4 Cluster parameters

In order to derive reddening, distance modulus and age of Melotte 105 and Hogg 15, we first matched the (V, B-V) and (V, V-I) CMDs to the Zero-Age Main Sequences (ZAMSs) of Schmidt-Kaler (1982) and Piatti et al. (1998), independently. We thus obtained for each cluster two apparent distance moduli V - M_v and two different colour excess E(B-V) and E(V-I) values. The errors in these quantities were estimated from the observed dispersion of MS stars. The average ratio E(V-I)/E(B-V) resulted in $1.28\pm0.05$, which is in very good agreement with the value 1.25 generally adopted for the normal extinction law (Walker 1985; Straizys 1990). Adopting 3.0 for the ratio R = A_v/E(B-V) of total to selective absorption, the true distance moduli were then derived for each cluster. Table 6 lists the resulting cluster parameters. The distance error was computed with the expresion: $\sigma (d) = 0.46\times[\sigma(V-M_v) + 3\times\sigma(E(B-V))]\times d$, where $\sigma(V-M_v)$ and $\sigma(E(B-V))$ represent the estimated errors in V-M_v and E(B-V), respectively. Figures 8 and 9 show the M_v vs. (B-V)₀ and M_v (V-I)₀ diagrams for Melotte 105 and Hogg 15, respectively. The ZAMS of Schmidt-Kaler (1982) and Piatti et al. (1998) have been adjusted to the adopted distance moduli in each cluster. Finally, cluster ages were derived by matching the (V, V-I) CMDs onto the empirical isochrones traced by Piatti et al. (1998) in the (M_v, (V-I)₀) plane. For that purpose, we used the mean reddening values and apparent distance moduli obtained previously. As shown in Fig. 10, both clusters seem to be moderately young.

Figure 8: (Mv, (B-V)0) and (Mv, (V-I)0) colour magnitude diagrams for stars in the field of Melotte 105. The solid lines represent the ZAMSs of Schmidt-Kaler (1982) and Piatti et al. (1998), respectively

Figure 9: (Mv, (B-V)0) and (Mv, (V-I)0) colour magnitude diagrams for stars in the field of Hogg 15. The solid lines represent the ZAMSs of Schmidt-Kaler (1982) and Piatti et al. (1998), respectively

Figure 10: (Mv, (V-I)0) colour magnitude diagrams (filled circles) with the isochrones of Piatti et al. (1998) superimposed. The big and small squares represent the position of the red giant clumps of NGC 6259 (age $\approx$ 0.2 Gyr) and NGC 3680 and IC 4651 (age $\approx$ 2.0 Gyr), respectively

As far as Melotte 105 is concerned, both the colour excess E(B-V) and the distance obtained in this study are in good agreement with the values derived by Sher (1965), i.e. 0.38 and 2.1 kpc, respectively. On the other hand, although Kjeldsen & Frandsen (1991) derived a distance similar to ours, the colour excess E(B-V) they obtained differs more than three times the error we estimated ( $\Delta E(B-V) = 0.09$). Indeed, the offset of 0.07 mags in the (B-V) colours found by Kjeldsen & Frandsen (1991) between their photometry and that of Sher (1965) explains, at least partially, the differences found in E(B-V). According to the present results, however, Melotte 105's age (350 Myr) is somewhat greater than those derived by Kjeldsen & Frandsen (1991) and Sher (1965), i.e. 150 Myr and 100 Myr, respectively. Balona & Laney (1995) also derived colour excess and distance similar to our values using CCD Strömgren photometry. They obtained E(b-y) = 0.34, equivalent to E(B-V) = 0.46 if the relation E(B-V) = 1.35 E(b-y) derived by Crawford (1978) is used, and $V_0 - M_v = 11.31\pm0.08$, equivalent to 1.8 kpc. Using their E(b-y) value, they estimated an age of 250$\pm$100 Myr for the cluster, closer to the one derived here. Balona & Laney (1995) explicitly suggested that a lower reddening produces a better agreement with an isochrone of 400 Myr. Indeed, as their Fig. 11 shows, the theoretical ZAMS does not fit the lower envelope of the cluster MS but rather the upper one. If we lower the E(b-y) reddening by $\approx$0.03 mag, then the cluster MS moves redwards, the fitting improves and the equivalent E(B-V) colour excess, distance modulus and age turn out to be in very good agreement with our present estimates. On the other hand, Santos & Bica (1993) and Ahumada et al. (2000) used integrated spectra to derive reddening and age for Melotte 105. Both studies agree that the reddening is approximately 0.3 mag and that the cluster is 200 Myr. Santos & Bica (1993) and Ahumada et al. (2000) argue that the lower colour excess obtained from integrated spectroscopy probably reflects the existence of internal dust associated to the cluster. However, neither the estimated age for this object nor the apparent width of the MS seen in the observed CMDs seem to be compatible with the probable existence of differential reddening within the cluster. We believe that the difference of scarcely more than 0.1 mag between the spectroscopic and the photometric reddenings is most probably due to the fact that the bright blue straggler (V = 11.29) contributes to the integrated light with a greater flux than the remaining cluster stars. We would like to note that the integrated spectral library used by Santos & Bica (1993) and Ahumada et al. (2000) have template spectra of 100 and 500 Myr, but no template in the 100-500 Myr range is yet available. Finally, according to Ahumada & Lapasset (1995) we should expect one blue straggler on average, which is in very good agreeement with the number of stars found in the blue straggler area of the CMDs of Melotte 105.

A comparison of the derived fundamental parameters of Hogg 15 with those given by Moffat (1974) reveals some discrepancies. Indeed, based on photoelectric photometry of only 15 MS stars, Moffat (1974) reached the conclusion that Hogg 15 is a very young cluster (8 Myr), reddened by E(B-V) = 1.16 and located in the inner arm-II at a distance of 4.2 kpc from the Sun. By contrast, the present study, based on the CCD photometry of approximately 200 probable MS stars, shows that Hogg 15 is a much older cluster (300 Myr), located at a significantly shorter distance (d = 2.6 kpc). Undoubtedly, the significant differences in age as well as distance, stem from the fact that Moffat included star WN6 HDE 311884 as a likely member of Hogg 15 with M_v = -5.9. This star, however, lies outside the cluster radius estimated by Moffat (see his Fig. 1) at a distance where the cluster star density drops off more than 8 times the central cluster star density, just close to the background star level. The differences in the E(B-V) values derived can be attributed to the different number of MS stars considered in either study and, probably, also to the fact that the interstellar material is not uniformly distributed in the direction towards the cluster. Based on integrated spectroscopy, Ahumada et al. (2000) derived a reddening of $1.05 \pm 0.05$ in better agreement with our estimate and an age of $5 \pm 2$ Myr. The significant age difference most probably arises from the contribution of the bright star HDE 311884 to the integrated light.

 

 

Table 6: Adopted cluster fundamental parameters

Cluster	E(B-V)	E(V-I)	V0 - Mv	d	Age
				(kpc)	(Myr)
Melotte 105	$0.42\pm0.03$	$0.57\pm0.03$	$11.75\pm0.25$	$2.2\pm0.3$	$350\pm50$
Hogg 15	$0.95\pm0.05$	$1.20\pm0.05$	$12.10\pm0.50$	$2.6\pm0.8$	$300\pm80$