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Astron. Astrophys. 360, 85-91 (2000)

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4. Results

4.1. Derivation of probable errors

Probable errors were derived from comparisons between the homogeneized data from various sources. Duplicate OHP observations were also considered, in an attempt to recover error estimates for this particular source.

4.1.1. Errors in colour gradients

Various possibilities were considered:

  1. The gradients from OHP observations and the various surveys were intercompared with the following results:

    . [FORMULA](OHP)-[FORMULA](Gal94): N=18; mean=-0.009; [FORMULA]

    . [FORMULA](OHP)-[FORMULA](Gal94): N=8; mean=-0.043; [FORMULA]

    . [FORMULA](OHP)-[FORMULA](Pal90): N=6; mean=-0.003; [FORMULA]

    . [FORMULA](OHP)-[FORMULA](Pal90): N=5; mean=-0.038; [FORMULA].

  2. The [FORMULA] from Gal94 and [FORMULA] from Fal89 and Pal89 together (or F&P) were intercompared. Since the [FORMULA] gradients are very small according to BM87, their "cosmic scatter" is expected to be also small, and the differences are largely due to errors of measurements. They thus may provide another estimate of these.

    The results are, respectively for the data before and after the present revision of gradients:

    . Before [FORMULA] (Gal94)-(F&P): N=26; mean=-0.019; [FORMULA]

    . After [FORMULA] (Gal94)-(F&P): N=26; mean=-0.016; [FORMULA]

    This comparison again shows the non negligible improvement resulting from our teatment of the original data.

  3. The tests from duplicate OHP data were performed as explained in our previous Paper V (see Michard & Poulain 2000), either measuring pseudo-colours from pairs of frames taken in the same pass-band, or comparing colours undependently measured. From 8 such experiments, we find a mean error of 0.035 for a single gradient estimate using OHP data.

Summing up the above results we note first that systematic errors in gradient measurement are not excluded! Our OHP data give V-I gradients smaller in the mean by 0.04 than the results derived from the Gal94 survey. This systematic effect dominates this particular comparison. For the other series, it appears that random errors in [FORMULA] and [FORMULA] may be about 0.02, but reaches probably 0.05 or more for [FORMULA], as a result of poorer S/N ratio and reduced contrast of E galaxies against background in the U band.

4.1.2. Errors in reference colours

The "reference colour" is calculated, at some specific r value, from a linear fit to the colour variations against [FORMULA]. Although the same sources have been used to recalibrate the various colour data, residual errors occur in reference colours, due primarily to background effects. Uncertainties in the description of the central ranges of the objects are also likely to introduces errors, as noted above. In the following comparisons, reference colours were taken at r values of 15, 20 or 25 arcsec depending upon the properties of the object (size and dust patterens).

  1. The comparison between reference colours from OHP data and other sources gives the following results:

    . B-V(OHP) - B-V(Gal94): N=18; mean=0.000; [FORMULA]

    . V-I(OHP) - V-I(Gal94): N=8; mean=0.020; [FORMULA]

    . B-R(OHP) - B-R(Pal90): N=5; mean=-0.008; [FORMULA]

    . U-B(OHP) - U-B(Pal90): N=4; mean=-0.019; [FORMULA]
    after rejection of an outlying value.

  2. The tests from duplicate OHP data give:

    . C1-C2: N=8; mean=0.002; [FORMULA]

From these comparisons it seems that the mean error of a reference colour is about 0.02 or somewhat better.This also applies to the mean colours derived below, because the number of multiple measurements is not large, except for B-V.

4.2. Mean results

In Table 1 are listed so called "mean" reference colours at a specified positions in V surface brightness and radius, corrected for galactic reddening and the K-effect according to the precepts and data in the RC3. Mean logarithmic gradients have also been obtained. It should be realized that there is often only one measurement for each object and colour. Indications upon the sources of measurements are given in the table. We emphasize that reference colours and gradients have been obtained outside the regions affected by important dust patterns.


Table 1. Mean colours and gradients. Reference colours, corrected for galactic extinction and K-effect, are given at the radius where the V-band surface brightness [FORMULA] is 20. The reference is taken farther out if an important dust pattern is present (noted in the right column). Abbreviations for sources: B: BM87; F: Fal89; P: Pal90; G: Gal94; M: OHP observations by Michard and Marchal; H: HYPERCAT data base.

A complete table of all new and "revised" measurements may be obtained from the author upon request.

4.3. Discussion of gradients

As examplified by Fig. 1, gradients in different colours are clearly correlated, notwithstanding the rather large errors of individual measurements. Relative values of the gradients thus convey information upon their physical cause(s). To obtain relative gradients less influenced by measuring errors, we proceeded as follows: first we defined a mean gradient for each object, as a weighted average of the gradients in the four derived colour indices. Several such mean gradients were tried, but they lead to similar results, so that only the simplest is used here, i.e. [FORMULA]. Then we calculated the regressions [FORMULA], and similar for other colours. No constant term is retained here, as they are thought to be physically meaningless, and proved to be of doubtful statistical significance. The results of the comparisons are then these 4 different a values with their mean errors, as derived from the dispersions around the regression.

On the other hand the same quantities [FORMULA] and corresponding relative slopes [FORMULA], [FORMULA], [FORMULA], [FORMULA] can be estimated from available theoretical work: we have derived these parameters from Worthey (1994), assuming that gradients result from the metallicity variations of a single burst stellar population, from similar work by Bressan et al. (1994) and also by Tantalo et al. (1996). On the other hand the same parameters can be estimated for gradients assumed to be due to diffuse dust, using calculations by Witt et al. (1992) and Wise & Silva (1996). Some approximations have to be made in using these works, but they should not have significant influence upon the conclusions: the colour systems in the various used theoretical works are not always the same, and eventually also differ from the one of the observations, but this is of negligible consequence for our purpose. Also the evaluation of colour gradients from Witt et al. (1992) tables is not rigorous (see below).

Table 2 contains observed values and theoretical estimates for the relative gradients [FORMULA], [FORMULA], [FORMULA], [FORMULA] in terms of the mean one [FORMULA]. The "sources" for various lines are as follows:


Table 2. Relative gradients in 4 colours expressed in terms of the mean [FORMULA]. Sources of data are: (1) Observed, Table 1. (2) Worthey (1994), (3) Bressan et al. (1994), (4) Tantalo et al. (1996), (5) Wise & Silva (1996), (6) Witt et al. (1992), (7) law of Galactic extinction

  1. Calculated values from observations in Table 1.

  2. Worthey (1994), Table 5A, colour differences for models of age 17 Gyr with [Fe/H] 0.5 and -0.5.

  3. Bressan et al. (1994), Table 3, colour differences for models of age 15.8 Gyr with Z=0.02 and Z=0.008.

  4. Tantalo et al. (1996), colour differences for models of age 15.8 Gyr with Z=0.02 and 0.004.

  5. Wise & Silva (1996), Table 2, their preferred model with [FORMULA] and [FORMULA]. Since only [FORMULA] and [FORMULA] are given, the [FORMULA] is here assumed to be equal to [FORMULA].

  6. Witt et al. (1992), E galaxy model with [FORMULA]. The colour gradients are estimated by comparing the tabulated emergent light at galaxian center, with the one along a line of sight at very large r, and therefore unaffected by dust and with zero colours in Witt at al. conventions.

  7. law of galactic absorption: it would correspond to a thin galaxy.

A glance at Table 2 shows that the models where colour gradients result exclusively from diffuse dust throughout the galaxies do not agree with the obsevations: the calculated [FORMULA] values are much too small and the [FORMULA] too large . On the other hand the relative observed colour gradients are compatible with gradients induced by metallicity variations. In the evaluation of the parameter [FORMULA], the theories of the evolution of old stellar populations deviate more from each other than they do from the present observed gradients!

In Fig. 2 we compare the correlations between the [FORMULA] mean gradients and the [FORMULA] and [FORMULA] gradients respectively. Other plots for [FORMULA] and [FORMULA] are of similar appearance as the one for [FORMULA], but for the average slope. The correlation between [FORMULA] and [FORMULA] is good and probably limited mainly by errors of measurements. On the other hand the correlation between [FORMULA] and [FORMULA] is very bad, as also illustrated by the large corresponding [FORMULA] in Table 2. Our estimate of random errors in the [FORMULA] is too uncertain to tell if this large dispersion is real, at least in part.

[FIGURE] Fig. 2. Correlation diagrams between the mean gradient [FORMULA] (abscissae) and the [FORMULA] (bottom) and [FORMULA] gradients. The U-B against [FORMULA] correlation may be even worse than implied by the large errors of measurements for this colour.

It should be noted however that [FORMULA] is very sensitive to metallicity variations and relatively little to the effects of diffuse dust. The reverse is true for the other colour gradients entering the [FORMULA] mean. If various amounts of diffuse dust, together with unequal metallicity gradients, occur in E-galaxies (as is probably true!), then important variations in the ratio of [FORMULA] to [FORMULA] (or other dust sensitive gradients such as [FORMULA]) are possible. As an argument in favor of this hypothesis one may note that the two objects with the smallest ratio of [FORMULA] to [FORMULA] are NGC3665 and 4278, that is the two galaxies with the largest amount of apparent dust in the sample (noted at the right in the graph of Fig. 2)

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© European Southern Observatory (ESO) 2000

Online publication: July 27, 2000