A reasonably discerning extrapolation procedure was required for the VPC galaxy sample as (1) most VPC galaxies are too bright and/or extended for their images to be seeing dominated, and (2) a wide variety of morphological types (including of course a very large number of low-surface-brightness galaxies) are represented. The total-magnitude system we adopted is the t system of Young (1994) and and Young et al. (submitted); as outlined by Young (in press). This system involves the smoothing of galaxy images prior to modeling them by means of Sérsic's (1968) law. Note that in the specific case of un-nucleated ellipticals, prior smoothing is not actually necessary as demonstrated by Young & Currie (1994) who fitted Sérsic's law to high-resolution images of dwarf and intermediate ellipticals.
In the case of the low-resolution VPC data, Sérsic's law was found to offer an excellent fit
to virtually every unsaturated surface-brightness profile, irrespective of morphological type.
This can be seen from the thirty example plots presented in Appendix A (click here).
No total magnitude estimates were attempted for saturated galaxies. Instead,
Young et al.
(in preparation) will present t-system total magnitudes for these objects based on
even lower-resolution CCD photometry.
During the image-segmentation stage of the reductions, profile information
was generated for each galaxy image in the form of ellipticities,
position angles and reduced radii, for all unsaturated isophotes in
intervals brightward
of the limiting one. In the case of the
plates, this corresponded to
a maximum of 12 levels (a maximum of 16 in the case of plate U9362 and
a maximum of 12 in the case of R2936).
The profile parameterizations were achieved by incrementing n from 0.2 through
3.0 in steps of 0.01, and attempting to fit a straight line to as a
function of rn. Points corresponding to isophotes that overlapped with
those of other images (as represented by five-pointed stars in Appendix A (click here))
were assigned weights 50% lower than those assigned to the remaining points
(as represented by asterisks in Appendix A (click here)).
was evaluated for each
fit, and the parameters (n, r0 and
) that provided the best fit
for a particular galaxy, were used to derive a total-magnitude estimate for
that galaxy by means of Young & Currie's (1994) Eq. (3).
In the case of the band,
although we had only parametrised the profiles from Plate J9229, as we had
already computed two usable
values for those galaxies
lying within Fields A and B (one value from each
plate),
we were still able to average the extrapolated total magnitude values.
This was achieved by subtracting
from the total magnitudes derived from
the parametrizations of the Plate J9229 images.
The transformation of total magnitudes from the system to the B
system was achieved by means of Eq. (1), and the approximate
relationship:
Figure 8: Unsaturated VPC galaxies for which (B-V) measurements have already
been published (see text for references). This two-colour plot was used to
derive a transformation equation between () equal-area colours and (B-V) by means
of the best-fitting least-squares (on (
) because the (B-V)
values are expected to be more accurate as they are photoelectric measurements
rather than photographic ones) straight line
which was derived from Fig. 8 (click here); a two-colour plot for
unsaturated VPC galaxies with (B-V) colours previously measured by Caldwell
(1983) Gallagher & Hunter (1986) Bothun et al. (1986) and/or
Drinkwater
& Hardy (1991). Note that although the () and (B-V) colour
measurements were not based on identical regions of each galaxy concerned,
errors due to colour-gradients are expected to be considerably smaller than
those due to the inherent scatter in such a colour-colour plot.
The total magnitudes listed in Table 4 of Young & Currie (1995)
as well as those VPC magnitude values listed in Table 9 of
Drinkwater et al. (1996),
were extracted from an earlier version of the VPC; that of Young (1994).
The magnitudes were computed by a variant on the method described in Sect. 4.2.
This method involved
adding the integral of the same function between the isophotal radius
r=r25 and to the linear-unit equivalent of the
value tabulated in the VPC for each galaxy. The integral was
evaluated numerically using the Compound Form of Simpson's Rule, with 2000
intervals spanning the range r=r25 to the point at which
had
dropped to
:
where and
.
It was adopted at a time when the catalogue listed
and
values for Field A and B objects; but did not list the senses
of the differences between the
and
values.
With this method, it was therefore still possible to obtain averaged total
magnitudes based on the isophotal magnitudes from two plates [together with
extrapolations from one plate] without knowing the senses of the differences
between the plates.
In a small minority of cases there was a significant difference between the
sizes of the extrapolations obtained by the different methods, but on average
the choice of method made little difference. The mean extrapolation [for the
VPC as a whole] beyond due to
the old method was 0.348 mag, compared to a mean of 0.352 for the more
rigorous method used in this paper; though these mean extrapolations were 0.670
and 0.696 respectively for the dwarf elliptical subsample of 64 objects
presented in Young & Currie (1995). The systematic
difference between the two sets of magnitude values is due to
the minority of objects for which the light contribution from
regions exterior to
would be significant should the
profiles be extrapolated to
.