4 Metallicities

Since, in contrast to the variations of the Si  IV line, differences of the C  IV line strength cannot be easily explained by population differences in the starburst galaxies, the observed decrease of the C  IV equivalent width values for z>2.5 in our sample can at present only be interpreted as a metallicity effect. Hence, the decrease of W₀(C  IV) with z is expected to contain information on the evolution of the metal content of starburst galaxies with cosmic age. In order to derive a more quantitative measure of the metallicity evolution apparently observed in Fig. 3, we made an attempt to calibrate the observed $W_{0}(\mbox{C~{\sc iv}})$ values in terms of the O/H ratios. For this purpose we used the oxygen abundances listed in Heckman et al. (1998) for all the local starburst galaxies of this sample and derived metallicities using the relation $\log Z = 12 + \log ({\rm O/H})$.

Figure 7: Metallicity $\log Z/Z_{\odot}$ in terms of oxygen abundance of 36 local starburst galaxies (from Heckman et al. 1998) as a function of the measured C  IV $\lambda$ 1550 equivalent width (open stars). The typical error for $\log Z/Z_{\odot}$ is $\leq$ 0.1 dex. The solid line gives the best linear fit to the data. For comparison the $W_{0}(\mbox{C~{\sc iv}})$ of synthetic starburst spectra (from Leitherer et al. 2001; see Fig. 2) at an age of 100 Myr for solar (filled circle) and LMC (0.25 solar, filled triangle) metallicity have also been included in the figure.

In Fig. 7 we plotted for the local starburst galaxies the metallicity relative to the solar value ( $\log Z_{\odot} = 8.93$) as a function of our measured $W_{0}(\mbox{C~{\sc iv}})$ values. We also included the theoretical values determined for synthetic starburst galaxies with solar and LMC metallicities taken from Leitherer et al. (2001). Although the scatter is rather large (rms = 0.27), the plot indicates a dependence of log Z on $W_{0}(\mbox{C~{\sc iv}})$ which can be approximated by a linear relation. The best linear least square fit to these data gives

$$% \log Z/Z_{\odot} = 0.13 (\pm 0.02) \times W_{0}(\mbox{C~{\sc iv}}) -1.10 (\pm 0.12).$$ (3)

This calibration of the C  IV strength in terms of metallicity should be a reasonable approximation for statistical applications at least for local starburst galaxies and the objects with z<2.5. However, in view of the population differences evident from the different Si  IV to C  IV ratio, its applicability to the z>2.5objects is less clear. Nevertheless, because of the absence of other more reliable calibration procedures, and since (in view of the physics of hot stars) the relation between the C  IV strength and the metallicity should not be much affected by population details of starbursts we will assume for the following that the correlation between the oxygen abundances and $W(\mbox{C~{\sc iv}})$ observed for low redshift starburst galaxies is also valid at high redshifts. With this assumption we convert our observed C  IV equivalent width values to metallicities using Eq. (3). In this way we obtain for our starburst galaxies with z>3 ( <z>  = 3.24) an average metallicity of about $0.16~Z_{\odot}$ and for <z>  = 2.34 a value of $0.42~Z_{\odot}$. The corresponding local (z = 0) value would be 0.56 $Z_{\odot }$. In terms of cosmic time scales (for a universe with $\Omega _{\Lambda } = 0.7, \Omega _{M} =0.3, H_{0}$ = 67 km s^-1 Mpc^-1 used throughout the paper) this would correspond to an increase of the mean metallicity in starburst galaxies by a factor of 2.5 within $\approx$1 Gyr between cosmic ages of about 1.9 Gyrs and 2.9 Gyrs. For later epochs the data suggest only little further enrichment. Because of the approximative nature of Eq. (3) these numbers are rough estimates only. Still, they agree surprisingly well with earlier theoretical predictions of the cosmic chemical enrichment history of the universe by e.g. Fritze-von Alvensleben (1998) and by Renzini (1998, 2000), who predicts that the metallicity had been $\approx$ $0.1~Z_{\odot}$ at z = 3 and has increased to a value of $\approx$ $1/3~Z_{\odot}$ in the local universe.

Two effects may affect the validity of Eq. (3) at high redshifts: First, in the IUE spectra of the local starburst galaxies contributions of the Milky Way halo components are present, while they are absent in the high-z spectra. Savage & Massa (1987) showed that the C  IV equivalent width of distant halo stars are normally <0.5 Å. This is one order of magnitude lower than the values measured in the local starburst galaxies. Hence its effect on Eq. (3) should be on a 10% level, at most. Secondly, the spectrum of the magnified high-z object MS1512-cb58 (z = 2.727) published by Pettini et al. (2000) suggests that the contribution of the interstellar line to the C  IV absorption feature increases with redshift. If this holds for all galaxies at similar redshifts, this could result in a general difference of the mean C  IV equivalent width between local starburst galaxies and high-redshift objects, but it could not explain the observed evolution of the C  IV equivalent width between z = 2.5 and z = 3.5. Furthermore, by applying the local relation to high redshifts we would overestimate the mean metallicity at young epochs.