Appendix. Resolution effects and bulge+disk luminosity mixing

The elements needed for the calculations are the following: a) the respective bulge and disk surface brightnesses; b) their rotation velocities and velocity dispersions; and, c) an estimate of the seeing conditions during the spectroscopic observations. Although an elaborate bulge+disk photometric decomposition was not attempted in the present work, we have been able to set boundaries to the range of possible values for the parameters involved, so that relevant simulations could be performed.

We consider an oblate bulge with a r^1/n luminosity law (Sérsic 1968). Although intrinsically bright bulges are well represented by a de Vaucouleurs law (n=4), small ones are better fit by exponential (n=1) models (Andredakis et al. 1995; Courteau et al. 1996). For the disk, we have assumed that, in the region most affected by resolution effects, its brightness is constant. For each galaxy, this value was estimated on the HS96 V-band photometric profile by extrapolating toward the center the exponential region of the disk; a correction was applied when there was evidence of a "type II'' profile (Freeman 1970). The apparent bulge central brightness was determined on the same photometric profile, after a crude correction to the same seeing conditions as for the spectroscopic observations. Let $\delta_{\rm mag}$ be the apparent, central magnitude difference betweeen the bulge and disk components; $\delta_{\rm mag}$, n and the effective radius $r_{\rm e}$ of the bulge fully determine the photometric structure needed for our calculations. $\delta_{\rm mag}$ is quite easy to determine; we found values from 1 to more than 3 mag arcsec^-2, with an average of 2.4 and a rms scatter of 0.7. But n and $r_{\rm e}$ are more complicated to determine, and we limited ourselves to the definition of the following range of values; for n: between 1 and 4; for $r_{\rm e}$: between a couple of arcsecs and an upper value leading to a profile obviously too bright in the disk region.

For the bulge, a dynamical model similar to that of Prugniel & Simien (1997) has been used, solving the Jeans equations for a r^1/n density law; in the present work, we included an intrinsic flattening ($\epsilon=0.3$ on average), and this resulted into a mean rotation curve determined by the assumed isotropy of the residual velocities. The rotation of the disk has been neglected at the center. For its velocity dispersion, we have adopted a central value connected to that of the bulge: from the data of Bottema (1993), we estimated that $\sigma_{\rm disk}/\sigma_{\rm bulge}=0.5$ for galaxies with a high bulge-to-disk ratio ($\delta_{\rm mag}\gt 2$ mag arcsec^-2), and $\sigma_{\rm disk}/\sigma_{\rm bulge}=0.7$ for galaxies with a smaller bulge.

For each galaxy, after setting the above parameters, we started with $\sigma_{\rm in}$, the velocity dispersion for the bulge model, averaged within $0.1 r_{\rm e}$, and we calculated the resulting disk-contaminated, projected, convolved and rebinned central velocity dispersion $\sigma_{\rm out}$; the calculation was made with different values of $r_{\rm e}$ and n, and we have adopted for $f_{\rm bulge}$the average value of the ratio $\sigma_{\rm out}/\sigma_{\rm in}$; the scatter of this ratio reflects the sensitivity to the parameter values; the typical uncertainty on $f_{\rm bulge}$ is $\pm 0.04$.