7.6 Correlations with the FP Residuals

As mentioned above (p. ), the FP has significant intrinsic scatter. The identification of the source of this intrinsic scatter could provide new insight into the physics of a galaxies, and give more reliable or even more precise distance determinations. We search for this source by searching for correlations between the FP residuals and a number of available parameters.

For the given galaxy we define the residual from the Gunn r FP (Eq. ) as

$${\Delta{\rm FP}}\equiv \log {r_{\rm e}}- 1.35 \log \sigma + 0... ...}+ 0.218 \quad \mbox{(${r_{\rm e}}$\space in kpc)} \enspace .$$ (7.34)

We tested for correlations between ${\Delta{\rm FP}}$ and a number of other parameters by means of either Spearman rank order tests, or for small sample sizes ($N \le 30$) Kendall's tau rank order tests. The results are given in Table  (`significant' correlations) and Table  (`non-significant' correlations). Here `significant' is defined as ${P_{\rm no\;corr.}}< 4.6$%, which corresponds to 2 sigma for a normal distribution. In the case of a significant correlation, the sign of the Spearman rank order coefficient ${r_{\rm S}}$ indicates the direction of the correlation (e.g. ${r_{\rm S}}> 0$: ${\Delta{\rm FP}}$ increases with the given parameter).

 

Table: `Significant' Correlations with the FP Residuals

	HydraI			Coma			HydraI+Coma
Parameter	N	${r_{\rm S}}$	${P_{\rm no\;corr.}}$	N	${r_{\rm S}}$	${P_{\rm no\;corr.}}$	N	${r_{\rm S}}$	${P_{\rm no\;corr.}}$
${\log\sigma}$	45	0.154	31.00%	114	-0.298	0.15%	159	-0.147	6.50%
$\log{< \hspace{-3pt} I \hspace{-3pt}>_{\rm e}}$	45	0.255	9.00%	114	0.130	17.00%	159	0.174	2.80%
${M_{\rm r_T}}$	45	-0.342	2.30%	114	-0.058	54.00%	159	-0.153	5.40%
${\log({\rm Mass})}$	45	0.042	78.00%	114	-0.299	0.15%	159	-0.180	2.40%
${ {\rm Mg}_2}$	42	-0.056	72.00%	113	-0.263	0.53%	155	-0.200	1.30%
${\log(M/L_{\rm r})}$	45	-0.644	<0.01%	114	-0.789	<0.01%	159	-0.751	<0.01%
${\log {\rm age}_{\rm Mg}}$	42	-0.776	<0.01%	113	-0.793	<0.01%	155	-0.795	<0.01%
${{\rm [Mg/H]}}$	42	0.421	0.71%	113	0.469	<0.01%	155	0.461	<0.01%
${{\rm [Fe/H]}}$	41$^{\rm a}$	0.434	0.60%	42$^{\rm a}$	0.472	0.25%	83	0.419	0.01%
${< \hspace{-4pt} c_4 \hspace{-4pt}>}$	45	0.296	4.90%	114	0.136	15.00%	159	0.174	2.90%
${< \hspace{-4pt} c_6 \hspace{-4pt}>}$	45	-0.260	8.50%	114	-0.135	15.00%	159	-0.165	3.70%
${c_{\rm 4}}$	44	0.327	3.20%	114	0.072	45.00%	158	0.133	9.60%
${(U-r)_{\rm e}}$	19	0.716	0.15%
${(U-B)_{\rm e}}$	19	0.712	0.23%
${(B-r)_{\rm e}}$	19$^{\rm b}$	0.526	3.30%
${\log R_{\rm cl}}$	45	0.291	5.30%	113$^{\rm c}$	0.205	3.00%	158	0.227	0.45%
${\log \rho_{\rm cl}}$	45	-0.291	5.30%	113$^{\rm c}$	-0.205	3.00%	158	-0.205	1.00%

 

Notes: This table shows results from Spearman / Kendall's tau rank order tests between the listed parameters and the Gunn r FP residuals (defined by Eq. ). Tests were performed for the HydraI, Coma, and HydraI+Coma samples. Parameters for which ${P_{\rm no\;corr.}}< 4.6$% for at least one of the three samples are included in this table, with the remaining results being given in Table . ${P_{\rm no\;corr.}}= 4.6$% corresponds to 2 sigma for a normal distribution. Values of ${P_{\rm no\;corr.}}< 4.6$% are shown in boldface. Unless otherwise noted, the number of galaxies N was set simply by the the number of galaxies for which ${\Delta{\rm FP}}$ and the given parameter were available. $^{\rm a}$ Galaxies with $\sigma_{\log{ <{\rm Fe}>}}>0.065$ excluded. $^{\rm b}$ Only galaxies with Johnson U photometry selected. $^{\rm c}$ D43/NGC4853 excluded.

 

Table: `Non-Significant' Correlations with the FP Residuals

	HydraI			Coma			HydraI+Coma
Parameter	N	${r_{\rm S}}$	${P_{\rm no\;corr.}}$	N	${r_{\rm S}}$	${P_{\rm no\;corr.}}$	N	${r_{\rm S}}$	${P_{\rm no\;corr.}}$
${\log{r_{\rm e}}}$	45	-0.038	80.00%	114	-0.052	58.00%	159	-0.057	47.00%
${\Delta({ {\rm Mg}_2}\mbox{--}\sigma)}$	42	-0.144	36.00%	113	-0.070	46.00%	155	-0.098	22.00%
$\log { <{\rm Fe}>}$	41	-0.245	12.00%	42	0.087	58.00%	83	-0.108	33.00%
${\Delta({ <{\rm Fe}>}\mbox{--}\sigma)}$	41	-0.306	5.30%	42	0.131	40.00%	83	-0.113	31.00%
${{\rm [Mg/Fe]}}$	41	0.199	21.00%	42	0.034	83.00%	83	0.150	17.00%
${< \hspace{-4pt} c_3 \hspace{-4pt}>}$	45	-0.272	7.10%	114	0.020	83.00%	159	-0.037	64.00%
${< \hspace{-4pt} c_5 \hspace{-4pt}>}$	45	0.150	32.00%	114	0.095	31.00%	159	0.097	22.00%
${< \hspace{-4pt} s_3 \hspace{-4pt}>}$	45	0.027	86.00%	114	-0.097	30.00%	159	-0.082	30.00%
${< \hspace{-4pt} s_4 \hspace{-4pt}>}$	45	-0.080	59.00%	114	-0.056	55.00%	159	-0.056	49.00%
${< \hspace{-4pt} s_5 \hspace{-4pt}>}$	45	0.125	41.00%	114	-0.056	56.00%	159	-0.013	87.00%
${< \hspace{-4pt} s_6 \hspace{-4pt}>}$	45	-0.141	35.00%	114	-0.039	67.00%	159	-0.076	34.00%
${\varepsilon_{\rm e}}$	45	0.133	38.00%	114	0.161	8.80%	159	0.152	5.70%
${\varepsilon_{21.85}}$	45	0.179	24.00%	114	0.156	9.70%	159	0.158	4.70%
${(B-r)_{\rm e}}$	45	0.070	64.00%

 

Notes: See the notes to Table . ${\Delta({ {\rm Mg}_2}\mbox{--}\sigma)}$ and ${\Delta({ <{\rm Fe}>}\mbox{--}\sigma)}$ are the residuals from the ${ {\rm Mg}_2}$-$\sigma$ relation (Eq. ) and the ${ <{\rm Fe}>}$-$\sigma$ relation (Eq. ), respectively.

From Table  it is seen that the FP residuals are significantly correlated with a number of parameters. We will discuss these in the following five groups: (1): Structural parameters ( ${\log\sigma}$ and $\log{< \hspace{-3pt} I \hspace{-3pt}>_{\rm e}}$) and related issues. (2): Mass-to-light ratios, ages, and metallicities. (3): Geometrical parameters ( ${< \hspace{-4pt} c_4 \hspace{-4pt}>}$, ${< \hspace{-4pt} c_6 \hspace{-4pt}>}$, ${c_{\rm 4}}$, and ellipticities). (4): Colors. (5): Environment (projected cluster center distances ${R_{\rm cl}}$ and projected cluster mass densities ${\rho_{\rm cl}}$).

(1): Structural parameters and related issues. From Table  it is seen that for the Coma sample there is a significant correlation with ${\log\sigma}$ ( ${P_{\rm no\;corr.}}= 0.15$%). If we use the residuals from the Coma FP (Eq. ) rather than the Hydra+Coma FP, we find ${P_{\rm no\;corr.}}= 7.0$% for ${\log\sigma}$ (and ${P_{\rm no\;corr.}}= 5.8$% for $\log{< \hspace{-3pt} I \hspace{-3pt}>_{\rm e}}$). For the combined HydraI+Coma sample there may be a correlation with $\log{< \hspace{-3pt} I \hspace{-3pt}>_{\rm e}}$ ( ${P_{\rm no\;corr.}}= 2.8$%). The above may indicate, that the samples deviate from the fitted models (for one cluster a plane, for two clusters two parallel planes). However, to assess whether this also pertains to the underlying distribution from which the samples were drawn, Monte Carlo simulations that take into account selection effects and measurement errors are needed.

${\Delta{\rm FP}}$ may be correlated with ${M_{\rm r_T}}$ ( ${P_{\rm no\;corr.}}= 5.4$%). JFK96 found that the residuals from their FP was not significantly correlated ${M_{\rm r_T}}$ (for their data). We find, that for our data there is a significant correlation between the JFK96 FP residuals and ${M_{\rm r_T}}$, ${P_{\rm no\;corr.}}= 0.01$% (and ${P_{\rm no\;corr.}}= 0.21$% for galaxies brighter than ${M_{\rm r_T}}= -20\hbox{$.\!\!^{\rm m}$ }75$). If the samples are selected in ${M_{\rm r_T}}$, this will cause a systematic effect on the derived distances.

For the Coma [and the combined] sample, ${\Delta{\rm FP}}$ is correlated with ${\log({\rm Mass})}= 2 \log\sigma + \log{r_{\rm e}}+ {\rm const}$ ( ${P_{\rm no\;corr.}}= 0.15$%) and with ${ {\rm Mg}_2}$ ( ${P_{\rm no\;corr.}}= 0.53$%). Part of this may be `left over' correlation with ${\log\sigma}$, as JFK96 noted - for ${\log({\rm Mass})}$ since ${\log\sigma}$ enters the calculation directly, and for ${ {\rm Mg}_2}$ through the ${ {\rm Mg}_2}$-$\sigma$ relation. In addition, ${\log({\rm Mass})}$ also has the parameter ${\log{r_{\rm e}}}$ in common with ${\Delta{\rm FP}}$. Common parameters are discussed further in point (2) below. For the Coma sample, if we use the Coma FP (where the ${\Delta{\rm FP}}$- ${\log\sigma}$ correlation is less significant), we find for ${\Delta{\rm FP}}$ versus ${\log({\rm Mass})}$ and ${ {\rm Mg}_2}$ ${P_{\rm no\;corr.}}$ = 3.1% and 8.1%, respectively. These values are indeed larger, but still leaves it as an open question whether the ${\Delta{\rm FP}}$- ${\log({\rm Mass})}$ and ${\Delta{\rm FP}}$- ${ {\rm Mg}_2}$ correlations are due to `left over' correlation with ${\log\sigma}$ only. The values of ${P_{\rm no\;corr.}}$ for the HydraI sample do not seem to agree with those for the Coma sample; however, this could be due just to the small sample size.

 

(2): Mass-to-light ratios, ages, and metallicities. In Fig.  we show ${\Delta{\rm FP}}$ versus ${\log(M/L_{\rm r})}$, ${\log {\rm age}_{\rm Mg}}$, ${{\rm [Mg/H]}}$, and ${{\rm [Fe/H]}}$. Highly significant correlations are found for all four quantities, both for the HydraI and Coma samples individually and for the combined sample (cf. Table ). The problem is to determine to what extend these correlations reflect intrinsic correlations.

Let us first consider the ${\Delta{\rm FP}}$- ${\log(M/L_{\rm r})}$ correlation. Recall the definitions of these two quantities, ${\Delta{\rm FP}}= \log {r_{\rm e}}- 1.35 \log \sigma + 0.83 \log {< \hspace{-3pt} I \hspace{-3pt}>_{\rm e}}+ 0.218$, and ${\log(M/L_{\rm r})}= -\log {r_{\rm e}}+ 2 \log \sigma -\log {< \hspace{-3pt} I \hspace{-3pt}>_{\rm e}}-0.733$. ${\Delta{\rm FP}}$ and ${\log(M/L_{\rm r})}$ have three common parameters (and nothing but that), and these are combined in a to some extend similar way. Another way of saying this is that the angle between the FP and the plane of ${\log(M/L_{\rm r})}= {\rm const}$ is only 9$^\circ$. This alone will cause ${\Delta{\rm FP}}$ and ${\log(M/L_{\rm r})}$ to be correlated. To assess whether the ${\Delta{\rm FP}}$- ${\log(M/L_{\rm r})}$ correlation that we find is due solely to this, some kind of Monte Carlo simulations are needed. Note, that common parameters per se do not necessarily give a correlation. For example, ${\Delta{\rm FP}}$ is not significantly correlated with x and y (Eq. , p. ). Of course, the planes of constant x and y are both at right angles to the FP.

Since ${\log {\rm age}_{\rm Mg}}$, ${{\rm [Mg/H]}}$, and ${{\rm [Fe/H]}}$ are based in part on $\log(M/L)$, simulations are also needed to assess to what extend the correlations between these three parameters and ${\Delta{\rm FP}}$ are spurious. However, there is the important difference, that unlike $\log(M/L)$, ages and metallicities could have been estimated using e.g. ${ {\rm H}_{\beta}}$ and thus independently of the three FP parameters. (Note that we do not have ${ {\rm H}_{\beta}}$ measurements for our samples.) And since the age-metallicity-sigma relation found by Worthey et al. (1995) without using $\log(M/L)$ is in qualitative agreement with the relation that we find using $\log(M/L)$, it seems likely that the correlations between ${\Delta{\rm FP}}$ and ${\log {\rm age}_{\rm Mg}}$, ${{\rm [Mg/H]}}$, and ${{\rm [Fe/H]}}$ are real.

 

Unlike for ${{\rm [Mg/H]}}$ and ${{\rm [Fe/H]}}$, we find that ${{\rm [Mg/Fe]}}$ is not significantly correlated with ${\Delta{\rm FP}}$, see Fig. . For the HydraI, Coma, and HydraI+Coma samples we find ${P_{\rm no\;corr.}}=$ 21%, 93%, and 17%, respectively.

The direct tests between the FP residuals on the one hand and ages, metallicities, and abundance ratios on the other hand have not previously been discussed in the literature.

 

(3): Geometrical parameters. In Fig.  we plot ${\Delta{\rm FP}}$ versus the geometrical parameters ${< \hspace{-4pt} c_4 \hspace{-4pt}>}$, ${< \hspace{-4pt} c_6 \hspace{-4pt}>}$, ${c_{\rm 4}}$, and ${\varepsilon_{21.85}}$. The correlations are marginally significant, with ${P_{\rm no\;corr.}}$ = 2.9%, 3.7%, 9.6%, and 4.7%, respectively. ${\Delta{\rm FP}}$ increases with ${< \hspace{-4pt} c_4 \hspace{-4pt}>}$, ${c_{\rm 4}}$, and ${\varepsilon_{21.85}}$, and decreases with ${< \hspace{-4pt} c_6 \hspace{-4pt}>}$. As JFK96 also found, all the correlations are caused by the 15 galaxies with ${\varepsilon_{21.85}}> 0.6$.

 

The correlations between ${\Delta{\rm FP}}$ and the geometrical parameters could be caused by the presence of a disk per se, i.e. without assuming the disk to have a different stellar population than the spheroid/bulge. JFK96 studied this by constructing simple axisymmetric galaxy models consisting of a disk with an exponential profile and a bulge with an r^1/4 profile. The intrinsic ellipticities of the disk and bulge were 0.85 and 0.3, respectively, and the two components were assumed to be oblate. The kinematical part of the models assumed the distribution function to be a function of energy and angular momentum around the z-axis, only. The models predict ${\Delta{\rm FP}}$ to increase with ${< \hspace{-4pt} c_4 \hspace{-4pt}>}$ and ${\varepsilon_{21.85}}$, in agreement with the data. However, JFK96 found that their data did not show a significant correlation between ${\Delta{\rm FP}}$ and the relative disk luminosity $L_{\rm D}/L_{\rm tot}$ as their models predicted. (We have not derived estimates of $L_{\rm D}/L_{\rm tot}$ for the HydraI data. To do this, new pseudo-photometry that matches the typical seeing should be produced; see JF94. This has yet to be done.)

It would be interesting to include the possible effects of stellar population differences between the disk and the bulge in the models. It could be, that it is not the presence of a disk per se that is causing the FP residuals, but that the stellar population in the disk differs from the stellar population in the bulge. In Fig.  we plot ${\log {\rm age}_{\rm Mg}}$ versus ${< \hspace{-4pt} c_4 \hspace{-4pt}>}$ and ${\varepsilon_{21.85}}$. It is seen that galaxies with high ellipticities and large values of ${< \hspace{-4pt} c_4 \hspace{-4pt}>}$ have lower mean ages than the rest of the galaxies. Since lower mean ages are found to give positive values of ${\Delta{\rm FP}}$ (Fig b), at least part of the ${\Delta{\rm FP}}$- ${< \hspace{-4pt} c_4 \hspace{-4pt}>}$ and ${\Delta{\rm FP}}$- ${\varepsilon_{21.85}}$ correlations could be explained by this. An elaborate analysis of these matters is beyond the limits of this work.

As mentioned before, E and S0 galaxies have similar FP residuals, with the median difference being $0.000 \pm 0.015$.

 

(4): Colors. For the HydraI sample, the color ${(B-r)_{\rm e}}$ is available for the full sample (N=45), and the colors ${(U-r)_{\rm e}}$ and ${(U-B)_{\rm e}}$ are available for a subsample (N=19). The FP residuals are significantly correlated with ${(U-r)_{\rm e}}$ and ${(U-B)_{\rm e}}$, with ${P_{\rm no\;corr.}}=$ 0.15% and 0.23%, respectively. See Fig. .

 

${\Delta{\rm FP}}$ is not correlated with ${(B-r)_{\rm e}}$ for the full sample ( ${P_{\rm no\;corr.}}$ = 64%), and the hint of a correlation for the subsample ( ${P_{\rm no\;corr.}}$ = 3.3%) could be spurious. An interesting result appears if we test for correlations between the colors one the one hand and either metallicity or age on the other hand. Specifically, let us on the one hand consider the following four quantities: ${(U-r)_{\rm e}}$, ${(U-B)_{\rm e}}$, ${(B-r)_{\rm e}}$ for the full sample, and ${(B-r)_{\rm e}}$ for the subsample. If we test for correlations between these four quantities and ${{\rm [Mg/H]}}$, we get ${P_{\rm no\;corr.}}$ = 0.01%, 0.04%, 0.01%, and 0.13%, respectively (all with ${r_{\rm S}}> 0$). If we test for correlations between these four quantities and ${\log {\rm age}_{\rm Mg}}$, we get ${P_{\rm no\;corr.}}$ = 2.1%, 4.5%, 97%, and 16%, respectively (all with ${r_{\rm S}}< 0$). It seems that all three colors are correlated with ${{\rm [Mg/H]}}$, but that only ${(U-r)_{\rm e}}$ and ${(U-B)_{\rm e}}$ are correlated with ${\log {\rm age}_{\rm Mg}}$. These correlations should be understood in the light of the age-metallicity[-sigma] relation that we have found the galaxies to follow. Note the sign of the ${(U-r)_{\rm e}}$- ${\log {\rm age}_{\rm Mg}}$ and ${(U-B)_{\rm e}}$- ${\log {\rm age}_{\rm Mg}}$ correlations: the galaxies get more blue for larger mean ages! See Fig. . This must be due to the counter-trend in metallicity more than balances the age-trend for these colors. In summary, the correlations between ${\Delta{\rm FP}}$ and some colors but not others are likely caused by the fact that galaxies follow an age-metallicity[-sigma] relation and that the different colors have different sensitivities to age and metallicity.

 

(5): Environment. Figure  shows ${\Delta{\rm FP}}$ versus ${\log R_{\rm cl}}$ and ${\log \rho_{\rm cl}}$. ${R_{\rm cl}}$ is the projected cluster center distance in Mpc, where the center of HydraI is defined as the position of the brightest galaxy R269/NGC3311, and the center of Coma is defined as the mean position of the two brightest galaxies D129/NGC4874 and D148/NGC4889. R269, which has ${R_{\rm cl}}= 0$, has been assigned the value ${\log R_{\rm cl}}= -1.5$. ${\rho_{\rm cl}}$ is the estimated projected cluster mass density, derived from

$${\rho_{\rm cl}}\propto {{\rm Mass}}/{R^2_{\rm cl}}\propto {\sigma^2_{\rm cl}}/{R_{\rm cl}}\enspace ,$$ (7.35)

as done by JFK96. ${\sigma_{\rm cl}}$ is the cluster velocity dispersion in ${\rm km}\,{\rm s}^{-1}$ (from Table , p. ). Our results indicate, that ${\Delta{\rm FP}}$ is correlated with environment. For the combined HydraI+Coma sample, we find ${P_{\rm no\;corr.}}$ = 1.0% for ${\Delta{\rm FP}}$ versus ${\log \rho_{\rm cl}}$. This result also holds for the JFK96 FP coefficients, where we find ${P_{\rm no\;corr.}}$ = 0.57%. JFK96 did not find a significant correlation between ${\Delta{\rm FP}}$ and ${\log \rho_{\rm cl}}$. Note, however, that JFK96 had ten clusters, and the FP zero point was a free parameter for each of them. This could hide a possible correlation between ${\Delta{\rm FP}}$ and ${\log \rho_{\rm cl}}$.

Figure (d) could indicate, that galaxies with large values of ${\log \rho_{\rm cl}}$, say ${\log \rho_{\rm cl}}> 6.75$, do not follow the same ${\Delta{\rm FP}}$- ${\log \rho_{\rm cl}}$ relation as the rest of the galaxies. However, the number of galaxies with ${\log \rho_{\rm cl}}> 6.75$ is only about 15.

Figure  shows ${\Delta{\rm FP}}$ versus ${\log R_{\rm cl}}$ for the HydraI Johnson B and U FPs. It is seen that the behavior in Johnson B resembles that in Gunn r, so the effect does not seem to be very wavelength dependent. This rules out the hypothesis that the ${\Delta{\rm FP}}$- ${\log \rho_{\rm cl}}$ correlation is caused by an intra-cluster dust, since the dust extinction in Gunn r is expected to be only 0.63 times that in Johnson B (Seaton 1979), at least for the kind of dust found in the Milky Way. This hypothesis is also unlikely for other reasons: any dust present in the intra-cluster medium would probably be destroyed by the hot ( $T_{\rm gas} =$ 4-8 keV) intra-cluster gas on a fairly short time scale. The Johnson U data only span a small range in ${R_{\rm cl}}$, and even though no correlation between ${\Delta{\rm FP}}$ and ${\log R_{\rm cl}}$ is found, this is not in contradiction to the results in Gunn r and Johnson B.

Is the ${\Delta{\rm FP}}$- ${\log \rho_{\rm cl}}$ correlation caused by the ${\Delta{\rm FP}}$-age and ${\Delta{\rm FP}}$-metallicity correlations? We find ${\log \rho_{\rm cl}}$ not to be significantly correlated with ${\log {\rm age}_{\rm Mg}}$, ${{\rm [Mg/H]}}$, and ${{\rm [Fe/H]}}$ ( ${P_{\rm no\;corr.}}$ = 21%, 13%, and 63%, respectively). However, this could be due to a somewhat limited range in ${\log \rho_{\rm cl}}$ - our data only go to ${\log \rho_{\rm cl}}$ = 5.5. J97 had data out to very low densities, ${\log \rho_{\rm cl}}$ = 4, and found significant ${ {\rm Mg}_2}$- ${\log \rho_{\rm cl}}$ and $\log { <{\rm Fe}>}$- ${\log \rho_{\rm cl}}$ correlations. These imply that metallicity and/or age is correlated with ${\log \rho_{\rm cl}}$. Therefore, it is possible that the ${\Delta{\rm FP}}$- ${\log \rho_{\rm cl}}$ correlation is caused by the ${\Delta{\rm FP}}$-age and ${\Delta{\rm FP}}$-metallicity correlations.

 

 

Finally, and not in the context of correlations with ${\Delta{\rm FP}}$, we investigate whether ${{\rm [Mg/Fe]}}$ is correlated with ${\log \rho_{\rm cl}}$. J97 found ${{\rm [Mg/Fe]}}$ to decrease about 0.1 dex between ${\log \rho_{\rm cl}}$ = 4.5 and 7. In Fig.  we plot ${{\rm [Mg/Fe]}}$ versus ${\log R_{\rm cl}}$ and ${\log \rho_{\rm cl}}$. Our HydraI sample does not show a ${{\rm [Mg/Fe]}}$- ${\log \rho_{\rm cl}}$ correlation, while there is some evidence of it from the Coma sample. However, there are selection effects that are not well understood for the subsample of the Coma sample that has ${ <{\rm Fe}>}$-data, for example there are few galaxies close to the center. Again, it is important to note that J97 had data out to very low densities, and that the effect found by J97 is large for ${\log \rho_{\rm cl}}<$ 5.0. From our data alone, we cannot claim a firm detection of a ${{\rm [Mg/Fe]}}$- ${\log \rho_{\rm cl}}$ correlation, but this is not in contradiction to the correlation found by J97.