Standard procedures have been used, with the ESO-Midas reduction package, to flatfield the spectra (using exposures taken on the illuminated dome) and to transform the abscissae into wavelength (with calibration He- and Ne-lamp spectra); the calibration spectra taken before and after each long exposure on a galaxy were checked for possible wavelength shift by a cross-correlation routine, and the result was considered acceptable for a shift smaller than a third of a pixel.
For the determination of the galaxy center, we have calculated the photometric
profile by averaging the pixel luminosities in the direction of the dispersion,
and we have adopted the position provided
by a gaussian fitting on a range of 10 pixels (
)
around the brightest point. This is close to the photometric center but,
obviously, this choice involves a part of arbitrariness,
since there is evidence for a slight asymmetry in some objects.
We have used a Fourier-Fitting technique similar to that of Franx et
al. (1989) for the simultaneous determination of the velocity
dispersion , and the rotational velocity V(r) at distance r
from the center; also determined was a parameter
related to the
absorption-line contrast with respect to an approximation of the continuum,
represented by a third-order polynomial fitting to the spectrum.
For the outer, faint spectra of a galaxy, removing the cosmic-ray hits was
done by a median filtering perpendicularly to the dispersion. For the inner
spectra, for which this procedure would have degraded the spatial resolution,
we relied instead on a three-sigma klipping on the residuals between the galaxy
spectrum and the (shifted and convolved) star spectrum: the V and
parameters were actually determined by two successive steps, the first using
the raw galaxy spectrum, and the second the spectrum with cosmic rays removed
as explained.
In order to enhance the S/N ratio of outer spectra, adjacent lines were
averaged: for a spectrum at radius r, a weight was assigned to the neighboring
lines () entering the average; for this weight, a gaussian
fall-off as a function of
was chosen, with a FWHM width between 0 and
3 pixels (0 and 3.5''); the central spectrum was never averaged. The two
successive spectra obtained at the same position angle were either co-added
before running the Fourier-Fitting code, or processed independently; in the
latter case, the
and V profiles were combined. The two approaches
have yielded very similar results.
For most galaxies, profiles of and the rotational velocity
V(r) were determined, and
presented in Fig. 1; for the latter, we adopted as the systemic velocity
the radial velocity measured at r=0. The determination of the maximun
rotation
was done as follows: on each semi-major axis, in a
region of reliable measurements, a radius
was determined, where the corresponding
was
thought to represent the maximum rotation,
and we adopted as
the mean of these two values. We note that
this definition bypasses the possible asymmetry of the rotation curve
with respect to the adopted center, and it is likely to provide a fair
approximation to the rotational kinetic energy.
Figure 1: Profiles of rotational velocities and velocity dispersions
Table 3 (click here) shows the values of the central velocity dispersion
and, except for three objects for which the spectra were faint,
the value of
, together with the mean of the two
determinations of
. For the two galaxies with major- and
minor-axis observations, Table 3 (click here) gives as
the average
of the two determinations. Table 4, which is available in electronic form
only, gathers the V and
profiles.