In order to increase our knowledge of extra-galactic stellar systems like elliptical galaxies, we observe the average galaxy brightness, which gives rise to the traditional broad-band colours and spectral-line indices. In addition, we observe the variance of the galaxy brightness, i.e., the surface-brightness fluctuations (Tonry & Schneider 1988). Of course, the ultimative goal is to obtain stellar luminosity functions and colour-magnitude diagrams, i.e., accurate photometry of individual stars.
Until recently, colour-magnitude diagrams have been obtained solely from ground-based imaging of stars in our local neighbourhood, i.e., field stars and stars in open- and globular clusters of our Galaxy, in addition to approaches to Local Group dwarf spheroidals and the Magellanic Clouds (low surface-brightness stellar systems) from ground (e.g. Freedmann 1992) and space (e.g. Mighell & Rich 1996). Then Grillmair et al. (1996) presented an impressive colour-magnitude (CM) diagram of M 32, our closests elliptical and companion to the Andromeda galaxy, based on Hubble Space Telescope imaging (archive data, ID 5233). Using the same data we have been able to reproduce the CM diagram of M 32 which in itself, however, was not the main goal of our work. We have carried out an investigation of the reliability of the CM diagram, that is, an estimation of the photometric quality of the detected stars. The image crowding in dense fields like that of the high surface-brightness elliptical M 32 may cause spurious detections and severely reduce the reliability of the photometry. In the present paper we discuss specific aspects of the photometric quality of extra-galactic stellar systems, aspects that supplement the discussion by Grillmair et al.
In our latest paper (Sodemann & Thomsen 1996)
we presented ground-based imaging of M 32
obtained with the Nordic Optical Telescope
with a seeing of FWHM 
using 
pixels.
We identified a systematic variation in the I and B-band
Surface-Brightness Fluctuations (SBF) of 0.2-0.3 mag
in the radial range 
.
In our search for the stars responsible for this variation
we made a comparison of simulated stellar fields with
the ground-based SBF observations.
From this it became clear
that it was not possible to supplement the measurements of
the SBF with stellar photometry of the most luminous stars,
due to excessive crowding.
However, at least in some cases
the superb resolution of the Hubble Space Telescope's (HST) Wide Field
Planetary Camera 2 -
the Planetary Camera (PC) with seeing of FWHM 
using 
pixels -
makes it possible to resolve more than just the very brightest stars.
Grillmair et al. (1996) presented a CM diagram based on
HST-imaging of a region 
from the centre of M 32.
From the surface brightness 
of M 32 we can compare this
off-centre field with a central field at 
from the centre.
Assuming that the same type of stars are responsible for the
surface brightness at the two distances,
the number of stars per area is 
times higher in the central field
(
and 
).
This merely indicates differing problems introduced by image crowding,
problems that may turn up
when dealing with CM diagrams of fields at various distances from the galaxy
centre. We shall return to this later.
When discussing luminosity functions and CM diagrams we are
interested in knowing to what magnitude limit we have actually
been able to observe stars, a limit set mainly by a compromise between the
image crowding and resolution, and the amount of exposure time.
This magnitude limit is usually measured
by addition and retrieval of a small number of faint artificial stars,
that is, the test of (in)completeness.
However, whereas the traditional method of adding artificial stars
estimates the detection probability it does
not measure the photometric quality of the detected stars or the effects
of spurious detections caused by severe image crowding.
That is, the estimate of the limiting magnitude
is based on information about the location
(the coordinates) of the added/recovered
star alone and not on the magnitude of the recovered star.
For the data presented here, one important result of the image crowding is
the following: An artificial star of known magnitude
added to the programme frame may be recovered with a magnitude
up to 1
brighter than its original magnitude, but
it turns out that it is not equally likely that this star will be
recovered with a magnitude 1 fainter than its original magnitude.
(In Sect. 3 (click here) we show that the asymmetry in the distribution of recovered
stars cannot be explained as a result
of plotting the data as a function of magnitude).
Thus, the typical measure 
,
the standard deviation, of the accidental error at a given magnitude
is not an adequate description for this asymmetric distribution of recovered
stars and has to be supplemented with additional error estimates.
Drukier et al. (1988) raised the problem of "bin jumping" and pointed out a way to account for this when correcting a measured luminosity function for incompleteness. LePoy et al. (1993) also discuss the effects of severe image crowding, which may produce an artificial enhancement of the bright end of the measured luminosity function if not dealt with in an appropriate way (see also Renzini 1992; Martinez-Delgado & Aparicio 1997).
We shall concentrate on the implications of crowding on stellar photometry
of HST imaging
of extra-galactic systems like the compact elliptical galaxy M 32.
We begin with a description of the data and image handling (Sect. 2 (click here)).
After that follows a discussion on the artificial-star experiments in
connection with the off-centre field at from the
centre of M 32 (Sect. 3 (click here)) and
the dense central field at (Sect. 4 (click here)).
We summarise the results in Sect. 5 (click here).