. The S/N is then computed by a semi-empirical model (Pozzetti et al. 1998; Williams et al. 1996): $S/N=R/\sigma_{{\rm tot}}$, where R are net counts and $\sigma_{{\rm tot}}^2=R/(\Gamma t_{{\rm exp}})+$ 2$\cdot$1.9 $^2\sigma_{{\rm sky}}^2A_{{\rm obj}}$ for WF sources, $\sigma_{{\rm tot}}^2=R/(\Gamma t_{{\rm exp}})+$ 2$\cdot$4$\cdot$1.9 $\sigma_{{\rm sky}}^2A_{{\rm obj}}$ for PC sources. In the above formulas $\sigma_{{\rm sky}}$ is the pixel-to-pixel sky RMS, $t_{{\rm exp}}$ is the exposure time, $\Gamma$ is the gain expressed in electrons per ADU, $A_{{\rm obj}}$ and $A_{{\rm sky}}$ are respectively the object and the sky isophotal areas (in pixel) used to estimate the local background.

The former term in the sum represents the Poissonian noise due to the source, the latter estimates statistical fluctuations in the mean value of sky, in the Poissonian approximation. The factor 2 is linked to uncertainties in the determination of local background: the correct term would be $1.9^2\Gamma^2\sigma_{{\rm sky}}^2A_{{\rm obj}}^2/A_{{\rm sky}}$, but since $A_{{\rm sky}}$ differs less than 30% by the mean value of $A_{{\rm obj}}$, we considered $A_{{\rm sky}}\approx A_{{\rm obj}}$.

Our detection threshold corresponds to a minimum signal-to-noise ratio of $S/N_{{\rm WF}}=1.34$ and $S/N_{{\rm PC}}=0.67$ for the faintest sources detectable on the WF area and on the PC area respectively.

In Table 2 we report for each filter the zeropoint (AB magnitude, Oke 1974), the sky RMS estimated by SExtractor and the corresponding 5$\sigma$ magnitude limit for a point source.

    Table 2: RMS sky values and 5$\sigma$ magnitude limit for the different bands

Filter	zeropoint	RMS	$m_{{\rm lim}}$
		(ADU/pix) $\times10^{-5}$
F300W	20.77	1.674	28.87
F450W	21.94	2.284	29.71
F606W	23.04	4.126	30.16
F814W	22.09	2.960	29.58

We treated this problem statistically, in the hypothesis that noise is symmetrical with respect to the mean sky value. Operationally we have first created for each filter a noise frame by reversing the original images, in order to reveal the negative fluctuations and to make negative (i.e. undetectable) real sources (Saracco et al. 1999). Then we run SExtractor with the same detection parameter set used to search for sources in the original images detecting, by definition, only spurious sources. Applying a S/N=5 cut off, after removing the edges of the images, we were able to reduce the spurious contamination to a negligible fraction (4%) on the WF area, while such a cut off is not able to reduce spurious detections to a reasonable level on the PC area being them more than 35%. In Fig. 4 the magnitude distribution of spurious sources obtained on the WF area and the PC area in the F606W band are shown. It is clear that the influence of spurious sources on the PC field is still remarkable after applying selection criteria, while the contamination is suppressed in the WF field.

Thus, to avoid introducing such a large number of spurious by the PC data, we restricted the selection of sources to the central WF area only corresponding to 4.38 arcmin². On this area 450, 1153, 1694 and 1416 sources have been selected accordingly to the above criteria in the F300W, F450W, F606W and F814W band respectively, while the raw catalogues had 6093, 4747, 9850, 5229 detections in the same bands.

In every magnitude bin we compared the number of sources in our final catalogue with the number of spurious detections in order to get the contamination of false detection, shown in Table 3.

    Table 3: Percentage of spurious detections in every magnitude bin, as estimated comparing detections on the on reversed (i.e. multiplied by -1) images with detections on real frames, that is percentage ratio of objects detected on reversed frames to sources detected in original frames in every magnitude bin

Pass-band	26.25	26.75	27.25	27.75	28.25	28.75
U300	1	5.8	-	-	-	-
B450	0	0	0.9	1.9	2.9	-
V606	0	0	0	0.3	1	3
I814	0	0.5	0.8	4.2	-	-

Figure 4: Spurious sources, defined as detections on the reversed (i.e. multiplied by -1) V606 image. The upper panel refers to the WF field, the lower panel to the PC field. The solid line represents the initial detections, the dashed line represents spurious sources left after applying our selection criteria

We then removed stars from the sample by using the SExtractor morphological classifier. We defined as stars those sources brighter than I₈₁₄=22 and having a value of the "stellarity'' index larger than 0.9. This choice tends to underestimate stars both at faint magnitudes where no classification is considered, and at bright magnitudes where some fuzzy stars could be misclassified as galaxy. On the other hand this will ensure that our galaxy sample is not biased against compact galaxies. The star "cleaning'' procedure has classified and removed 14 stars at I₈₁₄<22 in agreement with the number of stars found in the HDF-N by Mendez et al. (1998) to this depth and in excess by a factor of two with respect to the prediction of the galaxy model of Bahcall & Soneira (1981).