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

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 ( and ) and related issues. (2): Masstolight ratios, ages, and metallicities. (3): Geometrical parameters ( , , , and ellipticities). (4): Colors. (5): Environment (projected cluster center distances and projected cluster mass densities ).
(1): Structural parameters and related issues. From Table it is seen that for the Coma sample there is a significant correlation with ( %). If we use the residuals from the Coma FP (Eq. ) rather than the Hydra+Coma FP, we find % for (and % for ). For the combined HydraI+Coma sample there may be a correlation with ( %). 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.
may be correlated with ( %). JFK96 found that the residuals from their FP was not significantly correlated (for their data). We find, that for our data there is a significant correlation between the JFK96 FP residuals and , % (and % for galaxies brighter than ). If the samples are selected in , this will cause a systematic effect on the derived distances.
For the Coma [and the combined] sample, is correlated with ( %) and with ( %). Part of this may be `left over' correlation with , as JFK96 noted  for since enters the calculation directly, and for through the  relation. In addition, also has the parameter in common with . Common parameters are discussed further in point (2) below. For the Coma sample, if we use the Coma FP (where the  correlation is less significant), we find for versus and = 3.1% and 8.1%, respectively. These values are indeed larger, but still leaves it as an open question whether the  and  correlations are due to `left over' correlation with only. The values of 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): Masstolight ratios, ages, and metallicities. In Fig. we show versus , , , and . 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  correlation. Recall the definitions of these two quantities, , and . and 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 is only 9. This alone will cause and to be correlated. To assess whether the  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, 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 , , and are based in part on , simulations are also needed to assess to what extend the correlations between these three parameters and are spurious. However, there is the important difference, that unlike , ages and metallicities could have been estimated using e.g. and thus independently of the three FP parameters. (Note that we do not have measurements for our samples.) And since the agemetallicitysigma relation found by Worthey et al. (1995) without using is in qualitative agreement with the relation that we find using , it seems likely that the correlations between and , , and are real.
Unlike for and , we find that is not significantly correlated with , see Fig. . For the HydraI, Coma, and HydraI+Coma samples we find 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 versus the geometrical parameters , , , and . The correlations are marginally significant, with = 2.9%, 3.7%, 9.6%, and 4.7%, respectively. increases with , , and , and decreases with . As JFK96 also found, all the correlations are caused by the 15 galaxies with .
The correlations between 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 zaxis, only. The models predict to increase with and , in agreement with the data. However, JFK96 found that their data did not show a significant correlation between and the relative disk luminosity as their models predicted. (We have not derived estimates of for the HydraI data. To do this, new pseudophotometry 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 versus and . It is seen that galaxies with high ellipticities and large values of have lower mean ages than the rest of the galaxies. Since lower mean ages are found to give positive values of (Fig b), at least part of the  and  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 .
(4): Colors. For the HydraI sample, the color is available for the full sample (N=45), and the colors and are available for a subsample (N=19). The FP residuals are significantly correlated with and , with 0.15% and 0.23%, respectively. See Fig. .
is not correlated with for the full sample ( = 64%), and the hint of a correlation for the subsample ( = 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: , , for the full sample, and for the subsample. If we test for correlations between these four quantities and , we get = 0.01%, 0.04%, 0.01%, and 0.13%, respectively (all with ). If we test for correlations between these four quantities and , we get = 2.1%, 4.5%, 97%, and 16%, respectively (all with ). It seems that all three colors are correlated with , but that only and are correlated with . These correlations should be understood in the light of the agemetallicity[sigma] relation that we have found the galaxies to follow. Note the sign of the  and  correlations: the galaxies get more blue for larger mean ages! See Fig. . This must be due to the countertrend in metallicity more than balances the agetrend for these colors. In summary, the correlations between and some colors but not others are likely caused by the fact that galaxies follow an agemetallicity[sigma] relation and that the different colors have different sensitivities to age and metallicity.
(5): Environment.
Figure shows
versus
and
.
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
,
has been assigned the value
.
is the estimated projected cluster mass density,
derived from
(7.35) 
Figure (d) could indicate, that galaxies with large values of , say , do not follow the same  relation as the rest of the galaxies. However, the number of galaxies with is only about 15.
Figure shows versus 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  correlation is caused by an intracluster 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 intracluster medium would probably be destroyed by the hot ( 48 keV) intracluster gas on a fairly short time scale. The Johnson U data only span a small range in , and even though no correlation between and is found, this is not in contradiction to the results in Gunn r and Johnson B.
Is the  correlation caused by the age and metallicity correlations? We find not to be significantly correlated with , , and ( = 21%, 13%, and 63%, respectively). However, this could be due to a somewhat limited range in  our data only go to = 5.5. J97 had data out to very low densities, = 4, and found significant  and  correlations. These imply that metallicity and/or age is correlated with . Therefore, it is possible that the  correlation is caused by the age and metallicity correlations.
Finally, and not in the context of correlations with , we investigate whether is correlated with . J97 found to decrease about 0.1 dex between = 4.5 and 7. In Fig. we plot versus and . Our HydraI sample does not show a  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 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 5.0. From our data alone, we cannot claim a firm detection of a  correlation, but this is not in contradiction to the correlation found by J97.
Properties of E and S0 Galaxies in the Clusters HydraI and Coma
Master's Thesis, University of Copenhagen, July 1997
Bo MilvangJensen (milvang@astro.ku.dk)