7.4.2 The ${ <{\rm Fe}>}$-$\sigma$ Relation

 

$\log { <{\rm Fe}>}$ is also known to correlate with ${\log\sigma}$ (J97), although the scatter compared to the slope is much larger than for the ${ {\rm Mg}_2}$-$\sigma$ relation. For our data, ${ <{\rm Fe}>}$ has been measured for 42 of the HydraI galaxies and 44 of the Coma galaxies. Since our fitting method does not take into account the uncertainties on the individual data points, we exclude galaxies with an uncertainty on $\log { <{\rm Fe}>}$ larger than 0.065, corresponding to a relative uncertainty on ${ <{\rm Fe}>}$ of 15%. 3 galaxies are excluded by this: R293 in HydraI, and D15 and D110 in Coma.

We test if the ${ <{\rm Fe}>}$ indices and the velocity dispersions are significantly correlated by means of Spearman rank order tests. For our HydraI, Coma, and HydraI+Coma samples we find ${P_{\rm no\;corr.}}$ = 8.6%, 16.0%, and 3.6%, respectively. ${P_{\rm no\;corr.}}$ is the probability of no correlation. J97 found ${P_{\rm no\;corr.}}$ = 0.18%. Thus, it is clear that there is actually a ${ <{\rm Fe}>}$-$\sigma$ relation. However, J97 found that it was driven by galaxies with low and high $\sigma$. Specifically, she found that when excluding galaxies with ${\log\sigma}$ outside the range 2.0-2.4, there was no significant correlation between $\log { <{\rm Fe}>}$ and ${\log\sigma}$. For our HydraI+Coma sample we find the same to be the case: ${P_{\rm no\;corr.}}$ increases from 3.6% to 42% when we omit the 24 galaxies with ${\log\sigma}$ outside 2.0-2.4.

We test if the two samples follow the same ${ <{\rm Fe}>}$-$\sigma$ relation in the same way as done above for the ${ {\rm Mg}_2}$-$\sigma$ relation. For the HydraI and Coma samples we find $\Delta({\rm slope}) = -0.032 \pm 0.083$ and $\Delta(\mbox{zero point}) = 0.019 \pm 0.011$. The differences are not significant. When we fit the two samples together we get

$$\arraycolsep=2pt % \begin{array}{lllllll} {\rm HydraI+Coma} &... ...}=0.050 \quad & N=83 \\ & & & \pm & 0.041 & & \\ \end{array}$$ (7.17)

J97 found a slope of $0.075 \pm 0.025$ for 187 E and S0 galaxies mainly in clusters, consistent with our value. We note, that had we excluded the very deviating galaxy NGC4853 we would have got a slope of $0.095 \pm 0.043$, still in agreement with J97. The ${ <{\rm Fe}>}$-$\sigma$ relation is shown in Figure .