4 Comparison with HYPERCAT

  In Golev & Prugniel (1998) we have presented a catalogue of published absorption-line Mg₂ indices of galaxies and globular clusters. This catalogue is maintained up-to-date in the HYPERCAT database and gathers more than 4000 Mg₂-index measurements for $\sim$1500 objects from 69 observational datasets reported in 41 different publications. Below we have used this database for the sake of internal and external comparison of our measurements.

4.1 Internal comparisons

  During each observing run, we observed between 10 and 30 galaxies. In most cases, each observation consisted in two spectra with the same position angle interleaved with a calibration-lamp spectrum (needed for the kinematical analysis to control the possible flexures in the instrument). Two to five galaxies in each run were repeated in another run. This allowed two types of internal comparison: (1) between two consecutive spectra, and (2) between observation repeated during different observing runs. The relevant statistics of these comparisons is summarized in Table 2.

The results of these comparisons performed on the corrected measurements are:

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The rms difference between two consecutive observations of the same galaxy is 0$\hbox{$.\!\!^{\rm m}$}$000$\,\pm\,$0$\hbox{$.\!\!^{\rm m}$}$0096. The only significant differences allowed to reject discrepant measurements affected by badly placed spikes due to cosmic-rays.

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The internal comparison did not reveal any evidence for significant zero-point difference (greater than 0$\hbox{$.\!\!^{\rm m}$}$005) between the observing runs. But the relevance of this diagnostics is limited by the small number of comparison points (see below the external comparisons).

The internal comparison between the repeated measurements of the same galaxies reveals a mean error of 0$\hbox{$.\!\!^{\rm m}$}$008 (the same order of magnitude as the total mean internal error of 0$\hbox{$.\!\!^{\rm m}$}$0093), in agreement with the analysis of the error sources in the previous section.

4.2 External comparisons

 

  

Table 2: Internal and external comparisons. The first column lists our datasets (with the total number of observed spectra in brackets), Cols. 2 - 8 show the internal comparisons between these datasets. Columns 9, 10 and 11 show the comparisons (ours - literature) between the datasets of Col. 1 and, respectively, Lick98, LICK, and HYP (for HYPERCAT). The first row of each cell is the number of measurements compared. The second is the mean difference: (line)$\,-\,$ (Col.), and the third is the rms. The diagonal (in italics) shows the comparison between consecutive observations of the same galaxy

Most of the galaxies in our sample were previously measured, in particular by the Lick group (Davies et al.1987 - hereafter LICK, and Faber et al.1989 - hereafter 7Sam). Recently the full Lick/IDS (Image Dissector Scanner) database of $\mathrm{Mg}_2$ indices for 381 galaxies and 38 globulars was published by Trager et al.(1998 - hereafter Lick98). This dataset should be regarded as the last version of the Lick/IDS line-strength index system, and we re-scaled all the HYPERCAT data to it.

The estimate of the external errors, and of the corrections to the Lick98 system is done iteratively, and globally for all the HYPERCAT datasets, by inter-comparing these datasets. The comparisons are performed on the aperture-corrected data. For present datasets, the significant intersections are with the LICK dataset (Davies et al.1987) and with Lick98.

After these comparisons, for 59 galaxies in common with other datasets a difference of Mg₂(our) - Mg₂( HYPERCAT) = 0$\hbox{$.\!\!^{\rm m}$}$018$\,\pm\,$0$\hbox{$.\!\!^{\rm m}$}$002 was found. Such difference between flux-calibrated measurements, like ours, and the Lick/IDS data which are normalized via quartz flat field are indeed not surprising. Analysing the details of the pair-comparisons, we adopted a correction of 0.019 for all datasets except Mar93 (0.025) and Mar95 (0.016).

The parameters of our datasets are given in Table 3 (available in electronic form only).

We summarize in Table 2 the final comparisons between the LICK and Lick98 datasets, our datasets and the HYPERCAT homogenized data. The residual zero-points are negligible, and the mean differences give estimates of the internal errors (on the diagonal of the table are comparisons between consecutive observations; on the other positions are comparisons between different observing runs), and external errors (last three columns). The comparison between our fully corrected measurements and HYPERCAT values is presented in Figs. 1 and 2 (the distributions of residuals with the two major datasets of Table 2 have basically the same form).

Note that the mean residuals between the fully corrected data and the HYPERCAT values are not strictly null, but simply statistically unsignificant. This is because the homogenisation process (Golev & Prugniel 1998) rests on pair-wise comparison and iteratively determines zero-points and weights for all the datasets in HYPERCAT. Such process is not stable and thus is hand-controlled at each iteration (this control consists in under-relaxing the corrections to damp the oscillations).

We also searched for correlations between the mean difference of our Mg₂-index measurements and any of these datasets (as some non-linearity in the whole acquisition chain could produce). We did not find any significant effect.

In Table 4 we present the mean corrected value of Mg₂ rescaled to the Lick system and the corresponding rms error for the 87 galaxies in the sample. In the electronic version of the table more information for each galaxy is provided, e.g. the flow-smoothed velocity used for aperture correction (defined as the velocity of the cosmologic flow associated with the galaxy).

  

Figure 1: Comparison between our fully corrected Mg2-index measurements and HYPERCAT values for 59 galaxies in common

  

Figure 2: The distribution of the differences between our $\mathrm{Mg}_2$-index measurements and HYPERCAT values

  

Table 4: Fully corrected values of Mg₂ indices, rescaled to the Lick system. The galaxy's identifiers are listed in first column. Columns 2 and 3 contain corrected Mg₂-index values and the corresponding rms errors. In Col. 4 N are the numbers of individual spectra used

 

Table 4: continued