5.1 Effective Parameters

For each of the 227 observations, we derived effective radius, ${r_{\rm e}}$, and mean surface brightness within this radius, ${{< \hspace{-3pt} \mu \hspace{-3pt}>}_{\rm e}}$, by fitting an r^1/4 growth curve to the observed aperture magnitudes, ${m_{\rm ell}}(r)$. Only radii in the interval from $3 \cdot {\rm FWHM}$ to the radius where the uncertainty on ${m_{\rm ell}}$ exceeded $0\hbox{$.\!\!^{\rm m}$ }15$ were used for the fit. (FWHM is the seeing, cf. Sect. .) This applies to 215 of the observations. For 10 observations the minimum radius was decreased to $2.5 \cdot {\rm FWHM}$, and for 2 observation also the maximum allowed uncertainty on ${m_{\rm ell}}$ was increased to $0\hbox{$.\!\!^{\rm m}$ }2$. In this way, there was always at least 6 data points available for the fit.

It is important to take the seeing into account when deriving ${r_{\rm e}}$ and ${{< \hspace{-3pt} \mu \hspace{-3pt}>}_{\rm e}}$ (Saglia et al. 1993; see also JFK95a). We do this following JFK95a. First an initial guess on ${r_{\rm e}}$ is obtained from a fit that does not take the seeing into account. From the resulting ${r_{\rm e}}$ and the seeing of the data an intelligent guess on the real (i.e. seeing deconvolved) ${r_{\rm e}}$ is calculated. An r^1/4 growth curve corresponding to this ${r_{\rm e}}$ is then convolved with a model PSF that is scaled to the seeing of the data. This growth curve is fitted to the data, giving a new estimate of ${r_{\rm e}}$. The process is iterated until ${\log{r_{\rm e}}}$ is stable to within 0.005. Then ${{< \hspace{-3pt} \mu \hspace{-3pt}>}_{\rm e}}$ is calculated. Since the seeing convolved growth curve depends on ${r_{\rm e}}$ it is important to have a good guess on ${r_{\rm e}}$ to start with, which is why we calculate the above `intelligent guess'. The model PSF is taken to be the Fourier transform of $\exp [ -(kb)^{5/3} ]$ (cf. Wolf 1982; Saglia et al. 1993), which is the theoretical prediction for seeing caused by atmospheric turbulence. b is a scale factor that is proportional to the FWHM.

From the definition of ${r_{\rm e}}$ and ${{< \hspace{-3pt} \mu \hspace{-3pt}>}_{\rm e}}$ it follows that the total magnitude ${m_{\rm T}}$ is given by ${m_{\rm T}}= {{< \hspace{-3pt} \mu \hspace{-3pt}>}_{\rm e}}-5 \log {r_{\rm e}}-2.5 \log 2 \pi$.

At the effective radius in Gunn r the ellipticity ${\varepsilon_{\rm e}}$ and position angle ${{\rm PA}_{\rm e}}$ were determined.

We determined effective colors ${(B-r)_{\rm e}}$ and ${(U-r)_{\rm e}}$ as

$${(B-r)_{\rm e}} \equiv [{B_{\rm ell}}({r_{\rm e,Gunn\,r}}) - {r_{\rm ell}}({r_{\rm e,Gunn\,r}})]$$ (5.1)

$${(U-r)_{\rm e}} \equiv [{U_{\rm ell}}({r_{\rm e,Gunn\,r}}) - {r_{\rm ell}}({r_{\rm e,Gunn\,r}})]$$ (5.2)

where ${r_{\rm ell}}$, ${B_{\rm ell}}$, and ${U_{\rm ell}}$ simply are ${m_{\rm ell}}$ in Gunn r, Johnson B, and Johnson U, respectively. ${r_{\rm e,Gunn\,r}}$ is the effective radius in Gunn r, and for galaxies observed more than once in Gunn r the mean value was used. ${m_{\rm ell}}$ in the three filters were interpolated using a quadratic function to give the values at ${r_{\rm e,Gunn\,r}}$. Note that the elliptical apertures in the different filters are not forced to be the same, but will of course be almost the same. Had we used circular apertures instead of elliptical ones the colors would remain almost the same - the typical difference for ${(B-r)_{\rm e}}$ would be only $0\hbox{$.\!\!^{\rm m}$ }004$.