In order to increase the accuracy of the tidal radius of M 5 known from
Peterson & King (1975),
Bahcall & Hausman (1976), Kron et al. (1984)
and Trager et al. (1995) we used the full
APM scans of 8 Schmidt plates (cf. Table 1 (click here)) for star counts
(Lehmann 1996). The automated counts are
characterised by a higher statistical significance in the outer region
of globular clusters in comparison with the human detection. Due to
crowding effects
the central cluster region could not be resolved in a range of 
(in
dependence on the plate scale, seeing and limiting magnitude).
There were also significant crowding effects in the range of
arcmin (
- the mean radius of the annulus).
Therefore we applied a luminosity dependent crowding correction based
on the luminosity function in the outer cluster region and the statistical
probability of overlapping star images (for more details see Lehmann 1996).
Note that the crowding correction was not applied in the APM on-line reduction (improved image detection in crowded fields of Irwin 1985) as done in Grillmair et al. (1995). Instead here we used standard APM measurements, originally carried out for astrometry. The crowding correction converted the high number of images with non-stellar classification appearing in the inner annuli around the cluster centre on the basis of their pixel area into additional numbers of stellar images. For this purpose the luminosity function of stellar images in the outer cluster region (not affected by crowding) obtained after the subtraction of the background was assumed to be valid in the inner cluster region, too. The subtracted background surface density was determined from a large region adjacent to the cluster in an annulus between 25 and 50 arcmin from the cluster centre.
The projected surface density profiles of M 5 from the different plates
were matched to a single profile and correlated with photoelectric and
electronographic surface brightness measurements from Kron & Mayall (1960),
King (1966) and Kron et al. (1984). Because of the spread of
the surface brightness data in the innermost part of the cluster we used
the above mentioned data in different combinations for the fit of the whole
profile by the empirical density law of King (1962). The best fit was
obtained by combining our star counts with the data of King (1966).
By fitting with the Levenberg-Marquardt-method (Press et al. 1992)
we got the tidal radius of M 5 
arcmin, the core
radius 
arcmin and the concentration parameter
. Whereas the core radius agrees well with the data
from Trager et al. (1995) the tidal radius from our profil
is 1.7 arcmin lower than their value (see Table 5 (click here)).
Table 5: Structural parameters 
, 
and c of M 5
as obtained by different authors and methods
Figure 6 (click here) shows for 
an increased surface density
which may be an indication for a tidal tail - a halo of unbounded stars around the
globular cluster as recently discussed by Grillmair et al. (1995).
These authors investigated
12 Galactic globular clusters, mainly at southern declinations, measured
on UK Schmidt plates by means of the APM and found extra-tidal wings in the
density profiles for the majority of clusters in their sample.
The seven globular clusters studied
by Lehmann (1996) on the basis of Tautenburg, Palomar and UK Schmidt plates
also scanned with the APM are located at northern declinations. There is
only one cluster (M 15) included in both studies. It is interesting that
Lehmann (1996) also found indications of tidal tails for 5 clusters.
Grillmair et al. (1995) investigated the nearby cluster background in
more detail in order to decide whether the increased density at 
is physically existent or an artifact of an incorrect background subtraction.
Here we check the reliability of the tidal tail of M 5 obtained in the counts
of all objects measured on 8 different Schmidt plates using the member counts
for the King profile fitting. Tucholke (1992) proposed this method for
globular clusters with rich or variable background (and/or foreground)
of field stars.
on a second plate (8348) were
investigated. No further restrictions concerning the magnitude range of the
stars used in the member counts were made.
Figure 7: Density profile of M 5 from counts of cluster members
with membership probabilities 
(membership
determination using coordinates and proper motions).
Logarithm of surface density in stars per arcmin
versus
logarithm of the mean annulus radius 
[arcmin].
The line shows the best fit with the empirical
density law from King (1962). The dotted lines show the
radial fitting range
For the member counts we first used the stars with membership probabilities
and 
obtained in the four-dimensional analysis
including the coordinates. These membership probabilities are the most reliable
ones, although the assumption of a normal distribution of the coordinates
of the cluster stars (see Sect. 4) pre-determines the shape of
the density profile. For 
the fit with the
empirical density law of King (1962) was more
accurate. The results are shown in Fig. 7 (click here) and in
Table 6 (click here).
Figure 8: Density profile of M 5 from counts of cluster members
with membership probabilities 
(membership determination using proper motions
only). Logarithm of surface density in stars per
arcmin
versus logarithm of the mean annulus
radius 
[arcmin]. The line shows the
best fit with the empirical density law from King
(1962). The dotted line shows the subtracted
background of field stars with 
outside of 35 arcmin, the dotted-dashed lines
show the radial fitting range
Table 6: M 5 tidal radius from member counts
For the member counts based on membership probabilities obtained only from
the proper motions we present the result for the tidal radius for both using
all stars with 
and with 
in
Table 6 (click here). As one can see the radial fitting range is larger
than in the case of the member counts using the four-dimensional
membership analysis. Whereas in the member counts with 
there was
no background to be subtracted, here we had to consider the number of field
stars with proper motions similar to those of the cluster stars.
The values of 
obtained in the member counts are well in agreement with
those of Peterson & King (1975), Trager et al. (1995) and
of the complete scans of all Schmidt plates used in this project
combined to one profile (Lehmann 1996). But there is no indication of a
tidal tail for M 5 as found from the complete scans of the plates (Lehmann
1996). This discrepancy may be due to the different magnitude limits of
the full counts and of the member counts.