The detailed surface photometry of our sample of HDF ellipticals in the V606 band was performed using the AIAP package (Fasano 1990), which is equipped with a completely interactive graphical interface, allowing flexible tools for sky subtraction, drawing, masking and fitting of the isophotes, PSF evaluation, etc. These capabilities, as well as the allowance for checking "on-line'' all steps of the procedure, turn out to be particularly useful when handling morphologically complex structures and/or closely interacting objects, a situation quite common in the case of the HDF galaxies.
Our magnitudes are given in the STMAG system.
The second release of the HDF provided us with frames "ready to be used'', in the sense that all the standard reduction procedures (flat fielding, bias and dark-current removal, etc.), as well as the specific ones (drizzling, position weighting, etc...), were already performed and the proper (constant) sky background was subtracted from each frame.
Nevertheless, since not negligible and systematic residuals in the
backgrounds were detected, we decided to perform for each galaxy a
"local'' refinement of the background subtraction by linear
interpolation of the residuals. After this refinement the mean
(systematic) background variations were estimated to be of the order of
of the original sky levels. These systematic variations
have been used to estimate error bars in the outer luminosity and
geometrical profiles of each object (see next subsection).
The isophotes were drawn with a fixed surface brightness step of
. Therefore, at least in the inner part of galaxies having
steep luminosity profiles, isophotes might be oversampled, since the
difference of radius between two successive isophotes might be lower
than the pixelsize. We note, however, that the shapes of luminosity
profiles are not modified by the oversampling and that, whenever we
introduce luminosity profiles weighting (i.e. fitting with analytical
functions and extrapolation), we set
to zero the weight of oversampled isophotes.
Low surface brightness isophotes (usually ) were
drawn after rebinning of the frames. The AIAP package allows to
decide interactively when and how perform the rebinning, depending on
the noise of each isophote. The maximum reachable surface brightness
was not the same for all galaxies. It essentially turned out to depend
on the presence of close companions and/or irregular sub-structures
which often make useless to go much deep in drawing the isophotes.
We can reach easily the surface brightness level of
.
In the most favourable cases we were able to reach
.
The isophotes of HDF ellipticals are often quite irregular due to the intrinsic complexity of the structures (which is likely to increase at increasing redshift), as well as to the presence of close (possibly interacting) companions. Therefore, the flexibility of the AIAP masking and ellipse fitting tools turned out to be useful in order to secure reliable profiles even for very intriguing cases. We mention, among the other things, the possibility to take fixed or relaxed (for each isophote) the coordinates of the center of the fitting ellipses and the possibility to complete the masked parts of the isophotes by using the corresponding symmetric parts of the same isophotes with respect to the center.
Once the isophotes have been carefully masked and interpolated through ellipses, we obtained luminosity and geometrical profiles of all galaxies in our sample. In particular, we obtained surface brightness, ellipticity, position angle and coefficients of the Fourier analysis of the residuals as a function of the semi-major axes of the fitted isophote.
The most important contribution to the uncertainties in the outer
profiles of nearby elliptical galaxies from CCD data is usually given
by the possible errors in the estimate of the background.
In particular, an underestimation (overestimation) of the
average background level leads to a systematic distortion upwards
(downwards) of the outer luminosity profiles and then to an
overestimation (underestimation) of the total apparent luminosity. In
our case this kind of uncertainty is not the dominant one since the
average value of the background is very carefully estimated (well
outside the faint galaxy halos) by the above mentioned "
local refinement''. A more serious problem is represented by the
possible systematicity of the background residuals.
Fasano & Bonoli (1990)
analyzed the influence of an artificially tilted background on
the luminosity and geometrical profiles, giving a set of formulae to
estimate error bars of surface brightness, ellipticity and position
angle of each isophote, mainly depending on the relative background
variation ( in our case; see previous subsection) and on the
considered isophotal level. Error bars of our profiles were computed
according to these formulae, with an additional term (which could be
relevant for the outer isophotes) accounting for the number of points
belonging to each isophote. This term turns out to be usually
negligible for ground-based surface photometries, where the small
signal to noise ratio of the outermost regions is largely compensated
for the great number of points defining the isophotes. In our case,
the incredible deepness and resolution of the images allowed us to
perform the detailed surface photometry of galaxies in which even the
outermost isophotes are defined by a relatively small number of
points.