We did not attempt here to standardize the measurements of globular clusters.

Both the spectral resolution of the observation and the intrinsic broadening
of the spectral lines (velocity dispersion) affect the values of the Mg_{2}
measurements.

Corrections for these effect are small and often provided by the authors.
In general the observations are preprocessed to match the Lick/IDS resolution
and are usually normalized to 200 km s^{-1} (see
Gonzales 1993,
and JFK95). Recently
Worthey & Ottaviani (1997) provided an elaborate
mapping of the Lick resolution which is about 8.4 Å at 5300 Å thus
corresponding to instrumental km s^{-1}.
Hence, we did not make any further broadening correction than those already
applied by the authors.

Galaxies show radial (in general negative) gradients in the Mg_{2} index.
Thus, the derived central index depends on the size of the aperture used
during the observations. Therefore Mg_{2} index must be corrected for
the effect of the increasing projected aperture size in the more distant
galaxies which weakens their indices.

In their earlier works 7Sam have used the aperture corrected
values of the observed index, (Mg, given by

(2) |

The correction was calculated using the group velocity, , or heliocentric one if no group can be identified.

Perharps the better way to perform aperture corrections is proposed by JFK95:

(3) |

where is the physical radius sampled by
that circular aperture from which one obtains the same (Mgas through the actual aperture used.
For a rectangular aperture of angular dimensions *x* and *y* radians, and a
galaxy at distance *d*, the equivalent aperture is

(4) |

where the factor 1.025 is introduced by JFK95 to provide a better matching to detailed galaxy models.

For the normalization JFK95 have used a physical radius kpc, which is equivalent to an angular diameter of 3.4 arcsec for the distance of Coma cluster. We adopted this normalisation which corresponds to a mean correction in the whole sample of .

We have used distances based on
flow-smoothed velocity which is defined as the velocity of the cosmologic
flow associated with each galaxy ( km s^{-1} Mpcis adopted throughout this paper).

The flow-smoothed velocity is computed by averaging the velocity
of galaxies found in the neigborhood of any galaxy. This grouping of
galaxies is done iteratively. At each step the size of the neighbouring
region (in radius on the sky and in velocity interval) is computed
from the distribution of the galaxies grouped at the previous step.
The initial size goes from 0.5 Mpc for nearby galaxies to 3 Mpc for
galaxies at the distance of 130 Mpc (9000 km s^{-1}), the initial velocity
interval is 500 km s^{-1}.
The velocities are taken from HYPERCAT (in turn updated from LEDA).
The flow-smoothed velocity is then corrected for the deviations from the
linear flow assuming the three-component velocity field model
(Great Attractor, Virgocentric infall and Local Group Anomaly)
described in Faber & Burstein (1988)
and Burstein et al.(1989).
Thus, for example, for the distance of
Coma cluster the flow-smoothed velocity is 6903 km s^{-1}.

For Local Group galaxies the distances are taken from the literature, in particular from van den Bergh (1989).

We have determined these zero-points, together with a scaling of the error,
in an iterative algorithm. At each step, for each galaxy, we have
computed the error-weighted average Mg_{2} (using the internal error)
and we determined the mean
and rms residual for each dataset after summing over all galaxies.
The mean residual give the zero-point for the considered dataset,
the rms is an estimate of the external error. The comparison between
the external error and the mean internal error allows to re-scale the latter.
The process is iterated after zeropointing and rescaling the internal error.

As a primary dataset at the beginning of the process the most comprehensive subsample from 7Sam is taken - the LICK dataset with 502 measurements for 272 galaxies. The algorithm used is in principle not stable and depends on the subset of objects in common between datasets. Hence, we interactively decided of the relevance of the corrections between each iteraction.

The corresponding values of the mean zero-point corrections, together with their errors and the mean rescaled internal errors, are given for each dataset in the list of the observational parameters (Table 2).

This standardisation could be done for 42 datasets totalizing 1060 galaxies. These datasets and galaxies are flagged in Table 2 and Table 4 respectively. The "standard homogeneous system'' here is the union of all datasets which have been intercompared.

Copyright The European Southern Observatory (ESO)