We studied the fields of nine nearby open star clusters based on the Tycho–2 catalogue .
We determined membership probabilities for the stars in the cluster fields from the stellar proper motions and used the Tycho–2 photometry to compute the initial mass function ( IMF ) of the clusters from the main sequence turn-off point down to approx . 1 M _ { \odot } .
We found IMF slopes ranging from \Gamma = -0.69 down to \Gamma = -2.27 ( when the Salpeter ( [ 1955 ] ) value would be \Gamma = -1.35 ) .
We also studied the membership of individual stars of special astrophysical interest .
In some cases previous results had to be revised .
As a by-product , we investigated some general properties of the Tycho–2 catalogue ; we confirmed that the Tycho–2 proper motions show only marginal deviations from the Hipparcos catalogue .
On the other hand , in some regions the completeness of the catalogue seems to decrease at magnitudes brighter than claimed by Høg et al .
( [ 2000 ] ) .