Astron. Astrophys. 332, 575-585 (1998)

3. Analysis of observational data

The color-magnitude diagram of the sample is shown in Fig. 3. Due to high quality photometric data, the Pleiades main sequence is clearly outlined. The lower envelope at from to evidently coincides with the ZAMS. At brighter magnitudes up to the MS turn-off point at stars are already evolving off the ZAMS. Stars fainter than are lifted above the ZAMS and follow rather pre-MS isochrones, than the ZAMS. As isochrones show, the turn-on point is located within the interval from to . The upper MS envelope also being clearly defined by accurate data presumably indicates the equal mass unresolved binaries sequence. Lower quality photographic data show a definite scattering around the ZAMS, which could be attributed to higher photometric errors of photographic magnitudes. The scattering increases toward faintest magnitudes and reaches the maximum value at from to . For the adopted distance modulus and color excess, theoretical data are in good agreement with observed points for both upper and lower MS.

Fig. 3. Color - magnitude diagram of the Pleiades sample. Panel a: all stars, panel b: Pre-MS portion. Plus signs indicate the members with the high quality photometry, open circles are those with photographic magnitudes. The line denoted as "ZAMS" is the used theoretical ZAMS. The isochrones of , and 7.95 for both post-MS, and pre-MS stages are also shown.

In order to reveal details of the Pleiades LF, we have to use a technique more sophisticated than a histogram construction. We used the kernel estimation method with the simplest "naive" (rectangular) kernel (see Silverman (1986) for more details of the method)

where

and i goes through the data sample.

The smoothing procedure was applied to the theoretical LF with the same "naive" kernel as for the observed LF. The smoothing parameter and step were used in calculations. From numerical tests with our data sample we found that a larger smoothing parameter (, for instance) oversmoothes the resulting LF while undersmoothes.

The empirical LFs in for defined Pleiades members and non members in our preliminary sample of 1585 cluster candidates are shown in Fig. 4. The clear difference between the distributions confirms the correctness of the selection procedure. As the proper motion survey is complete down to (Meusinger et al. 1996), we considered the LF as reliable in the absolute magnitude range from to and concluded that all structural details within this interval reflect the real behaviour of the LF. We considered the LF drop at as a possible incompleteness at fainter magnitudes.

Fig. 4. The observed Pleiades LFs. Panel a: raw LF, binned in 0.2 mag. boxes, panel b: smoothed LFs. Thick continuous line for all members, dotted curve - "inner" members (i.e. located inside the circle in Fig. 2), thin continuous line - "outer" members (i.e. located outside the circle in Fig. 2), dashed line - non member stars assuming the same distance as for the Pleiades. 1 - MS/pre-MS transition dip, 2 - Wielen dip, 3 - Kroupa et al. (1990) dip.

The Pleiades LF obviously consists of several sections. The first one () is, in fact, the MS LF portion and reveals the behaviour typical for young open cluster LFs. The second portion () represents a plateau with three dips at , and . The first dip together with the adjacent maximum has a pre-MS nature and is discussed in Sect. 4. The fainter dips could be identified with the features known from the field star LF: the well established Wielen dip () and a dip which was discussed first by Kroupa et al. (1990). To our knowledge, this is the first time when both of these field star LF features were discovered in a star cluster LF also. All these dips could be also seen in the Pleiades CMD (see Fig. 3b). The last LF section () is a domain of further increase of the LF. Unfortunately, due to the survey limit we could not safely realize how steep the slope of the faint LF is and where the LF turnover point will be reached.

In order to evaluate independently the statistical significance of the proposed dips in the LF, we performed a series of Monte Carlo experiments with a probability distribution function equal to a raw luminosity function shown in Fig. 4a and with a suitable photometric error distribution with stellar magnitude. We removed consequently from the LF the proposed dips to prove whether they could appear as a result of small number statistics. As the simulations showed, the existence of the gaps could not be rejected at 87% confidence level for the first feature, 94% level for Wielen dip, and 98% level for Kroupa et al. dip. Furthermore, we applied Monte Carlo simulations as described by Meusinger et al. (1996) to study the effect of a correction for unresolved binaries. In general, such a correction will slightly smooth out the observed LF fine structure. However, the resulting LFs showed clearly the three dips in 95 out of 100 simulation runs.

© European Southern Observatory (ESO) 1998

Online publication: March 23, 1998
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