6 Modeling of the galaxy colour-distributions in B_j-R and R-K

The colour trends seen in the colour magnitude diagrams in Sect. 4.2 are caused by a combination of different stellar populations sampled in galaxies of higher redshift (and therefore observed at fainter magnitudes) and colour corrections introduced through cosmological effects, the so called k-corrections. A method to compute colour distributions taking into account those effects involves the so called pure luminosity evolution models (Gardner 1998; Pozzetti et al. 1996). The data in our surveys give the unique opportunity to compare two observed colour distributions with those models. Our large number of sources allows us to reject models which do not reproduce the observed distribution with a high significance. Note, that in R-K the comparison is not affected by an incomplete coverage of red K-objects in R.

Figure 9: The colour-distribution of galaxies in Bj-R(solid line) in comparison with the distribution of the model described in the text (dashed line)

   
6.1 Modeled colour distributions

This modeling is based on theoretical spectral energy distributions (SEDs) computed with evolutionary synthesis techniques by Bruzual & Charlot (1993). To derive the colour-distributions from the input parameters SED, luminosity function, cosmology and SED-mix (or type mix) we used the program ncmod developed by Gardner (1998). The basic characteristics of the SEDs used in terms of corresponding galaxy type, metallicity, star formation rate, and epoch of first stars $z_{{\rm form}}$ are given in Table 10. The last column indicates whether passive evolution of the galaxy luminosity is taken into account or not. In all models presented here the cosmological parameters $H_0 = 50~{\rm km}\,{\rm s}^{-1}/{\rm Mpc}$, q₀=0.02 and $\lambda_0=0.0$ have been used. Likewise, all models consider internal absorption by dust according to Wang (1991).

For the theoretical distribution of B_j-R we assume the B_j-based luminosity function of Loveday et al. (1992) and a type mix of 0% E1, 10% E2, 10% Sa, 15% Sbc, 45% Scd, and 20% Irr.

In R-K we show two models using the K-luminosity function from Gardner et al. (1997). The type mix is 16% E1, 16% E2, 28% Sa, 29% Sbc, 5% Scd, and 6% Irr for model 1, and 25% E1, 25% E2, 36% Sa, 10% Sbc, 3% Scd, and 1% Irr for model 2.

Figure 10: The colour-distribution of galaxies in R-K(solid line) in comparison with the distribution of the models described in the text (model 1: dashed line, model 2: dotted line)

 

 

Table 10: Description of the SEDs used to model the galaxy colours

type	metalicity	star formation rate	$z_{{\rm form}}$	evolution
E1	2.5 $\times$ solar	exp., $\tau=1~$Gyr	15	y
E2	1.0 $\times$ solar	exp., $\tau=1~$Gyr	15	y
Sa	1.0 $\times$ solar	exp., $\tau=4~$Gyr	15	y
Sbc	0.4 $\times$ solar	exp., $\tau=7~$Gyr	15	y
Scd	0.2 $\times$ solar	const.	15	y
Irr	0.2 $\times$ solar	const.	1	n

6.2 Comparison of modeled and observed colour distribution

Figures 9 and 10 show the comparison between the models and the observed colour distribution in B_j-R and R-K. The data are shown in solid, the models in the dashed and dotted lines. While the observed distributions have been corrected for galactic absorption by $\Delta (R-K) = -0.10~{\rm mag}$and $\Delta (B_j-R) = -0.08~{\rm mag}$ (see Table 1 and Schmidt-Kaler 1982), the theoretical distributions in Figs. 9 and 10 were folded with a Gaussian of $0.2~{\rm mag}$ FWHM in order to mimic photometric errors.

In the comparison between models and data we had to treat the colour distributions in B_j-R and R-K separately since none of the models reproduces the colour distribution in B_j-R and R-Ksimultaneously for a single luminosity function and type mix.

Figure 9 compares the B_j-R-colour distribution of galaxies in bins of different apparent magnitude B_j to the best fitting theoretical colour distribution (computed as described in Sect. 6.1). The agreement of the models with the data is very good throughout the magnitude range covered. There are small deviations only in the last two panels ( $B_j>22~{\rm mag}$). In the $B_j=22.5~{\rm mag}$ bin an agreement could easily be reached using a broader Gaussian filter, which is justified by the larger photometric errors at the faint end. The last panel at $B_j=23.5~{\rm mag}$ is seriously affected by incompleteness in both B_j and R, which affects the observed colour distribution.

Figure 10 shows the R-K-colour distribution of galaxies together with the two models outlined in Sect. 6.1. Neither model 1 nor model 2 is able to reproduce the observed galaxy colours in R-K over the complete range in apparent magnitude in K. This is caused by the strong evolution of the whole population to redder colours as already demonstrated in Sect. 4.2. While model 1 agrees with the observed distribution at the bright end, but is too blue at the faint end, model 2 agrees at the faint end but is too blue at bright K-magnitudes. None of the models can follow the trend of the observed distributions which become redder by $\sim$1 ${\rm mag}$ in the range $K=13.5-17.5~{\rm mag}$.