4 Galaxy colours

Changing slopes in number counts can lead to identifications of additional components contributing to the entire sample of objects, but it is impossible to constrain the nature of such additional components from number counts alone. Surveys in multiple colours provide further insight.

4.1 Matching of the $\mathsfsl{B_j}$-, R- and K-catalogs

The colours of objects are derived by matching the independently produced catalogs in B_j, R and K. For every entry in the R-catalog we searched the B_j-catalog for an object closer than 2'' to the R-position. If there exists such an entry in B_j, The R and the B_j object are considered to be identical, and an entry in the B_j-R-colour catalog is made. The same procedure was applied to the K and R catalogs to assemble the R-K-colour catalog. Finally, we matched the B_j catalog with the colour catalog in R-K to get the full colour information of all objects. Since the magnitudes derived as outlined in Sect. 2.4 are "total'' magnitudes, the colours were calculated as the difference between the magnitudes in each passband.

We took 2'' as the largest distance for the identification of objects in two catalogs. At distances >2'' an increasing number of object pairs would enter the colour-catalogs which are just a positional coincidence by chance of two individual objects in the catalogs of each passband.

   
4.2 The colour-magnitude diagram in $\mathsfsl{B_j-R}$and $\mathsfsl{R-K}$

Figures 5 and 6 show the colour-magnitude diagrams of extended objects in B_j-R and R-K, respectively. In those diagrams the morphological classification is based on the FOCAS-classifier in one filter. For B_j-R we took the classification in B_j, and for R-K the classification in R, since the PSF of the K-images is grossly undersampled (see Paper I). Obviously the statistical extension of the FOCAS-classification for the number counts (see Sect. 3 and Paper I) could not be applied to the individual entries in Figs. 5 and 6.

Because of the misclassification at the faint end $m_{B_j}>23.5~{\rm mag}$(see Sect. 2.5) some actually extended objects in B_j-R were marked as point-like sources. Those sources are not represented in Fig. 5 and the true population is underestimated there. In R-K this effect starts at $R>22.5~{\rm mag}$ and affects only the red faint end in Fig. 5 to a rather negligible degree.

As already argued in Sect. 2.6 sources with magnitudes down to $mag_{{\rm 50}}$ in B_j, R and K enter the colour-magnitude diagrams. The sharp cutoffs in Fig. 5 at the right (faint end) and lower right (blue-faint end) reflect the limited depth of the B_j- and R-exposures. Because of the colour-term in the transformation of the instrumental- to the B_j-magnitudes (see Eq. (1)) the cutoff at the faint end is not parallel to the ordinate. Due to the large difference in the limiting depth of the R- and K-survey the R-cutoff in Fig. 6 is almost unrecognizable in the sparsely populated faint red end of the colour-magnitude diagram.

Objects with unusual colours were individually inspected for errors in the reduction or matching process. Whenever a problem was detected, e.g. a different splitting of neighboring objects in the two passbands or a problem in the determination of the background near bright stars, the objects were excluded from the colour-catalogs. In B_j-R and R-K the numbers of removed objects is 30 and 20, respectively. Therefore all objects in Figs. 5 and 6, even if isolated in colour, are real objects with good photometry and colours. There are $23\,000$ and $4\,900$ points in the colour-magnitude diagrams Figs. 5 and 6, respectively.

Figure 5: The colour-magnitude diagram of extended sources in Bj-R. In the inset median colours and standard deviations for magnitude bins indicated by the horizontal bars are plotted

Figure 6: The colour-magnitude diagram of extended sources in R-K. In the inset median colours and standard deviations for magnitude bins indicated by the horizontal bars are plotted

4.3 The two-colour diagram

Figure 7: The two colour diagram for extended (right) and point-like (left) sources The line drawn in both panels divides point-like and extended objects in the region Bj-R<1.9

Figure 7 shows the two-colour diagram B_j-R vs. R-Kwith the point-like and extended objects in the left and right panels, respectively. As in Figs. 5 and 6 the classification into point-like (5300 objects) and extended sources (4200 sources) in Fig. 7 is based on the FOCAS-classification in the R-band. As in the colour-magnitude diagrams, only objects brighter than $mag_{{\rm 50}}$ in B_j, R, and K were matched and plotted in Fig. 7.

Most of the point-like objects in the left part of Fig. 7 are concentrated along a well defined line of $\sim$0.3 ${\rm mag}$width. While the blue objects are assumed to be halo stars several kpc above the galactic disc, the red objects can be identified as faint M-dwarfs within the disc, in the immediate vicinity of the sun (Bahcall 1986; Robin & Crézé 1986; Baraffe et al. 1998). The two populations are not well separated but are connected with a less densely populated regime at $B_j-R\sim 1.7~{\rm mag}$.

Compared to point-like objects the distribution of extended objects in the two-colour diagram is much broader. Furthermore, the extended objects usually have a redder R-K colour. Following Huang et al. (1997) this allows a separation of point-like and extended objects based on colours alone in the blue part to $B_j-R< 1.6~{\rm mag}$ at both sides of the line drawn in Fig. 7. In the red part such a colour based separation is no longer possible, since the locus of the point-like objects then lies above the separating line in the colour region populated by extended objects. Most of the 10% contamination of unresolved galaxies in our list of point-like objects are likely to have the same distribution in the two-colour diagram as the objects classified as extended. They would hence be the dominant contribution in the sparsely populated regime with blue B_j-R and red R-K colours.

4.4 Colour trends in $\mathsfsl{B_j-R}$ and $\mathsfsl{R-K}$

In order to study the colour evolution we derived the median colour and its standard deviation in bins of apparent magnitude. The values are given in Table 7 and displayed in the insets of Figs. 5 and 6. The horizontal bars mark the widths of the bins in magnitude. For the last two bins in Fig. 5 a standard deviation could not be determined, since a significant population of blue objects are beyond the depth of the R-survey. In a similar way the last bin in Fig. 6 is affected by very red objects being missed in the R-survey. Nevertheless it is possible to put those B_j-objects without R-counterparts at the blue end of the colour distribution to compute the median displayed in Fig. 5.

The median B_j-R colour of the galaxies remains constant at $\langle B_j-R \rangle =1.36$from the brightest objects down to $m_{B_j}=22.3~{\rm mag}$. Then follows a rapid evolution to bluer colours, reaching $\langle B_j-R \rangle =0.92$at the faintest bin. This evolution is triggered by the onset of the population of faint blue galaxies, with $m_{B_j}>22.5~{\rm mag}$ and $\langle B_j-R\rangle <0~{\rm mag}$. While the full population is present down to $m_{B_j}>23~{\rm mag}$, only its reddest part can be seen in Fig. 5 at fainter magnitudes, because the bluer ones have no counterparts in the R-survey.

In R-K there is a steady trend to redder colours towards fainter magnitudes. The median of $\langle R-K\rangle =2.60~{\rm mag}$ at the bright end changes to $\langle R-K\rangle =3.82~{\rm mag}$ at $K=17.8~{\rm mag}$. In the last two bins the evolution to red colours seems to level off with the median colour remaining almost constant.

 

 

Table 7: The median colours ( med_{BjR, RK}) and standard deviations ( $\sigma _{B_jR,RK}$) in B_j-R and R-Kfor magnitudes slices in B_j and K, respectively

Bj-range	medBjR	$\sigma_{B_jR}$	Kj-range	medRK	$\sigma_{RK}$
16.0-18.0	1.27	0.23	10.5-13.5	2.60	0.39
18.0-19.0	1.36	0.35	13.5-14.5	2.74	0.35
19.0-19.5	1.31	0.40	14.5-15.0	2.94	0.60
19.5-20.0	1.23	0.39	15.0-15.5	3.22	0.67
20.0-20.5	1.36	0.45	15.5-16.0	3.38	0.57
20.5-21.0	1.34	0.46	16.0-16.5	3.50	0.66
21.0-21.5	1.38	0.53	16.5-17.0	3.66	0.75
21.5-22.0	1.36	0.59	17.0-17.5	3.79	0.85
22.0-22.5	1.36	0.62	17.5-18.0	3.82	0.87
22.5-23.0	1.28	0.70
23.0-23.5	1.11
23.5-24.0	0.92

4.4 An upper limit to $\mathsfsl{B_j}$ dropouts

An obvious aim for wide-angle surveys is the derivation of number densities of rare classes of objects. Cosmologically important targets are highly redshifted targets which can be identified as drop-out objects when the Lyman edge is redshifted to long wavelengths, out of the bandpass of individual filters. We determine limits to the surface density of candidates for high redshifted objects. This allows constraints on the bright end of the luminosity function of highly redshifted sources. The K-band limits are not faint enough to include R-K colour as selection criterion, and we are confined to the B_j-R index, which does not provide a unique identification of highly redshifted sources. Nevertheless, it is interesting for deep wide-angle surveys to determine the surface density of candidate sources. All R-band sources above the completeness limit of our sample have a counterpart in the B_j catalog. The only exceptions to this are a small number of faint sources close to very bright stars, where the decomposition of faint sources and halo has different efficiency in the two bands (see Sect. 4.2). There are no true drop-outs in our sample. The amount of the decrement at the Lyman break is discussed controversially. For non-active galaxies without Lyman $\alpha$ lines of high EW, a break of about $2.6~{\rm mag}_{{\rm AB}}$ magnitudes has been determined (Steidel et al. 1999). In the filter-system used in our survey, the Lyman $\alpha$-break is between B_j and R for objects with $z\sim 3.8$. Thus all objects with $B_j-R>2.6~{\rm mag}$ can be regarded as candidates for $z\ge 3.8$ galaxies. In Table 8 we give the surface density of those candidates in subsurveys with different depth in B_j. The last column of Table 8 gives the upper limit in absolute magnitude for an object with $R = R_{{\rm lim}}$ at z=3.8. The two values refer to the cosmologies $(q_0, \lambda_0) = (0.5,0.0)$ and (0.1,0.0); $H_0 = 50~{\rm km}\,{\rm s}^{-1}/{\rm Mpc}$, respectively. Out of the 9464 point-like as well as extended sources down to $R=21.0~{\rm mag}$ we detected no B_j-band dropout over the entire $1~{\rm deg}^2$ field. The reddest objects are at $B_j-R\sim 3.5~{\rm mag}$. According to Steidel et al. (1999) Lyman-break colours $G-R > 3.6~{\rm mag}$for redshifts z>4.15-4.45, depending on the extinction. Transforming this criterion to our filter set, we expect colours $B_j-R>3.6~{\rm mag}$ for objects with z>4.35-4.65. Using the formulas given in Steidel et al. (1999) we can compute from the limit in apparent R-magnitude an upper limit for the absolute magnitude of objects at $z\sim 4.5$. Depending on cosmology, there are no objects with $M_{{\rm AB}}(1280~{\rm\AA}) < -25.0,\, -26.2~{\rm mag}$ for $(q_0,\, \lambda_0) = (0.5,0.0),\, (0.1,0.0); H_0 = 50~{\rm km}\,{\rm s}^{-1}/{\rm Mpc}$ respectively.

 

 

Table 8: The density of high redshift candidates from the $Ly_{\alpha }$ decrement in the B_j-R-colour

$B_{j_{{\rm lim}}}$	$R_{{\rm lim}}$	area	$N_{{\rm cand}}$	$\rho _{{\rm cand}}^{\ast}$	$M_{{\rm AB}}(1350~{\rm\AA})$
<24.375	<21.775	0.3	131	451	-24.00, -25.08
<24.125	<21.525	0.8	312	371	-24.25, -25.33
<23.875	<21.275	1.0	287	287	-24.50, -25.58

^* The densities are given in $N{\rm deg}^{-2}$.