8. Conclusions

We have investigated properties of E and S0 galaxies in the central parts of the clusters HydraI (Abell 1060) and Coma (Abell 1656) using large magnitude limited samples. The investigations serve the following main purposes: (1) They add pieces to our knowledge about galaxy formation and evolution, including the formation and evolution of the stellar populations of the galaxies. (2) They help establish a good reference point at $z \approx 0$ needed for the similar studies of high redshift galaxies. (3) They help identify possible limitations in the use of the Fundamental Plane (FP) as a distance determinator.

For the HydraI cluster we have presented CCD surface photometry for 64 E and S0 galaxies. The galaxies have been observed in Gunn r and Johnson B, and for a subset of 22 galaxies also in Johnson U. The observations were made with the Danish 1.5 meter telescope at La Silla, equipped with the DFOSC instrument. The surface photometry was done by fitting ellipses to the images. This gave the radial profiles of surface brightness, ellipticity, and position angle, as well as the deviations from elliptical isophotes described by Fourier coefficients. In addition, the color profiles were derived. From the surface photometry we have derived effective radius, mean surface brightness, and total magnitude by fitting an r^1/4 growth curve. We take the seeing into account. We have also derived global Fourier coefficients. From external comparisons we find the following typical uncertainties: $\log {r_{\rm e}}\!\!: \pm 0.028$; $\log {< \hspace{-3pt} I \hspace{-3pt}>_{\rm e}}\!\!: \pm 0.039$. For the combination that enters the FP we find: $(\log {r_{\rm e}}+ 0.82 \log {< \hspace{-3pt} I \hspace{-3pt}>_{\rm e}}) \!\!: \pm 0.011$.

For the HydraI cluster, the spectroscopical parameters $\sigma$, ${ {\rm Mg}_2}$, and ${ <{\rm Fe}>}$ for 21 E and S0 galaxies have been presented. These data are also from the Danish 1.5 meter telescope and the DFOSC instrument. Together with data from the literature, spectroscopy is available for 51 E and S0 galaxies in HydraI, of which 45 are part of our magnitude limited photometric sample. From external comparisons we find the following typical uncertainties: $\log \sigma \!\!: \pm 0.036$; ${ {\rm Mg}_2}\!\!: \pm 0.013$; $\log { <{\rm Fe}>}\!\!: \pm 0.030$.

From the literature and from work not yet published we have compiled a magnitude limited sample of 114 E and S0 galaxies in the central part of the Coma cluster. All the galaxies have photometry in Gunn r and spectroscopy.

From the analysis of the HydraI and Coma samples we draw the following conclusions:

The FP in Gunn r is not significantly different for the two samples, although differences in the ${\log\sigma}$ coefficient $\alpha$ on the 10% level cannot be ruled out. For the combined sample, we find the FP to be $\log{r_{\rm e}}= 1.35 \log\sigma - 0.83 \log{< \hspace{-3pt} I \hspace{-3pt}>_{\rm e}}+ \gamma$. This is in agreement with most previous studies, e.g. JFK96. The distribution within the FP is not significantly different for the two samples. Based on typical measurement errors derived from external comparisons we find that the FP has an intrinsic scatter of 0.087 in ${\log{r_{\rm e}}}$. The FP zero points imply a non-significant peculiar velocity for HydraI relative to Coma. When we assume Coma to have zero peculiar velocity, we find $v_{\rm pec,HydraI} = -93 \pm 152 \,{\rm km}\,{\rm s}^{-1}$ and $v_{\rm pec,Coma} = 0 \pm 160 \,{\rm km}\,{\rm s}^{-1}$. E and S0 galaxies are found to have FP zero points that are not significantly different (as also found by JFK96), and also the distribution within the FP is not significantly different when taking into account the fact that few (if any) S0 galaxies exist brighter than ${M_{\rm r_T}}= -23\hbox{$.\!\!^{\rm m}$ }1$ (JF94).

For the HydraI sample we find that the intrinsic scatter is not significantly different in Gunn r, Johnson B, and Johnson U. This is in agreement with the findings of JFK96. This implies that the scatter cannot be caused by variations in only the age or only the metallicity. Changes in the age must be balanced to some extent by changes in the metallicity. This is compatible with the age-metallicity-sigma relation that we find (cf. below).

We find that the ${ {\rm Mg}_2}$-$\sigma$ relation is not significantly different for the HydraI and Coma samples. The ${ {\rm Mg}_2}$-$\sigma$ relation for the combined sample is in agreement with previous determinations by Burstein et al. (1988), Bender et al. (1993), JFK96, and J97. The iron index ${ <{\rm Fe}>}$ is also correlated with velocity dispersion (at the two sigma level for the HydraI+Coma sample). The ${ <{\rm Fe}>}$-$\sigma$ relation is not significantly different for the HydraI and Coma samples. For the combined sample, the ${ <{\rm Fe}>}$-$\sigma$ relation is in agreement with J97. As pointed out by J97, the different slopes of the ${ {\rm Mg}_2}$-$\sigma$ and ${ <{\rm Fe}>}$-$\sigma$ relations combined with predictions from stellar population models imply that the abundance ratio [Mg/Fe] increases with velocity dispersion.

For the HydraI sample, we find tight relations between effective colors (measured within a radius of 0.8-53 kpc, typically 3.6 kpc) and ${ {\rm Mg}_2}$ and ${\log\sigma}$ (measured within a radius of 0.5-0.9 kpc and corrected to a radius of 1.2 kpc). This could mean that the variations in radial gradients in colors and line indices from galaxy to galaxy are small (e.g. Burstein et al. 1988, Franx & Illingworth 1990, Bender et al. 1993). However, these tight relations could also be due to the gradients being correlated with e.g. the central values.

We have used the ${ {\rm Mg}_2}$-$\log(M/L)$ and $\log { <{\rm Fe}>}$-$\log(M/L)$ diagrams in combination with predictions from the stellar population models of Vazdekis et al. (1996) to derive estimates of the metal abundances [Mg/H] and [Fe/H], the abundance ratio [Mg/Fe], and ages. These quantities should be understood as luminosity weighted mean values.

The derived abundance ratio [Mg/Fe] increases with the velocity dispersion. This is mainly due to an increase in [Mg/H], with [Fe/H] being constant or slightly decreasing. For high velocity dispersion galaxies [Mg/Fe] is larger than solar and can reach values of 0.3 dex or more. This can be explained by an increase in the fraction of type II supernovae over type Ia supernovae with velocity dispersion. This could for example be caused by a variation in IMF slope or in the time scale for star formation (e.g. Worthey et al. 1992).

Both [Mg/H], [Fe/H], [Mg/Fe], and age show a much smaller scatter for galaxies brighter than ${M_{\rm r_T}}\approx -23\hbox{$.\!\!^{\rm m}$ }1$ (corresponding to ${M_{\rm B_T}}\approx -22\hbox{$.\!\!^{\rm m}$ }0$) than for galaxies fainter than this magnitude. The galaxies brighter than ${M_{\rm r_T}}\approx -23\hbox{$.\!\!^{\rm m}$ }1$ have an old stellar population, with ${{\rm [Mg/H]}}$ a bit above average, ${{\rm [Fe/H]}}$ a bit below average, and thus ${{\rm [Mg/Fe]}}$ somewhat above average. Interestingly, JF94 found ${M_{\rm r_T}}\approx -23\hbox{$.\!\!^{\rm m}$ }1$ to demarcate two classes of galaxies, with the brighter ones showing no signs of disks, and with the fainter ones having a broad distribution of relative disk luminosities.

We find that the ages and metallicities are related, with the metallicity increasing with decreasing age. Further, galaxies of higher velocity dispersion follow an age-metallicity relation at higher metallicity (or older age). The `Mg-version' of this relation is ${{\rm [Mg/H]}}= 1.15\log\sigma - 0.78\,{\log {\rm age}_{\rm Mg}}+ c$. Our results are in qualitative agreement with the ones from Worthey et al. (1995). It is important to note that these authors did not use mass-to-light ratios and ${ {\rm Mg}_2}$ (or ${ <{\rm Fe}>}$) to derive ages and metallicities, but rather Balmer lines indices and the C₂4668 index. One consequence of the age-metallicity-sigma relation is that it allows for a large variation in age and metallicity while still keeping e.g. the FP and the ${ {\rm Mg}_2}$-$\sigma$ relation thin. This was also the conclusion of Worthey et al. (1995). Another consequence is that the FP scatter independent of passband is compatible with the models, which otherwise would not be the case.

To search for the source of the intrinsic scatter in the FP we have tested for correlations between the FP residuals ( ${\Delta{\rm FP}}$) and a number of available parameters. Highly significant correlations are found with [Mg/H], [Fe/H], and age (but not [Mg/Fe]). Therefore, age or metallicity differences can cause systematic errors in the distances determined by the FP. Caution should be exercised when interpreting these correlations, since [Mg/H], [Fe/H], and age in part are calculated from ${\left( M/L \right)}$, which in turn have common parameters with the FP. However, since Worthey et al. (1995) find an age-metallicity-sigma relation in qualitative agreement with our relation without using ${\left( M/L \right)}$, it seems likely that the found correlations reflect intrinsic relations. It would be valuable to quantify these matters by means of Monte Carlo simulations. And it would be very valuable to get e.g. ${ {\rm H}_{\beta}}$ data for our samples, since from the $\log{ {\rm H}_{\beta}}$- ${ {\rm Mg}_2}$ and $\log{ {\rm H}_{\beta}}$- $\log { <{\rm Fe}>}$ diagrams it would be possible to derive ages and metallicities independent of the FP parameters.

We also find weaker ${\Delta{\rm FP}}$-correlations with geometrical parameters ( ${< \hspace{-4pt} c_4 \hspace{-4pt}>}$, ${< \hspace{-4pt} c_6 \hspace{-4pt}>}$, ${c_{\rm 4}}$, and ellipticities) and the colors ${(U-r)_{\rm e}}$ and ${(U-B)_{\rm e}}$. These correlations are at least in part related to the correlations with age and metallicity. In addition we find weak ${\Delta{\rm FP}}$-correlation with the projected cluster mass density ${\rho_{\rm cl}}\equiv {\sigma^2_{\rm cl}}/{R_{\rm cl}}$ (where ${\sigma_{\rm cl}}$ is the cluster velocity dispersion and ${R_{\rm cl}}$ is the projected cluster center distance). This was not seen in the study by JFK96. We do not find that ${\log \rho_{\rm cl}}$ is significantly correlated with age or metallicity. However, the results from J97 indicate that age and/or metallicity are correlated with ${\log \rho_{\rm cl}}$. The reason that we do not find these correlations could be the limited interval in ${\log \rho_{\rm cl}}$ that our data cover. Thus, it is possible that also the ${\Delta{\rm FP}}$- ${\log \rho_{\rm cl}}$ correlation is related to the ${\Delta{\rm FP}}$-correlations with age and metallicity.

For none of the relations studied do we find any significant differences between HydraI and Coma. This is despite the fact that Coma is 2-3 times more massive than HydraI and has a smaller fraction of spiral galaxies. This suggests that the environmental differences between rich and less rich clusters have only a small effect on the properties of the E and S0 galaxies found in clusters as rich as HydraI and Coma.