1 Introduction

  The existence of the the Fundamental Plane (FP) of early-type galaxies (Djorgovski & Davies 1987) results from very simple scaling relations (de Carvalho & Djorgovski 1989). The equilibrium status of galaxies (Virial Theorem) can be written (Prugniel & Simien 1997):

 

$$k_{\mathrm K}\sigma^2_0 = (2\pi)^{-1}k_{\mathrm S}({\cal M}/L) L r_{\rm e}^{-1},$$ (1)

where $L, r_{\rm e}$ and $\sigma_0$ are respectively the luminosity, the effective radius, and the central velocity dispersion. $k_{\mathrm S}, k_{\mathrm K},$ and ${\cal M}/L$ are the three functions entering in the relations scaling respectively the gravitational energy, the kinetic energy, and the mass of galaxies.

The FP equation has the simple form

 

$$k_{\mathrm S} k_{\mathrm K} {\cal M}/L = L^\beta,$$ (2)

with $\beta$ ranging from 0.2 to 0.1 when going from the B to K-color band (e.g. Djorgovski & Santiago 1993). This weak dependence on the luminosity (the so called "tilt'' of the FP - see Renzini & Ciotti 1993) implies the quasi-linearity of the scaling relations, i.e., the kinetic energy must be almost proportional to $\sigma_0$, the mass to the luminosity, and so on.

Studying the residuals from the FP as a function of other parameters gives insights into the details of the scaling relations. For instance, Prugniel & Simien (1994) expressed the contribution of the rotational support to the total kinetic energy as $k_{\mathrm K} = 1 + 0.81 (V_\mathrm{max}/\sigma_0)^2$. The nonlinearity of the scaling of the gravitational energy (nonhomology of the spatial structure) has also been found by Busarello et al.(1996) (see also Prugniel & Simien 1996). Combined, these two effects account for roughly half the tilt of the FP in the B-band. The scaling of the mass is more complicated since it combines the characteristics of the stellar population to those of the dark halo. However, the correlation between the residuals to the FP and the color or $\mathrm{Mg}_2$ (Prugniel & Simien 1996) indicates a strong contribution of the diversity of the stellar populations to the spread around the FP (Guzmán et al. 1992; Jørgensen et al. 1996). Because of the color-magnitude (and $\mathrm{Mg}_2$magnitude) relations, this accounts for the rest of the tilt of the FP in the B-band. The smaller tilt observed in the near IR (Recillas-Cruz et al. 1990; Scodeggio et al. 1998) confirms this. Then, unless some other unidentified phenomena add other compensatory tilts, the fraction of dark matter can be considered constant in the region probed by this analysis (i.e. within $1\,-\,2\/r_{\rm e}$).

These effects are of interest for the understanding of the physics of galaxies, but are also important when dealing with large-scale streaming, using the FP as a distance indicator (Dressler et al. 1987), since they potentially result in spurious peculiar velocities (e.g. Gregg 1992).

In order to go deeper in the analysis of the connection between the residuals to the FP and the characteristics of the stellar population we are continuing observational programs.

In the present paper we measure the central $\mathrm{Mg}_2$-index for the 87 galaxies already accumulated in our library. This material consists in medium resolution spectra (3.2 Å FWHM), and relevant details on it are given in Sect. 2. In Sect. 3, we describe the measurements method and error analysis and present their reduction to the homogeneous system defined in Golev & Prugniel (1998). A comparison with other series of measurements (Sect. 4), taken from the HYPERCAT database, ascertains the level of reliability of our data and measurement procedure.