5 Luminosity effects

When interpreting the data described above one has to keep in mind that for local ( $z\approx 0$) galaxies the metallicities are known to depend on the galaxies' blue and infrared luminosities, with luminous galaxies tending to have higher metallicities (see e.g. Kobulnicky & Zaritsky 1999; Heckman et al. 1998). Since at high redshifts we observe only very luminous galaxies. Therefore, if a metallicity-luminosity correlation exists these bright objects should be metal rich and we should find an opposite correlation between metallicity and redshift than the one detected in this work. To test whether at high redshifts a metallicity-luminosity correlation does exist and may affect our detected metallicity evolution we plotted in Fig. 8 the absolute B-magnitudes M_B of all high-redshift FDF galaxies as well as M_B for the local starburst galaxies. For the local objects the M_B was taken from Heckman et al. 1998 (transformed to the cosmology used in this paper), for the FDF galaxies we computed M_B as follows: We derived the best fitting SED, scaled to the total I flux derived by SExtractor (FLUX_AUTO) as determined by our photometric redshift code (see Bender et al. 2001). Then this SED was transformed to z=0 (using the observed spectroscopic redshift) to derive the rest-frame B-magnitude of the galaxies. Since for the redshift range in question the measured J and K bands bracket the rest-frame B, this procedure is nearly equivalent to an interpolation, minimizing the uncertainties in the K corrections. A detailed description of the method can be found in Gabasch et al. (2002). Using the photometric instead of the spectroscopic redshifts would produce a typical variations of $\pm$0.2 mag. Absolute magnitudes were derived assuming the cosmology parameter H₀=67, $\Omega_m=0.3$, $\Omega_{\Lambda}=0.7$. Our M_B have been corrected for foreground Galactic extinction but not for any internal extinction in the starburst galaxies. From Fig. 8 we see that the local starburst galaxies indeed show the expected correlation between $W_{0}(\mbox{C~{\sc iv}})$ and the luminosity. On the other hand, for the high-redshift galaxies we cannot determine whether a metallicity-luminosity relation does exist or not, since we do not have any faint objects in our high-z sample. But it is evident that the high-redshift galaxies are on average overluminous for their metallicities compared with local starburst galaxies. This agrees well with earlier results from Pettini et al. (2001) and Kobulnicky & Koo (2000) who find this trend for Lyman-break galaxies. Hence, if a metallicity-luminosity relation does exist at high redshifts, our data suggest that it has a clear offset to the local correlation, which seems to evolve with redshift. Moreover, from Fig. 8 it is obvious that for the high-redshift galaxies there is no correlation between the measured $W_{0}(\mbox{C~{\sc iv}})$ and the luminosity that could cause the correlation with z found in this paper.

Figure 8: Measured C  IV $\lambda$ 1550 rest-frame equivalent widths of the local starburst galaxies (open stars) and the high-z FDF (filled symbols) versus the absolute B-magnitude. For the latter ones we indicated objects within the different redshift bins $1 \leq z < 2$, $2 \leq z < 3$ and $z \geq 3$ by filled circles, triangles and squares, respectively. The solid vertical line indicates MB = -22.36 mag, while the dashed vertical lines indicate MB = -21.52 mag and MB = -20.38 mag.

Since at high redshifts we do not have any faint objects in our sample, while in the local universe we do not find bright starburst galaxies, we have to make sure that our detected metallicity evolution with redshift is not produced by comparing different objects at different redshifts. For that reason we separately investigated all galaxies, which are brighter than the faintest one at $z \geq 3$ (which is M_B = -22.36 mag; solid line in Fig. 8). In our sample we only find galaxies brighter than this limit for $z \geq 2$. Their average values of the measured $W_{0}(\mbox{C~{\sc iv}})$and the mean error at redshift 2.4 and 3.3 as well as the single $W_{0}(\mbox{C~{\sc iv}})$ measurement for this brightest local galaxy are additionally indicated by open triangles in Fig. 4. Obviously these subsample show the same trend with decreasing redshift as the total galaxy sample at $z \geq 2$. Furthermore we investigated all galaxies fainter than M_B = -21.52 mag (brightest local galaxy) and brighter than M_B = -20.38 mag (faintest galaxy with $z\geq 1$). The average values of the measured $W_{0}(\mbox{C~{\sc iv}})$and the mean error at redshift 0, 1.5 and 2.4 are also indicated in Fig. 4 by open squares and again show the same trend with decreasing redshift. From these test we conclude that the observed dependence of $W_{0}(\mbox{C~{\sc iv}})$ on redshift is not caused by a luminosity effect. Moreover the two open symbols in Fig. 4 for $z \approx 2.4$ indicate that a metallicity-luminosity correlation also exists at this redshift.

The following additional selection effects could be present (and possibly weaken) the observed correlation between metallicity and redshift at high-z: It could, in principle, be possible that at high-z we preferentially see objects with low internal extinction, which have low dust content and hence low metallicity. In this case we would expect to find a negative correlation between the UV luminosity of our galaxies and their metallicity. To test whether this correlation is present in our high-z galaxies we calculated the UV luminosity as follows:

$$% \log (L_{{\rm UV}}) = \log <F>_{1432}^{1532} +~ \frac{(m-M)}{2.5} + \log \left(4~\pi (10pc)^2\right)$$ (4)

where <F>₁₄₃₂¹⁵³² is the mean flux between 1432 Å and 1532 Å (as defined by Kinney et al. 1993), (m-M) is the distance modulus calculated using the cosmological parameters mentioned above. We did not correct for intrinsic reddening since such a correction would have involved considerable uncertainties and is not needed for the the present test. From Fig. 9, where we plotted the C  IV equivalent widths for the high-z FDF galaxies as a function of $L_{{\rm UV}}$, we see that no such correlation is evident for our high-z objects. Hence our galaxy sample seems not to be affected by this selection effect.