5. Derived parameters and comparison with RC3

 

We ran the growth curve fitting program only for the galaxies cross-identified in LEDA. Out of them the photometric type (see Sect. 4 (click here)) was determined for 3262 galaxies. Figure 4 (click here) shows the histogram of for the whole sample and for galaxies of quality .

  
Figure 4: Histogram of total B-magnitude, , for the whole sample and for galaxies with a quality (hatched)

  
Figure 5: Relation between the effective colour indices and the photometric type. The continuous lines are the least square fitted solution adopted for reducing the data to the B-band when no direct calibration were available (See Sect. 5.2)

  
Figure 6: Relation between the colour gradients (in ordinates) and the photometric type. The points are the average gradients (in computed in bins of width . The error bars are the uncertainty on this mean gradient, i.e., , where rms is the dispersion within a given box and N the number of galaxies in this box. Typically, and . The continuous lines are the least square fitted solution adopted for reducing the data to the B-band when no direct determination of the colour gradients were possible

 

U-B 0.300 -0.027 -0.084 -0.002

B-V 0.870 -0.019 -0.071 -0.004

V-R 0.570 -0.006 -0.030 -0.002

V-I 1.179 -0.011 -0.059 -0.006

Table 5:   Coefficients of the linear regression between colour indices (, ) and colour gradients (, ) with . Coefficients u are the ordinates for and v the slopes. (See Figs. 5 (click here) and 6 (click here))

 

Q Nb of gal

0 2191

1 751

2 2253

3 751

4 823

5 152

6 371

Table 6:  Distribution of the galaxies with the quality (Q)

 

Quantity N Mean difference rms PH - RC3

1648 -0.057 0.242

1509 0.159 0.485

1172 -0.006 0.083

1501 0.003 0.045

376 0.009 0.050

374 0.007 0.090

Table 7:   Comparisons with RC3. N is the number of galaxies used for the comparison ( and error on ). The units mag/arcsec² for and mag for the other quantities

5.1. Derived parameters

 

The derived parameters are summarized in Table 4 for the 5169 galaxies for which a growth curve could be fitted (2229 were rejected because only one aperture or two apertures from different references were available).

5.2. Comparisons with RC3

  
Figure 7:  Comparison between total magnitudes from RC3, (in ordinate), and from this study, (abscissa). The comparison is done for 1403 galaxies having the quality flag: . The straight line corresponds to

Figure 7 (click here) compares the total B magnitudes from RC3 and this study, respectively (RC3) and (PH), and Table 7 (click here) summarizes the results of the comparison of different derived parameters. The comparisons were restricted to the galaxies with and with an error on BT(RC3) smaller than 0.4.

The systematic differences are significant. In average, our determinations are more luminous, and less bright than those in RC3. The differences in colours are consequences of those on and , taking the colour gradients into consideration. These differences are due to the choice of the set of growth curve, as when using the RC3 set of growth curves our determinations are consistent with RC3 to within 0.01 mag on .

The few outliers apparent in Fig. 7 (click here) are galaxies for which the RC3 fit was based on very few apertures. They are: IC 5273 and NGC 4603 4679 5085 5398 7649

 
Figure 8:   Correlation of the errors on and . Abscissa: Difference between the total magnitude () from INTERP growth curves and from RC3 (in mag). Ordinate: Difference between the mean surface brightness within from INTERP growth curves and RC3 in . The comparison is done for 1389 galaxies having the quality flag:

Figure 8 (click here) shows the error correlation between and , the line is the correlation observed for internal errors (see Fig. 1 (click here)). As already noticed by, e.g., Hamabe & Kormendy (1987), this correlation is important. It may significantly biases physical relations, in particular those used as distance indicator. As illustrated by the comparisons with RC3, the external errors on and are much larger than those derived from the formal errors on our fitting parameters. If we a priori suppose that the errors on both determinations are comparable, the external errors are 0.15 mag on and on . The comparisons between the results obtained with the three sets of growth curves (INTERP, Sérsic, and RC3) give comparable rms differences. This shows that the intrinsic deviations from any set of growth curves for individual galaxies is the dominant source of error.

Using a one-parameter family of growth curves can probably not represent the diversity of the galaxies, and even for well observed galaxies we do not expect to reach a precision on better than 0.1 mag.