In order to determine the distance moduli of the clusters, we have
plotted intrinsic ,
;
,
;
,
and
,
; diagrams for each cluster in Figs. 13 (click here),
14 (click here), 15 (click here) and 16 (click here). Stars (mostly proper motion and
photometric cluster members) observed photoelectrically by others but not
present in our sample have also been included in the plots, since the
photoelectric data show good agreement with the present CCD measurements.
They are taken from Hogg (1963) for NGC 3228, from
Wesselink (1969) for NGC 4103, from Clariá et al.
(1991) for NGC 5662 and from Fernie (1961),
Breger (1966) and Turner (1986) for NGC 6087. In
NGC 3228, we plotted the members assigned by Hogg (1963) using
proper motion, photometric and spectroscopic data as there are no other
membership studies available for the cluster. Proper motions for stars
brighter than
have been derived in the regions of NGC
4103, NGC 5662 and NGC 6087 by King (1979, 1980 and 1982
respectively). Stars with photoelectric and/or CCD measurements but having
proper motion cluster membership probability less than 50% have been
excluded from the plots. In NGC 5662, Clariá's et al. (1991)
photometric members not present in our sample have also been plotted in the
CM diagram. In plotting these figures, we have converted apparent V
magnitudes and (B-V), (U-B), (V-R) and (V-I) colours into intrinsic
ones using the values of E(B-V) derived in Sect. 6 and the following
relations for E(U-B) (cf. Kamp 1974; Sagar & Joshi
1979); E(V-R) (cf. Alcalá & Ferro 1988);
and E(V-I) (Walker 1987):
where for
and for
;
where and
;
and
As the interstellar extinction seems to be uniform in
front of the imaged cluster regions (see Sect. 6), we have used the same
value of E(B-V) for all the stars of a cluster.
In the ,
and
,
diagrams, we
have fitted the ZAMS given by Schmidt-Kaler (1982), while the ZAMS
given by Walker (1985) has been fitted in the
,
and
,
diagrams. The
colour for the ZAMS on
the present photometric system was taken from Sagar & Cannon
(1994). After accounting for the colour dispersion expected from the
error in observations, the visual fit of the ZAMS to the bluest envelope of the
stars in each of the CM diagrams gives the
values
indicated in Figs. 13 (click here)-16 (click here). The visual fit has been done
mainly for stars brighter than
. Most of the stars in
our sample of NGC 3228 are well below the cluster MS sequence defined by
the brighter members having UBV photoelectric data.
Consequently, the
,
and
,
diagrams could not
be used for the distance determination of this cluster.
The mean values of are
,
,
and
for NGC 3228, NGC 4103, NGC 5662 and
NGC 6087 respectively. The uncertainty is estimated from the errors in
R, E(B-V) and the errors in fitting the ZAMS. The distance modulus
determined above yields a distance of
to NGC 3228;
to NGC 4103;
to NGC 5662 and
to NGC 6087. For NGC 4103, our value of distance
modulus is in good agreement with the value of 11.35 given by Stetson
(1981) and Becker (1971), but somewhat larger than the
value of 11.0 given by Wesselink (1969). The present determination
of distance modulus for NGC 5662 is the same as that recently determined by
Clariá et al. (1991). However, it is larger than the values of
8.82, 8.98 and 9.10 determined by Moffat & Vogt (1973),
Haug (1978) and Turner (1982) respectively. For NGC
6087, the values of distance modulus determined by Landolt (1964),
Breger (1966) and Graham (1967) are 9.8, 9.7 and 9.9.
They are in good agreement with the distance modulus determined by us. However,
these values are larger than the values 9.4 and 9.6 given by Fernie
(1961) and Schmidt (1980). The present determinations of
the distances to the clusters should be reliable because they have been derived
by fitting the ZAMS over a wide range of the unevolved part of the cluster MS,
except in the case of NGC 3228.
Figure 13: The ,
;
,
;
,
and
,
diagrams for stars observed by us
(filled circles), as well as for stars (crosses) observed
photoelectrically in the UBV passbands by Hogg (1963), in NGC 3228.
The continuous curves are the ZAMS fitted to the unevolved part of the
cluster MS for the values indicated in the diagram. The dotted curves
are the isochrones for Pop I stars fitted to the bright cluster members
for the values (in log of years) indicated in the diagram. The mean value of
the distance modulus
to the cluster is 8.5 mag, while its
age is
100 Myr
Figure 14: The ,
;
,
;
,
and
,
diagrams for stars observed by us
(filled circles), as well as for stars (crosses) observed
photoelectrically in the UBV passbands by Wesselink (1969), in NGC
4103. Others lines are the same as in Fig. 13. The mean value of
the distance modulus
to
35 Myr old cluster is 11.5 mag
Figure 15: The ,
;
,
;
,
and
,
diagrams for stars observed by us
(filled circles), as well as for stars (crosses) observed
photoelectrically in the UBV passbands by Clariá (1991), in NGC
5662. Other details are the same as in Fig. 13. The mean value of
the distance modulus
to the cluster is 9.5 mag, while its
age is
80 Myr
Figure 16: The ,
;
,
;
,
and
,
diagrams for stars observed by us
(filled circles), as well as for stars (crosses) observed
photoelectrically in UBV passbands by Fernie (1961), Breger (1966) and
Turner (1986), in NGC 6087. Other details are the same as in Fig. 13.
The mean value of the distance modulus
to the cluster is
9.9 mag. The object is
65 Myr old