3 Data reduction

 

3.1 Measurements and errors

  We have used the wavelength-calibrated and sky-subtracted spectra resulting from the kinematical reduction presented in SP. In order to extract the central $\mathrm{Mg}_2$-indices we have integrated the signal in the aperture of 2.2$\,\times\,$5.5 arcsec.

The flux calibration has been performed using spectra of the kinematical template stars common with the KPNO Coudé Feed Spectrophotometric Library (The Jones library - see Leitherer et al. 1996). The spectra in this library are flux-calibrated and can be regarded as "approximately spectrophotometric'' (Worthey & Ottaviani 1997). Seven late-type stars observed by us could be used for that purpose, totalling 11 spectra. The wavelength response of the system (atmosphere + telescope + spectrograph + CCD) was modelled by a second degree polynomial.

This small number of flux calibrators does not allow to perform a monitoring of the change in the atmospheric absorption, hence we determined the error due to the change in the flux calibration by comparing the $\mathrm{Mg}_2$-values obtained with the 11 different response functions. Assuming that the distribution of these 11 calibrations is representative of changes of the flux calibration during the whole runs, we found the corresponding error on $\mathrm{Mg}_2$ to be 0$\hbox{$.\!\!^{\rm m}$}$004.

Recently Worthey & Ottaviani (1997) provided an elaborate mapping of the Lick system resolution which is about 8.4 Å at 5300 Å. Our spectra were transformed to this resolution by convolving them with an appropriate gaussian. The raw values of $\mathrm{Mg}_2$-indices, ($\mathrm{Mg}_2$)$_\mathrm{obs}$, were measured according to the Lick definition (see Worthey et al.1994):

 

$$(\mathrm{Mg_2})_\mathrm{obs} = -2.5 \log \left[\left(\frac... ..._{{\rm I}\lambda}}{F_{{\rm C}\lambda}} {\rm d}\lambda\right],$$ (3)

where $F_{{\rm I}\lambda}$ is the flux (in ergs s^-1 cm^-2 Å^-1) in the Mg H and Mg b which are located at $\lambda\lambda\/5154.125$ - 5196.625 Å. Here the local continuum, $F_{{\rm C}\lambda}$, represents the run of flux defined by a line connecting the flux levels at midpoints of the corresponding blue and red "continuum'' bandpasses (which are actually pseudocontinua) at $\lambda\lambda\/4895.125 - 4957.625$ Å and $\lambda\lambda\/5301.125 - 5366.125$ Å.

For each individual spectrum the Mg₂-index error was first estimated as described in Cardiel et al.(1998), then the flux-calibration error was added quadratically to the obtained value.

We performed a series of tests to determine the sensitivity of our measurements to different sources of errors. The dominant uncertainty comes from the photon noise (typically $\sim\,$0$\hbox{$.\!\!^{\rm m}$}$007). The uncertainty on the flux calibration and on the sky subtraction come after (the overall effect of both these sources of errors is 0$\hbox{$.\!\!^{\rm m}$}$006).

3.2 Velocity dispersion correction

  Using the tabulation in Longhetti et al.(1998), we have adopted the following formula for the velocity dispersion correction:

 

$$(\mathrm{Mg}_2)_{\sigma=0} = (\mathrm{Mg}_2)_\mathrm{obs} + 0.001 \log\/\sigma.$$ (4)

This correction (typically $\sim\,$0$\hbox{$.\!\!^{\rm m}$}$002) is in general well within the errors, but we applied it because it may bias the measurements in a systematic way.

3.3 Aperture correction

  Because galaxies show radial gradients for the $\mathrm{Mg}_2$-index, this index must be corrected for the effect of the increasing projected aperture size in the more distant galaxies which weakens their indices. The aperture correction of the observed index (Mg₂)$_\mathrm{obs}$ was performed as it is proposed by Jørgensen et al.(1995) consistently with the procedures described in Golev & Prugniel (1998) catalogue. The adopted normalized aperture is equivalent to an angular diameter of 3.4 arcsec for the distance to the Coma cluster. The distances were estimated as in Golev & Prugniel (1998).

The mean aperture correction added to the raw measurements is -0$\hbox{$.\!\!^{\rm m}$}$016 with an rms of 0$\hbox{$.\!\!^{\rm m}$}$012. The negative mean correction reflects the fact that our observations sample a physical aperture smaller than the normalisation aperture adopted in HYPERCAT (Golev & Prugniel 1998). Inverting Eq. (3) from Golev & Prugniel tells that in average the apertures used in our observations are 0.4 the normalisation radius.

The Mg₂-index measurements for the 210 individual spectra are presented in Table 1 (in electronic form only). This table gives the individual velocity-dispersion-corrected and aperture-corrected measurements. The distances (in km s^-1) used to compute the aperture correction can be found in the electronic version of Table 4. The mean internal error of individual measurements is 0$\hbox{$.\!\!^{\rm m}$}$0093$\,\pm\,$0$\hbox{$.\!\!^{\rm m}$}$0032 which is typical of the values collected in HYPERCAT.