7 Internal and external comparisons

7.1 Internal comparisons

The reliability of the determinations of the spectroscopic parameters was checked by comparing the results from repeat observations of the same galaxy. There are 30 galaxies of which two spectra were obtained for each, and for these galaxies the differences in parameters were found.

7.1.1 Redshifts

Internal comparisons of radial velocities are shown in Fig. 6 for 30 galaxies with two spectra each. The order (cz₁ and cz₂) in which the two results have been considered is arbitrary. The rms scatter is $\Delta cz_{\rm hel}$ = 40.7 km s^-1for the comparisons of repeat observations.

7.1.2 Velocity dispersions

In Fig. 7, internal comparisons of velocity dispersions are shown for 29 galaxies with two spectra each. An estimate of the accuracy is the rms scatter of $\vert\log \sigma_1 - \log \sigma_2\vert$, which is 0.045. In Fig. 8, the errors in repeat measurements of $\sigma$ are also shown as a function of S/Nper $\mbox{\AA}$. It is clear from the plot that the repeatability depends on the S/N of the spectrum. For a S/N of 40 - 50, velocity dispersions can be determined to within 4 - 5% (from $\Delta \sigma/\sigma$) and for a S/N of $\sim$ 20 (which is the case for most of the galaxies in the sample) the accuracy is about 8 - 10%.

Figure 9 is a histogram of the fractional errors in $\sigma$ for 29 repeat observations. The rms scatter in $\Delta \sigma/\sigma$ is 0.103, which means that $\sigma$ can be determined to 10% accuracy. The galaxies for which there are repeat measurements are typical of those in the whole sample, so these estimated errors are representative of the true errors.

Figure 12: Comparison of the results for velocity dispersions of standard galaxies with values from the literature: a) McElroy (1995); b) Davies et al. (1987); c) J$\o$rgensen et al. (1995); d) González (1993)

7.2 External comparisons

7.2.1 Redshifts

Results for redshifts were compared with values from NED (Madore et al. 1992) and from the ZCAT compilation of redshifts (Huchra et al. 1992), and the differences were found to be relatively small. Redshift comparisons were possible for 32 standard galaxies and 20 sample galaxies. (Redshifts were available for only a small fraction of the galaxies in the sample regions, since the South Equatorial Strip had not been well studied before.)

The determinations of radial velocity for these two sets of galaxies were compared with redshifts from the literature, and the results are shown in Fig. 10. For both data sets the agreement is good. For all 52 galaxies for which literature redshifts were available, the distribution of differences between the measured redshifts and the literature values is shown in the histogram of Fig. 11. The values of the mean absolute difference $\vert cz - cz_{\mbox{NED}}\vert$ are 42.4 km s^-1 and 37.3 km s^-1 for the standard galaxy and sample galaxy comparisons respectively; the rms differences are 56.0 km s^-1 and 45.8 km s^-1. This shows that the redshifts are of adequate reliability.

7.2.2 Velocity dispersions

In order to make sure that the values of velocity dispersions determined here are scaled to the standard system, the results for the velocity dispersions of standard galaxies were compared with published values. Our data set overlapped with the following sets: (i) the compilation of McElroy (1995) (17 galaxies in common); (ii) Davies et al. (1987) (7S) (15 galaxies in common); (iii) J$\o$rgensen et al. (1995) (7 galaxies in common); and (iv) González (1993) (5 galaxies in common).

The data set of Davies et al. (the 7S data) defines a good standard system since it is frequently used for comparisons. The comparison with the results of Davies et al. is shown in Fig. 12 together with comparisons with data from the other sources. The difference between the values from this study and the literature data, $\Delta \log \sigma = \log \sigma$(this study) $- \log \sigma$(literature), are shown plotted against $\log \sigma$(literature). There do not appear to be any offsets or systematic differences relative to the velocity dispersions of the four data sets. The rms scatter of $\Delta \log \sigma$ is 0.066, 0.111, 0.036, and 0.021 for the plots in (a), (b), (c), and (d) respectively. The agreement is best for comparisons with González (1993) and J$\o$rgensen et al. (1995), which are the most recent data sets, although the numbers of galaxies in common are smaller.