Type-dependent luminosity function

In Sect. 5.4 we show the luminosity functions in different redshift bins and filters subdivided into the 4 different SED types described in Sect. 5.2. We chose the redshift binning as described in Tab. 4.1 in order to get good statistics for all analyzed bands: 0.45<z≤0.85, 0.85<z≤1.31, 1.31<z≤1.91,

1.91<z≤2.61, and 2.61<z≤3.81. Furthermore we add a high redshift bin of 3.81<z≤4.51. We follow the same recipe as described in Sect. 3.5.1 to derive the LF for the different types, i.e. we account not only for the statistical errors, but include also the photometric redshift errors. Furthermore we limit our analysis of every luminosity function to the limiting magnitude where the V/Vmaxbegins to contribute by at most a factor of 1.5.

As it is very instructive to follow the type dependent LF evolution not only as a function of redshift, but also as a function of waveband, we show both groupings: In Fig. 5.3, Fig. 5.4, Fig. 5.5, Fig. 5.6, Fig. 5.7, Fig. 5.8, and Fig. 5.9 the luminosity functions are grouped according to the filter for the different redshift bins. In Fig. 5.10, Fig. 5.11, Fig. 5.12, Fig. 5.13, Fig. 5.14, and Fig. 5.15 we group the LF according to redshift for the UV (1500 ˚A, 2800 ˚A), u’, g’, r’, and i’ bands (we do not show the z’-band, as it behaves like the i’-band). In all plots we show the LF for SED type 1 (red dots), type 2 (green dots), type 3 (cyan dots), and type 4 (blue dots). For clarity we connect the dots. The total LF is shown by open black circles. Furthermore, we mark in every plot the best fitting Schechter function of the total number density for our low redshift bin (0.45<z≤0.85) by a dashed line. The redshift binning used to derive the LFs and the filter is given in the upper right and the upper left corner of every figure, respectively.

First of all we can see from the figures in Sect. 5.4 that independent of the waveband the SED type 1 and type 2 do not contribute at all to the LF for redshifts larger than z∼1.9. As the depth of the FDF allows us to detect early-type galaxies down to M_B<_∼−20.5 at z∼1.9 (see Fig. 3.4), the absence of those galaxy is probably real and not due to a selection effect (provided their dust extinction is not exceedingly large). Another argument against a large biasing due to a selection effect is given by Fig. 3.1. There we show that the I-band FDF catalog might be missing only about 10 % of the galaxies that would be detected in a deep K-band selected survey with magnitude limit K_AB≈26 (like in Labb´e et al., 2003).

If we focus on the first two redshift bins (Fig. 5.10 and Fig. 5.11) the errors of the LFs are small for all types and we can see that the number densities of SED type 1 and type 2 galaxies are about the same for all filters. There seems to be no strong correlation with the absolute magnitude, i.e. in the optical bands we see the same number density for bright and faint SED type 1 and type 2 galaxies. If we assume that there is no magnitude dependence of the number-density for SED type 1 galaxies (and exclude the brightest bin in every band), we can derive a mean value of≈0.00034 galaxies per mag per Mpc3 with a typical error of 20% in every waveband for the redshift bin 0.45<z≤0.85. This assumption is justified since the reduced χ_red2 of the fit is about unity (0.8<χ2

red<∼1.8 for all wavebands).

On the other hand, the contribution of SED type 1 and type 2 to the total luminosity function (black open circles) increases from the UV to the z’-band: In the UV the bright end of the LF is purely dominated by SED type 3 and type 4, whereas SED type 1 and type 2 dominate the bright end of the LF in the r’- and z’-band. Moreover, the faint end of the total LFs in Fig. 5.10 and Fig. 5.11 is dominated by SED type 3 and type 4 galaxies in all bands.

The relative contribution of type 1/2 and type 3/4 SEDs to the total LF may also explain the steeper slope in the red bands (Table 4.3) if compared to the blue bands (Table 3.3). We see in Fig. 5.10 and Fig. 5.11 that for the UV bands the bright end of the LF is dominated by the SED of type 3 and type 4. If we look at the LF for increasing wavebands (u0 →g0→r0→i0), the bright end is more and more dominated by SED of type 1 and type 2. On the other hand bright galaxies of SED type 4 decrease in number density very fast for increasing wavebands (u0→i0). This decrease can hardly be compensated by the other SED types. Ergo, the slope of the total luminosity function steepens for

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increasing wavebands (u0 →g0 →r0,i0,z0). For 1.31<z≤1.91 (Fig. 5.12) the contribution of SED type 1/2 to the bright end in the red filters is still non negligible supporting the interpretation of the steeper slope in the red bands (see Table 4.2 for the 3-parameter Schechter fits).

For 1.91<z≤2.61 (Fig. 5.13) and higher redshift the LF is entirely dominated by galaxies of SED type 3 and type 4. The slope as derived by the single 3-parameter Schechter fits (Table 4.2) seems to decrease for the red bands, which also supports the interpretation given before. Please note that since in our high redshift bins withhzi ∼3.2 or higher all the luminosity functions are extrapolations for the red bands (at redshifthzi ∼2.5 restframe r’ roughly corresponds to the observerframe K-band) we have to make a note of caution at this point. One would need deep data at wavelength larger than 2.2µm (K-band) to address this issue in a more quantitative way. This point will be addressed very

soon by the Spitzer (alias SIRTF) satellite (Fanson et al., 1998). Spitzer will obtain images and spectra by detecting the infrared energy, or heat, radiated by objects in space between wavelengths of 3µm and 180µm.