## 5. The relations between the measured parametersIt is well known that the observational parameters describing
spiral galaxies are correlated, in such a way that two quantities can
describe most of the variance in the parameter space. In his
pioneering analysis, Brosche (1973) used the method of the Principal
Component Analysis (PCA) to study the data (morphological type,
optical size, color, absolute luminosity, maximum rotation velocity
and HI mass) of 31 spiral galaxies. He found that the parameter space
has two significant dimensions. Bujarrabal et al. (1981) also used the
PCA to study a sample of 100 objects
with optical and radio data and also conclude that 2 parameters could
suffice to describe the data: Even if the PCA has some limitations related with the bias in the results that could be introduced if the number of parameters involved in the analysis is not big enough (Magri 1995), or the fact that it assumes that the correlations among the parameters are strictly linear, it appears as a well suited method to find the minimum number of variables describing the data set we have constructed for isolated spiral galaxies. In our case, given that all possible effects of the interaction are in principle excluded, what could be expected from that kind of analysis is to obtain the bare, intrinsic structural correlations between the parameters. We have already discussed how the inclusion of interacting galaxies could increase the scatter in the relations between parameters. In the same sense, Folkes et al. (1996) have shown that the inclusion of perturbed or peculiar galaxies could produce misleading results, in the sense of smoothing the morphology-spectrum relationship found for normal galaxies. The main result that emerges from the PCA of our data is that the
parameter space has essentially 2 dimensions, in agreement with all
the previous results. The new aspects of our analysis are that till 95
of the variance of the sample is
explained, and the identification of a better suited form parameter.
Indeed, the first
It is the first time that the G-parameter is revealed as equivalent
to the form Indeed, a number of strong linear correlations between parameters does exist. Regarding the photometric data, we have already pointed out that the optical size and the luminosity in each band are well correlated. The disk and bulge parameters, that have been discussed in the previous section, also present good correlation, the tightest being between the surface brightness and the size, both for the bulge (the Kormendy relation), and for the disk. For the bulge parameters, we find , i.e., somewhat smaller slope but compatible with that of the Kormendy relation for other spiral bulges (Andredakis et al. 1995; Hunt et al. 1998) and for ellipticals (Bender et al. 1992). Among the relations involving kinematical parameters, we find a
correlation between V
The new result is the tight correlation between the inner gradient,
G, and the bulge to disk ratio, B/D (Fig. 8) we have found. The slope
is (6.80
0.16)10
The correlation between G and the B/D ratio can in principle be used for distance determination. We notice however that, as just mentioned, the scatter of the relation increases when non isolated galaxies are considered, so only strictly isolated galaxies should be used. © European Southern Observatory (ESO) 1999 Online publication: March 18, 1999 |