8 Galaxy number counts

The number counts serve as a quick check of the approximate photometric calibration and for the depth of the data. We did not put much effort in star-galaxy separation at the faint end, where the galaxies dominate the counts anyway. At the bright end, where SExtractor is able to disentangle a stellar and a galaxy profile, we derived limits by investigating the class-FWHM diagram for the objects. In the following figures, the counts for all objects are shown as dashed histograms, while for the solid line histograms obvious stellar objects have been omitted. The magnitudes are given in the Vega-system. The number counts are given only for the area with maximum integration-times (weight-map $\approx$1) for the optical data and for ${\rm weight-map} \ga 0.25$ for the NIR-data (i.e. we exclude the edges of the fields). They are not corrected for incompleteness. Also indicated is the 50% completeness limit for the detection of point sources. For each filter we also included for comparison number-magnitude-relations obtained in earlier observations which are compiled and transformed to standard filter systems in Metcalfe et al. (2001) for the optical filters. In all cases we plot raw number counts only, i.e. we do not correct for incompleteness at the faint end.

Figure 5: Galaxy number counts of the FDF in the U band (not corrected for incompleteness) as compared to other deep surveys. The vertical dash-dotted line indicates the 50% completeness limits.

Figure 6: Galaxy number counts of the FDF in B band (not corrected for incompleteness) as compared to other deep surveys. The vertical dash-dotted line indicates the 50% completeness limits.

Figure 7: Galaxy number counts of the FDF in R band (not corrected for incompleteness) as compared to other deep surveys. The vertical dash-dotted line indicates the 50% completeness limits.

Figure 8: Galaxy number counts of the FDF in I band (not corrected for incompleteness) as compared to other deep surveys. The vertical dash-dotted line indicates the 50% completeness limits.

Figure 9: Galaxy number counts of the FDF in J band (not corrected for incompleteness) as compared to other deep surveys. The vertical solid line indicates the 50% completeness for the shallower exposed part of the field, whereas the vertical dash-dotted line indicates the 50% completeness for the deeply exposed part of the field.

In the U-band the FDF is 50$\%$ complete to U = 25.64 mag for a point source. The slope agrees with earlier measurements (roughly 0.4-0.5) for U<23 and it becomes shallower (0.35 at U=23-25), in agreement with the slopes of the HDF-S, WHDF and Hogg et al. (1997) (see Metcalfe et al. 2001). In Fig. 5 we have transformed the HDF number counts as proposed by Metcalfe et al. using $F_{\rm 3oo,Vega}=U-0.4$ and Table 5 in their paper. We further assume $U_{\rm WHDF}\approx U$ to include the WHDF U-band-raw counts (Table 4 of Metcalfe et al. 2001) - in fact the central wavelengths and the transmission curves of the U filters used for the FDF and WHDF observations are similar. The values of Hogg et al. (1997) have been obtained from their Fig. 3 and been transformed as proposed by Metcalfe, $U\approx U_{\rm Hogg}+0.08$. The HDFN/S and WHDF number counts are not corrected for reddening (Metcalfe, private comm., $E(B-V)_{\rm WHDF}\approx 0.02$which is similar to the FDF and thus would shift the number counts by $\approx$-0.1).

Our B-band number counts (Fig. 6) are 50$\%$-complete at 27.69 mag. Within the field-to-field variations they agree well with the HDFS/N (we follow Metcalfe et al. (2001) and use the transformation $F_{450,\rm Vega} \approx B -0.1$) and the raw-counts in the NTT deep field (Arnouts et al. 1996). We also included the raw counts in the Herschel deep field, assuming $B_{\rm FDF}\approx B_{\rm WHDF}$.

For the g-band, we just show our results in Fig. 10 without comparison, since no adequate number counts have been presented in the literature for this passband. Our estimated 50% completeness limit is 26.86 mag in this filter.

Figure 10: Galaxy number counts of the FDF in g band (not corrected for incompleteness). The vertical dash-dotted line indicates the 50% completeness limits.

Our R-band and I-band data are $50\%$-complete at 26.68 mag and 26.37 mag, respectively. Amplitude and slope agree well with previously published fields. For the transformation of the HDF-counts we followed Metcalfe et al. 2001) and used $R\approx R_{606,\rm Vega}-0.1$ and $I\approx I_{814,\rm Vega}$; we also assumed that $R \approx R_{\rm WHDF}$. The counts are shown in Figs. 7 and 8.

Figure 11: Galaxy number counts of the FDF in Ks band (not corrected for incompleteness) as compared to other deep surveys. The vertical solid line indicates the 50% completeness for the shallower exposed part of the field, whereas the vertical dash-dotted line indicates the 50% completeness for the deeply exposed part of the field.

Our number counts in the J-band (Fig. 9) agree with those derived by Saracco et al. (1999), and precisely match those of Teplitz et al. (1999). The completeness is 22.85 mag and 23.60 mag for the shallower and deeply exposed (factor of four in integration time) part of the field, respectively. Our number counts in the K-band (Fig. 11) agree well with those of Kümmel & Wagner (2001) and Huang et al. (1998). The completeness limits are 20.73 mag and 21.57 mag for the shallow and deep exposed part of the field. For fairly shallow J and K pointings ($J\la 22$ and $K\la 20$) the field-to-field variations are expected to be significant for our field size, since the distribution of massive, old systems dominating the NIR frames varies considerably on small scales. This has been demonstrated e.g. in the different pointings of the MUNICS survey by Drory et al. (2001). The agreement with other surveys is good and the quoted detection limit correspond to the 50% completeness limit of our sample.

Acknowledgements

We thank the Paranal and NTT staff at ESO for their excellent and very efficient support at the telescope. We also thank the referee (Dr. M. Franx) for his constructive comments. This work has been supported by the Deutsche Forschungsgemeinschaft (SFB 375, SFB 439), the VW foundation (I/76520) and the German Federal Ministry of Science and Technology (Grants 05 2HD50A, 05 2GO20A and 05 2MU104).

We have made use of the Simbad Database, operated at CDS, Strasbourg, France, and the NASA/IPAC Extragalactic Database (NED), operated by the Jet Propulsion Laboratory, California institute of Technology under contract with the National Aeronautics and Space Administration.