3 Object counts

3.1 Extended and point-like sources in $\mathsfsl{B_j}$ and R

Figures 1 and 2 display the object counts in B_j and R, respectively. In both figures the counts of point-like sources are marked with open circles, the counts for extended sources are denoted with the filled symbols. We made no attempt to correct the counts beyond the incompletentness of the individual frames. The counts were only derived from fields complete to the specific magnitude. Tables 2 and 3 give the number counts (in $objects/0.5~{\rm mag}/{\rm deg}^2$) B_j and R, respectively. The counts for extended objects are listed in Col. 3 and counts for point-like objects in Col. 5. The fourth column reflects pure Poissonian error of the counts for extended objects. The last column gives the area of the sub-survey complete to the specified depths. To complete the information concerning number counts in our surveys we added the corresponding data for the K-survey in Table 4.

The point-like sources in Figs. 1, 2 and in Tables 2-4 are only given down to the magnitude of reliable classification. The deeper counts of extended objects have been derived by subtracting the expected number of point-like objects from the counts of all objects (see Sect. 2.5 and below). No number densities can be given at the bright end of the point-like sources because the objects saturated the CCD. The solid line in Figs. 1 and 2 shows the theoretically expected stellar counts according to the Bahcall-Soneira model (Bahcall & Soneira 1980; Bahcall 1986). To calculate the model counts in B_j we transferred the original V-counts with the model B-V-colours and equations given by Gullixson et al. (1995). For the R-counts we changed the code according to Mamon & Soneira (1982). No attempts were made to improve the fit to our data by changing the parameters of the model. This is justified by the good agreement between our counts and the model.

The Bahcall-Soneira model does not take into account the so called thick disc introduced by Gilmore & Reid (1983). However, the scope of the comparison done in this paper is not to test a particular model of the Galaxy. The agreement between the counts for point-like objects and the Bahcall-Soneira model is taken as confirmation of the statistical classification applied to the total counts to derive the fraction of extended objects (see Chap. 2.5).

3.2 Number densities of galaxies

Figure 4: The galaxy counts in R from the NEP compared to counts from various other surveys

In Figs. 3 and 4 we compare counts of galaxies at the NEP with published counts from other surveys in B_j and R, respectively. The reference data are from Bertin & Dennefeld (1997), Jones et al. (1991), Huang et al. (2001) and Metcalfe et al. (1991, 1995). All B_j-counts except Huang et al. (2001) were either performed in a B_j-filter or transformed to B_j using equations given by the authors. To the Huang et al. (2001) photometry we applied the transformation $B_j = B-0.19~{\rm mag}$, according to Bertin & Dennefeld (1997) for $B-R=1.0~{\rm mag}$. In the Figs. 3 and 4 the slope 0.5 and 0.4 is subtracted from the logarithm of the counts to expand the ordinate and to make differences between the counts clearly visible. In order to do a quantitative comparison we fitted power-laws of the form

N(mag) = a*10^b*(mag-c) (4)

to the data. Tables 5 and 6 show the results of those fits. Both tables give the literature reference and the survey area, respectively, (in deg²) in the first two columns. The next columns show the slope b, amplitude aand the magnitude range in which the fits were done. In B_j and R the fits were done for $c=22.0~{\rm mag}$ and $20.0~{\rm mag}$, respectively. The faintest magnitude bins are not included in the fit. The numbers in those bins might be affected by Eddington-bias (Eddington 1913), and could influence the fits presented in Tables 5 and 6 significantly since their high values are associated with small (relative) errors.

We fitted different power-laws above and below $19.4~{\rm mag}$ to the R-band data from the NEP, since there is a clear break in the number counts at this level. While the slope is almost 0.5 for the bright magnitudes, it flattens by more than 0.1 towards fainter magnitudes.

The slopes in B_j are in good agreement with other surveys with the exception of Metcalfe et al. (1995). As can be seen in Fig. 3, the change in slope at $B\sim 24$ (Arnouts et al. 1999; Williams et al. 1996) flattens the slope in the deep surveys of Metcalfe et al. (1995). While the slope of the NEP-counts in B_j is comparable to the slope of other surveys to the same limiting magnitudes, the amplitude is at a=566 very low compared to the others, which show values around 720.

In R the NEP-counts clearly resolve the break in the slope at $19.0~{\rm mag}$ leading from 0.5 at the bright counts to 0.37 at the faint end. As is the case in B_j the slopes at the NEP agree well with the other surveys, but the amplitudes are lower.

The main reason for the low amplitudes in both the B_j- and the R-filters can be attributed to the low galactic latitude and therefore high extinction value. While typical extragalactic survey fields used e.g. in Metcalfe et al. (1995) have E_B-V=0.02 the extinction at the NEP is E_B-V=0.05. This can be translated into a fading of $0.12~{\rm mag}$ and $0.07~{\rm mag}$ (Schmidt-Kaler 1982) of the NEP-sources with respect to sources from other surveys in B_j and R, respectively. This is supported by the fact that at the longest wavelength Kthere is no such effect (see Paper I) while the difference in the amplitude is strongest in B_j, the shortest wavelength.

Assuming all of the offset is due to extinction, would lead us to shift our B_j- and R-counts by $\Delta B_j=0.2$ and $\Delta R = 0.15~{\rm mag}$, respectively, corresponding to an extinction of $\Delta E_{B-V} = 0.05$ more than those adopted for the fields observed e.g. by Metcalfe et al. (1995). The extinction at the NEP then would have to be E_B-V=0.07, 0.02 higher than the values from Schlegel et al. (1998) (see Table 1), or the extinction towards the Metcalfe et al. (1995) fields would have to be negligibly small. If the extinction given by Schlegel et al. (1998) is taken into account, the difference between the counts at the NEP and other surveys reduces to an acceptable amount of $\sim$10%.

 

 

Table 5: A quantitative comparison of galaxy counts in different B_j-surveys

survey	area	slope	amplitude	range
Bertin	140	$0.464\pm 0.001$	$663\pm 5$	16.0-21.0
Jones	2.1	$0.442\pm 0.003$	$801\pm 5$	18.96-23.46
NEP	1.0	$0.479\pm 0.005$	$566\pm 7$	14.38-23.63
Metc. $_{{\rm 91}}$	0.079	$0.491\pm 0.009$	$748\pm 27$	18.88-24.38
Huang	0.19	$0.473\pm 0.006$	$764\pm 18$	16.75-24.75
Metc. $_{{\rm 95}}$	0.005	$0.396\pm 0.001$	$1125\pm 143$	22.37-26.87

 

 

Table 6: A quantitative comparison of galaxy counts in different R-surveys

survey	area	slope	amplitude	range
Bertin	140	$0.537\pm 0.001$	$579\pm 3$	14.5-19.5
NEPa	1.0	$0.480\pm 0.020$	$397\pm 30$	14.13-19.38
NEPb	1.0	$0.498\pm 0.044$	$424\pm 54$	17.88-19.38
Jones	3.0	$0.360\pm 0.002$	$448\pm 4$	18.13-22.13
NEPc	1.0	$0.368\pm 0.006$	$368\pm 5$	18.88-22.38
Metc. $_{{\rm 91}}$	0.079	$0.370\pm 0.008$	$432\pm 21$	19.0-23.5
Huang	0.19	$0.357\pm 0.009$	$397\pm 14$	19.25-22.75
Metc. $_{{\rm 95}}$	0.006	$0.399\pm 0.017$	$315\pm 55$	21.75-25.25