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

2. Input data

2.1. Observations and data

An essential part of the observations for the proper motion survey was obtained with the Tautenburg Schmidt telescope (134/203/401) between 1961 and 1992. Eleven partly overlapping plate pairs with epoch differences from 23 to 30 years cover a total region of about 17 square degrees centered near Alcyone. Additionally, three second epoch Tautenburg plates were also included in the programme. In contrast to our previous proper motion determination based on these data (Meusinger et al. 1996), we added further 14 Astrographic Catalogue plates (Paris and Oxford zones) with observational epochs from 1891 to 1909.

The photometric survey is based on Tautenburg plates and plates taken with the Schmidt telescope (90/152/316) of the Observatoire de la Côte d'Azur (OCA). The observations, plate measurements and data reduction for the determination of the photographic B, V and R magnitudes as well as the discussion of the survey completeness are given in Meusinger et al. (1996).

2.2. Reductions

A central field of the proper motion survey of about 5.5 square degrees is overlapped by all 25 Tautenburg plates whereas field edges of 2 square degrees in total are covered only by one plate pair. The proper motions were determined for stars which were detected at least on one first and one second epoch Tautenburg plate. Additionally, there are at least two AC observations for stars brighter than .

To derive proper motions of the measured stars, we used the block-adjustment of overlapping plates by Eichhorn (1960). In this method the plate constants as well as the star constants - positions and proper motions - are regarded as unknowns in one least squares solution. In contrast to the usual plate-to-plate reduction, this approach allows to derive proper motions in a common reference system. With the AC measurements in the solution, the proper motion accuracy of stars brighter than could be increased simply by a longer time base. On the other hand, as the AC stars are distributed over the whole field of the survey, a better accuracy of bright stars improves the proper motion system and, consequently, the systematic accuracy of proper motions of faint stars becomes also better. Because of the very large system of equations (about 1 000 000 equations for 200 000 unknowns), an iterative solution was used where plate constants and star constants are determined alternatively.

The PPM was chosen as a reference catalogue. Altogether 269 PPM-stars were used to derive first estimates of the plate constants. On each Tautenburg plate we had 104 to 129 PPM-stars and on an AC-plate between 12 and 87 PPM-stars depending on the percentage of overlap with Tautenburg plates. Therefore, we used a second order polynomial for the Tautenburg and a first order polynomial for the AC-plates. With these plate constants, positions and proper motions were determined.

After the first iteration systematic errors in the proper motions were found. They are caused by the random errors of the catalogue. Therefore, a new catalogue was constructed containing all stars with accurate positions and proper motions smaller than 25 mas/yr and the reduction was newly started. For the new computations only the positions of the new catalogue were used assuming that all proper motions are zero. Now sixth order polynomials were applied for Tautenburg and first order polynomials for AC-plates. After 20 iterations the solution became stable and did no more show the systematic effects (Röser et al. 1995).

The proper motion survey includes about 40 000 stars. Fig. 1 shows the histogram of proper motion errors in declination as an example of the final accuracy of the solution.

Fig. 1. Histogram of the proper motion errors in declination (similar for right ascension).

2.3. Pleiades membership

In order to obtain the final member list, both kinematic and photometric selection procedures were applied to the data. These procedures considered loci of stars in the proper motion vector point diagram (VPD) and in the color-magnitude diagram (CMD). The selection was carried out in several steps.

Whereas the bulk of field stars in the VPD are concentrated towards the point mas/yr, mas/yr, the Pleiades show a clear concentration toward the center of their distribution at mas/yr, mas/yr. At the first step, we considered all stars around this point inside a circle with a radius of 25 mas/yr as preliminary cluster candidates. Due to significantly higher proper motion errors of stars with , the selection radius for faintest members in our sample was increased to 27.5 mas/yr. This preliminary proper motion selection yielded 1585 candidates including 234 stars with only V and R magnitude measurements. The most of the stars from the latter group belong to the faintest objects () in the survey which were not detected on B plates limited at mag. For each candidate, the proper motion membership probability was computed in accordance with the method described in Meusinger et al. (1996) using information on proper motion error distribution over magnitude and location of objects in the VPD.

As the second step, the following procedure was used for the photometric selection of the Pleiades members. The Pleiades candidates with the highest proper motion membership probabilities () and with available photoelectric photometry were used to construct their diagram. The diagram shows a clear cluster MS with a sharply defined blue edge. This "blue envelope" was quantified as a representative of the cluster ZAMS. Photometric membership probabilities were derived from the location of the preliminary candidates relative to the cluster MS taking into account the photometric accuracy of the data.

All Pleiades candidate stars having colors (1346 stars) were passed through the "photometric" filter. For the cluster candidates, the color deviation out of the blue envelope was computed. The stars to the right of the envelope were considered as the photometric cluster candidates with the highest photometric probability. All stars which deviate blue-ward out of the envelope further than were classified as field stars (i.e. zero photometric probabilities).

The final selection was carried out in the third step by the combining of the photometric and proper motion probabilities. We rejected from the cluster candidate list those stars which got one of the probabilities equal to zero. The stars with and (i.e. deviations larger than ) were excluded from the sample, too. Generally, the astrometric and photometric criteria showed a good coincidence. For a few critical cases, an additional analysis was necessary considering also individual proper motion and color errors. This step yielded 629 Pleiades candidates.

Since 239 faint candidate stars have no colors, the previous considerations could not be applied. We used the following procedure for these stars. The diagram was constructed for definite Pleiades members selected at the previous step, which have both and colors. The positions of 239 faint member candidates were compared with definite member positions in the diagram. The similar procedures as described in two previous steps were applied. As a result, 108 additional cluster candidates were selected. ¹

For 43 bright well established Pleiades members no reliable data could be obtained from Schmidt plate measurements. These stars were added to the sample with data taken from the literature. The sample defined by the photometric and proper motion constraints includes 780 Pleiades members in total.

2.4. Final sample

The proper-motion survey covers a quite unregularly shaped area (Fig. 2). This may lead to selection effects, e.g. due to the well-known fact of mass segregation. In order to avoid a possible bias, we have selected Pleiades members only which fall inside the maximum circle around the cluster center (see Fig. 2). The cluster center was determined from star counts at ). The radius of the circle is 111.68 arcmin. Altogether, there are 647 cluster members within this circle. We use this sample throughout the paper.

Fig. 2. Distribution of 780 Pleiades members in x,y-plane. The broken line indicates the area covered by the proper motion survey limits. The cross of lines corresponds to the cluster center derived by star counts. The circle is the edge of the area where the final list of Pleiades members was selected from. Scale is .

2.5. Adopted parameters

The distance modulus as derived by HIPPARCOS parallax observations (Mermilliod et al. 1997) was applied with the color excess , which is close to from Crawford and Perry (1976) and to the standard value of (Meusinger et al. 1996).

2.6. Evolutionary tracks

In order to construct theoretical isochrones and LFs which include both post-MS and pre-MS stages for ages typical to that of the Pleiades (about 100 Myrs), we combined Population I pre-MS evolutionary tracks of D'Antona and Mazzitelli (1994) and Maeder group post-MS calculations (Schaller et al. 1992). We selected the MLT convection and Alexander opacities subset of D'Antona and Mazzitelli tracks which is in the best agreement with observations of M-dwarf binaries (Malkov et al. 1997). Both systems were properly tuned to provide continuous transition from pre- to post-MS ages at the same mass as well as smooth and uniform mass-luminosity and mass-radius relations along the ZAMS.

To conform the new Pleiades color - absolute magnitude diagram (i.e. the new trigonometric parallax distance modulus, derived by HIPPARCOS) with the theoretical ZAMS for normal metallicity (Z=0.02), the helium abundance which fits the cluster ZAMS best (Y=0.34) was derived. The model positions in the theoretical HRD were corrected for the difference between the original model helium content and the "best" Pleiades Y-value of 0.34 according to

valid for pp-cycle and (see Sears and Brownlee 1965). It should be stressed that there is no direct observational evidence supporting such a high helium abundance of Pleiades stars. But in absence of a general idea how to remove a discrepancy of order of between the Pleiades and Preasepe group clusters main sequences (see Mermilliod et al. 1997), we used helium abundance as a free parameter to provide the fine adjustment of the observed and theoretical CMDs. We can state that with the corrections applied the agreement between the theoretical and the observed CMD became even better, than it was with older distance and normal helium abundance.

The isochrones were interpolated from the track system according to the technique described by Belikov and Piskunov (1997b).

2.7. Scales

In order to convert theoretical coordinates of the Hertzsprung-Russell diagram, , to the observed ones, , we used bolometric corrections and - relations from Schmidt-Kaler tables (1982) for the luminosity classes I, III and V.

© European Southern Observatory (ESO) 1998

Online publication: March 23, 1998
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