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7. Distances to the clusters

In order to determine the distance moduli of the clusters, we have plotted intrinsic tex2html_wrap_inline3162, tex2html_wrap_inline3164; tex2html_wrap_inline3166, tex2html_wrap_inline3168; tex2html_wrap_inline3170, tex2html_wrap_inline3172 and tex2html_wrap_inline3174, tex2html_wrap_inline3176; 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 tex2html_wrap_inline3178 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); tex2html_wrap_inline3196 and E(V-I) (Walker 1987):
displaymath3154
where tex2html_wrap_inline3200 for tex2html_wrap_inline3202
and tex2html_wrap_inline3204 for tex2html_wrap_inline3206;

displaymath3155
where tex2html_wrap_inline3208 and tex2html_wrap_inline3210;
displaymath3156
and
displaymath3157
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 tex2html_wrap_inline3214, tex2html_wrap_inline3216 and tex2html_wrap_inline3218, tex2html_wrap_inline3220 diagrams, we have fitted the ZAMS given by Schmidt-Kaler (1982), while the ZAMS given by Walker (1985) has been fitted in the tex2html_wrap_inline3222, tex2html_wrap_inline3224 and tex2html_wrap_inline3226, tex2html_wrap_inline3228 diagrams. The tex2html_wrap_inline3230 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 tex2html_wrap_inline3232 values indicated in Figs. 13 (click here)-16 (click here). The visual fit has been done mainly for stars brighter than tex2html_wrap_inline3234. 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 tex2html_wrap_inline3238, tex2html_wrap_inline3240 and tex2html_wrap_inline3242, tex2html_wrap_inline3244 diagrams could not be used for the distance determination of this cluster.

The mean values of tex2html_wrap_inline3246 are tex2html_wrap_inline3248, tex2html_wrap_inline3250, tex2html_wrap_inline3252 and tex2html_wrap_inline3254 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 tex2html_wrap_inline3260 to NGC 3228; tex2html_wrap_inline3262 to NGC 4103; tex2html_wrap_inline3264 to NGC 5662 and tex2html_wrap_inline3266 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.

  figure687
Figure 13: The tex2html_wrap_inline3268, tex2html_wrap_inline3270; tex2html_wrap_inline3272, tex2html_wrap_inline3274; tex2html_wrap_inline3276, tex2html_wrap_inline3278 and tex2html_wrap_inline3280, tex2html_wrap_inline3282 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 tex2html_wrap_inline3286 to the cluster is 8.5 mag, while its age is tex2html_wrap_inline3288 100 Myr

  figure692
Figure 14: The tex2html_wrap_inline3290, tex2html_wrap_inline3292; tex2html_wrap_inline3294, tex2html_wrap_inline3296; tex2html_wrap_inline3298, tex2html_wrap_inline3300 and tex2html_wrap_inline3302, tex2html_wrap_inline3304 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 tex2html_wrap_inline3308 to tex2html_wrap_inline3310 35 Myr old cluster is 11.5 mag

  figure697
Figure 15: The tex2html_wrap_inline3312, tex2html_wrap_inline3314; tex2html_wrap_inline3316, tex2html_wrap_inline3318; tex2html_wrap_inline3320, tex2html_wrap_inline3322 and tex2html_wrap_inline3324, tex2html_wrap_inline3326 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 tex2html_wrap_inline3330 to the cluster is 9.5 mag, while its age is tex2html_wrap_inline3332 80 Myr

  figure702
Figure 16: The tex2html_wrap_inline3334, tex2html_wrap_inline3336; tex2html_wrap_inline3338, tex2html_wrap_inline3340; tex2html_wrap_inline3342, tex2html_wrap_inline3344 and tex2html_wrap_inline3346, tex2html_wrap_inline3348 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 tex2html_wrap_inline3352 to the cluster is 9.9 mag. The object is tex2html_wrap_inline3354 65 Myr old


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