2 Observational data

We selected in the BDA database (Mermilliod 1995) clusters with distance less than 1 kpc as explained above. For extended clusters, the basic hypothesis of the statistical method, that all the stars of a cluster have about the same proper motion, may not be valid. Other methods, like the convergence point method, would be preferable. In addition, for extended regions, a too large a number of field stars would have to be considered. For this reason, we excluded clusters more extended than about 2 degrees, like those studied by Platais et al. (1998).

We searched for the selected clusters in the Tycho2 Catalogue, using the central coordinates and the radius taken from the database. In many cases the central coordinates of the cluster are different from those given in the ESO Catalogue (Lauberts 1982); in these cases we opted to use the ESO coordinates. All the stars situated within the limits of the clusters were investigated. For open clusters with an apparent diameter less than $15^{\prime}$ we searched for stars in an area 4 times the cluster area and if $D \geq 15^{\prime}$ we used an area covered by the cluster.

In Table 1 (available in electronic form at the CDS) are given the other clusters for which the statistical method was unable to provide accurate proper motions. From a total of 168 clusters initially selected, we obtained satisfactory results for 112.

The Tycho2 Catalogue is based on the original Tycho Catalogue (ESA 1997); it contains accurate photometry and astrometry of about 2.5 million stars. For the faintest stars in common with Tycho1, Tycho2 has better positional and photometric accuracies. This is because the new method of reduction applied to Hipparcos data uses photon superposition for each star, for the ensemble of observations made during the entire mission, instead of treating each observation separately.

The Tycho2 Catalogue presents very precise proper motions. The internal or random errors are generally between 1 and 3 mas/yr. Tycho2 proper motions are in the Hipparcos system; there are no significant systematic differences between the proper motions of the two catalogues, as shown by Urban et al. (2000). The systematic errors, under 0.5 mas/yr, are typically 10$\%$ of the random errors, and are about equal to the formal errors for the rotation of the Hipparcos proper motion with respect to the ICRS, estimated to be 0.25 mas/yr (Kovalevsky et al. 1997). More details on the construction of the Tycho2 Catalogue are given by Hog et al. (2000). The high quality of the Tycho2 proper motions and their agreement with the Hipparcos set allow the determination of mean proper motions and memberships of open clusters.