When interpreting the data described above one has to keep in mind
that for local (
)
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 MB of
all high-redshift FDF galaxies as well as MB for the local starburst galaxies.
For the local objects the MB was taken from Heckman et al. 1998
(transformed to the cosmology used in this paper),
for the FDF galaxies we
computed MB 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
0.2 mag. Absolute magnitudes were derived assuming the
cosmology parameter H0=67,
,
.
Our MB 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
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
and the luminosity that could cause
the correlation with z found in this paper.
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
(which is
MB = -22.36 mag; solid line in Fig. 8).
In our sample we
only find galaxies brighter than this limit for
.
Their
average values of the measured
and the mean error at redshift 2.4 and 3.3 as well as the
single
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
.
Furthermore we investigated all galaxies fainter than
MB = -21.52 mag
(brightest local galaxy) and brighter than
MB = -20.38 mag
(faintest galaxy with
). The average values of the measured
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
on redshift
is not caused by a luminosity effect.
Moreover the two open symbols in Fig. 4 for
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:
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