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Astron. Astrophys. 357, 471-483 (2000)

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3. NGC 1960

3.1. Proper motion study

With the method described above, we determined the proper motions of 1,190 stars within the entire field of the photographic plates. We found that the limiting magnitude of the second epoch plates is brighter than that of the first epoch plates. This effect is compensated by the addition of the CCD data, so that in the cluster region we reach fainter stars than in the outer region of the field. Therefore, the limiting magnitude of the proper motion study is fainter in the area for which the CCD data were available.

After four iterations of proper motion determination, the comparison of the computed proper motions with ACT led to systematic positional differences of the order of [FORMULA] and [FORMULA] and for the proper motions of around [FORMULA]. The internal dispersion of the proper motions was computed from the deviations of the positions from a linear fit of [FORMULA] and [FORMULA] as functions of time. We derived mean values of [FORMULA] and [FORMULA] for individual stars.

We detected a slight, but systematic slope of the proper motions in [FORMULA] depending on the magnitude of the stars resulting in a difference of approximately [FORMULA] for the proper motions between the brightest and faintest members. As the magnitude range of the ACT catalogue within our field of view is limited to approximately 11 mag, we used the positions provided by the Guide Star Catalog (GSC) Version 1.2 (Röser et al. 1998), which covers stars over the entire range of our proper motion study, for further analysis. The disadvantage of GSC is the fact that it does not provide proper motions. Therefore, all results obtained with this catalogue are relative proper motions only. Fig. 7 shows the proper motions in [FORMULA] and their dependence on the magnitudes derived from this computation for the stars in the inner region of the photographic plates. The diagram shows that only the stars brighter than [FORMULA] are influenced by a clear magnitude term leading to deviations of up to [FORMULA] with respect to the stars fainter than [FORMULA] which do not show any systematic trend. We included a magnitude term into our transformation model, however, since the behaviour is not linear with magnitudes and different from plate to plate we were unable to completely eliminate the effect. Furthermore, taking into account that many of the ACT stars are brighter than [FORMULA], it is clear that this deviation was extrapolated over the entire range of the proper motion study.

[FIGURE] Fig. 7. Dependence of the proper motions in [FORMULA] on the magnitude for the stars in the field of NGC 1960. The diagram shows a clear magnitude term for the stars brighter than 10.5 mag. Note that these proper motions were computed on the basis of GSC 1.2 so that we deal with relative proper motions here. The solid line sketches the mean proper motion for the cluster member stars. See the text for further discussion

Meurers (1958), who had used the same first epoch material for his proper motion study, found a similar phenomenon and suggested that the bright and the faint stars in the region of NGC 1960 form independent stellar "aggregates". In his study the proper motion difference between bright and faint stars is much more prominent. Taking into account his smaller epoch difference of 36 years this could be explained assuming that the effect is caused by (at least some of) the first epoch plates on which the positions of the brighter stars seem to be displaced by an amount of approximately [FORMULA] to [FORMULA] compared to the fainter objects, whereas both his and our second epoch data are unaffected. This proposition would also explain why we did not detect this inaccuracy during the determination of the positions on the plates, since the uncertainties of single positional measurements are of the same order of magnitude.

The proper motions in [FORMULA] proved to be unaffected by this phenomenon.

We found that when using the ACT based proper motions, the membership determination is not affected by this problem, since the magnitude trend in [FORMULA] is smoothed over the magnitude range (in comparison with Fig. 7). On the other hand, in the GSC solution, the bright stars have proper motions differing too much from the average so that almost all of them are declared non-members. Therefore we used the results based on the ACT data for the computation of the membership probabilities. Table 7 shows a list of all proper motions determined on the base of the ACT catalogue.


[TABLE]

Table 7. List of all stellar proper motions determined from the photographic plates and the additional CCD images of NGC 1960. The positions are given for the epoch 1950.0 in the equinox J2000.0 coordinate stystem. The stellar id numbers are the same as in Table 2. Again, the stellar numbers from Boden (1951) are listed in addition. Only the proper motions of the same stars as in Table 2 are presented here, the complete table is available online at the CDS archive in Strasbourg


The vector point plot diagram as determined on the base of ACT for the stars in the central region of the plates is presented in Fig. 8. Membership determination resulted in 178 members and 226 non-members of NGC 1960. The distribution of membership probabilities sketched in Fig. 9 shows a clear separation of members and non-members with only a small number of stars with intermediate membership probabilities. The centre of the proper motion distribution of the cluster members in the vector point plot diagram is determined to be

[EQUATION]

[FIGURE] Fig. 8. Vector point plot diagram of the stars in the region of NGC 1960. The stars with a membership probability of less than 0.8 are indicated by small, the others by larger dots. The width of the distribution of the stars with a high membership probability is of the order of [FORMULA] which coincides with the standard deviation of the proper motion of a single star

[FIGURE] Fig. 9. Histograms of the membership probabilities for the stars of NGC 1960 (upper diagram) and NGC 2194 (lower diagram). All stars with membership probabilities of 0.8 or higher are considered cluster members. Note that the separation between members and non-members is less prominent for NGC 2194 than for NGC 1960

The width of the Gaussian distribution of the proper motions is around [FORMULA] and hence the same as the [FORMULA] error of the proper motion of a single object. The field moves very similarly with

[EQUATION]

The similarity of field and cluster proper motions makes membership determination a difficult task: Several field stars which by chance have the same proper motion as the cluster stars will be taken for members.

These results cannot be used for a determination of the absolute proper motion of the cluster, since the centre of the distribution can be assumed to be displaced upwards in the vector point plot diagram as a consequence of the magnitude dependence of the [FORMULA] values. To obtain reliable absolute proper motions, nevertheless, we used the fainter ([FORMULA]) part of the proper motions computed on the base of GSC 1.2 which are stable with magnitudes and compared their relative proper motions with the values given for the corresponding stars in the ACT. We found a difference of [FORMULA] and [FORMULA] and centres of the GSC based proper motion distributions of [FORMULA] and [FORMULA]. As a consequence we determined the absolute proper motions of NGC 1960 to be

[EQUATION]

As expected, the value of the proper motion in right ascension is - compared to Eq. (7) - unaffected within the errors, whereas [FORMULA] is different from the value of Eq. (8) by a value which corresponds to the [FORMULA] error of [FORMULA].

3.2. Colour magnitude diagram properties

The CMD of NGC 1960 (Fig. 10) shows a clear and narrow main sequence with an indication of a second main sequence including approximately 15 stars from [FORMULA] to [FORMULA] (corresponding to masses from [FORMULA] to [FORMULA]). These stars might be Be stars (see, e.g., Zorec & Briot 1991) or unresolved binaries (see, e.g., Abt 1979or the discussion in Sagar & Richtler 1991).

[FIGURE] Fig. 10. Colour magnitude diagram of all members of NGC 1960 as determined with the proper motions ([FORMULA]) and statistical field star subtraction ([FORMULA]). The dashed line stands for the borderline between the two methods of membership determination; the dotted lines indicate the corridor containing the main sequence for the IMF computation (see Sect. 2.5 for details). The parameters of the isochrone plotted in the diagram are listed in Table 8. The three stars marked with special symbols are discussed in Sect. 3.2

Slettebak (1985) reports on two Be stars in NGC 1960. One of them, our star 1374 (Boden's (1951) star No. 505, erroneously named No. 504 by Slettebak), clearly fails to fulfil our membership criterion with a proper motion of [FORMULA] and [FORMULA]. In addition, it is located so far off the centre of the cluster that it is even outside the field of our CCD images. On the other hand, star 4 (Boden's (1951) star No. 101, [FORMULA], [FORMULA]) shows a proper motion of [FORMULA] and [FORMULA] which makes it a very likely cluster member with a membership probability of 0.95. In Fig. 10, this object is marked with a circle. A third Be star in the region is mentioned in the WEBDA database (Mermilliod 1999): Boden's (1951) star No. 27, or our star 8. We obtained a proper motion of [FORMULA], [FORMULA]. From these figures we computed a membership probability of 0.89 so that this star is a likely cluster member. We marked this object in Fig. 10 with a cross. As there is no evidence for any further Be stars, it is plausible to assume that the other stars forming the second main sequence most likely are unresolved binary stars.

The star at [FORMULA], [FORMULA] (star 29 of our sample, marked with a triangle in Fig. 10) does not fit to any isochrone which properly represents the other stars in this magnitude range. It shows a proper motion of [FORMULA] and [FORMULA] resulting in a membership probability of 0.97. This object may be an example for a star which coincidentally shows the same proper motion as the cluster, but being in fact a non-member.

From our isochrone fit, we derived the parameters given in Table 8. Age determination was quite a difficult task for NGC 1960, as there are no significantly evolved (red) stars present in the CMD. We found that the 16 Myr isochrone might be the optimal one, since it represents the brightest stars better than the (in terms of ages) neighbouring isochrones. The comparably large error we adopted reflects this consideration.


[TABLE]

Table 8. Parameters of NGC 1960 and NGC 2194 as derived from isochrone fitting to the colour magnitude diagram


3.3. Initial mass function

The determination of the IMF slope from the completeness corrected data obtained from the CMD (Fig. 10) leads to the value of [FORMULA] for NGC 1960 in a mass interval from [FORMULA] down to [FORMULA] (corresponding to [FORMULA] to [FORMULA]). This restriction was chosen to guarantee a completeness of the photometry of at least 60%. To test the stability of the IMF concerning the probable double star nature of several objects, we assumed the stars above the brighter part of the main sequence (a total of 18 objects) to be unresolved binary stars with a mass ratio of 1 and computed the IMF of this modified sample, as well. The slope increased to the value of [FORMULA] within the same mass range, representing a slightly shallower IMF. Anyway, the influence of a binary main sequence is negligible within the errors. We also experimented with leaving out the magnitude range critical for membership determination (see Sect. 3.1 and Fig. 7), i.e. the stars brighter than [FORMULA] ([FORMULA]), and derived [FORMULA] - a result which coincides well within the errors with the above ones. This shows once more that the membership determination - and therefore the IMF - was almost not affected by the magnitude term of our proper motion study. Fig. 12 sketches the IMF of NGC 1960.

[FIGURE] Fig. 11. Luminosity function of NGC 1960. The solid line stands for the completeness corrected data, the dotted line for the uncorrected values. The rightmost bin almost reaches the limit of our photometric study so that it cannot be taken for reliable

[FIGURE] Fig. 12. Initial mass function of NGC 1960. The solid histogram corresponds to the completeness corrected values, the dotted one to the original data. The IMF slope calculated with a maximum likelihood analysis is determined to be [FORMULA]. The stars with [FORMULA] (i.e. [FORMULA]) were not taken into account for the slope determination as the average completeness for those stars is below 60%. The limits of the IMF line illustrate the mass range under consideration. The probable binary nature of some objects is not taken into account in this plot

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Online publication: June 5, 2000
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