7.5.2 The Galaxian Age-Metallicity Relation

In Figure we plot , , and versus . Both and are highly (anti-)correlated with . Part of the age-metallicity relation may be due to measurement errors. This is because the lines of constant age and metallicity are not quite perpendicular to each other in the - and - diagrams (see Fig. ). To quantify this effect, Monte-Carlo simulations are needed. This is planned for a future extension of this work.

is not significantly correlated with . For the combined HydraI+Coma sample, we find %.

A fit to the Mg and Fe age-metallicity relations
for the combined HydraI+Coma sample
gives

and

The `mixed' relation with and , which is what is plotted in Fig. (c-d), gives

We also tried to include a
term
in the age-metallicity relations.
Still for the combined HydraI+Coma sample, a fit gives

and

The terms are highly significant. The two relations look similar, but there is the important difference, that while is correlated with ( %), is not significantly correlated with ( %). Both and are correlated with ( % and %, respectively). There is also the difference, that for the Mg relation the scatter decreases when we add a term, while it

The above restates the result from
Worthey, Trager, & Faber (1995),
that
(a) there is an age-metallicity relation
with a large span in age, and
(b) galaxies of higher velocity dispersion follow an age-metallicity relation
at higher metallicity (or older age).
These authors used
the index C_{2}4668 and several Balmer line indices
(probably
,
,
and
)
to derive mean metallicities and ages,
not
and
(or
and
)
as we did.
It is therefore encouraging that our result is in qualitative agreement
with their result.

Worthey et al. report that they were not able to establish the slope nor the zero point of this age-metallicity-sigma relation. No doubt they could have made a fit to their data, so what they mean is probably that the different indices give different ages and metallicities. For example, they find that an Mg index gives a significantly different age than an Fe index. While we also find our two ages to be significantly different, the size of this difference is small. In accordance with this, the coefficients for ` ' in Eq. () and () are not significantly different. We are not able to establish the true zero point.

We can now revisit two problems raised earlier, namely the interpretation of (a) the intrinsic scatter in the - relation, and (b) the similar intrinsic scatter in the FP in Gunn r, Johnson B, and Johnson U.

If we take the Mg-version of the age-metallicity-sigma relation
(Eq. )
*at face value*
and insert it
in the analytical approximation to the predictions from the
Vazdekis et al. models for
(J97; Eq. ),
we can eliminate either
or
.
We get

where the constants

In a similar manner, we insert the Mg-version of the
age-metallicity-sigma relation (Eq. )
into the analytical approximations to the predictions from the
Vazdekis et al. models for
(Eq. -).
When eliminating either
or
,
the result is

where the constants

The intrinsic scatter in the relation is 0.103 dex in Gunn r. This translates into a variation in of 0.24 dex, or a variation in of 0.19 dex. This is substantially less than the variation needed to explain the intrinsic scatter in the - relation in the same way. Since we do not have a detailed understanding of the origin of these two relations, it might well be, that galaxy formation and evolution made be less well determined from than from mass.

Properties of E and S0 Galaxies in the Clusters HydraI and Coma

Master's Thesis, University of Copenhagen, July 1997

Bo Milvang-Jensen (`milvang@astro.ku.dk`)