Kinematic ages of OB associations

Astrometric data from the HIPPARCOS mission include measurements of early-type stars in nearly all OB associations within 1 kpc from the Sun, and are available as of 1996. In anticipation thereof we studied the determination of kinematic ages and initial sizes of OB associations, These studies have traditionally been done using proper motion data. We investigate their reliability by generating synthetic data, using self-consistent N-body simulations of an OB association. We consider two classical methods for deriving the kinematic age. First, the proper motions of the stars are traced back in time to the smallest configuration in the past, which is assumed to correspond to the initial state of the association. Secondly, the proper motion in a certain direction is plotted versus the corresponding coordinate, and then the linear expansion coefficient is measured to derive the kinematic age. We find that the first method always leads to underestimated ages. All age estimates converge to similar to 4 Myr. The second method can lead to overestimated as well as underestimated ages, depending on the chosen coordinate direction and the magnitude of the effects of virtual expansion caused by radial motion. The first method also provides an estimate of the initial size of the OB association, which is always overestimated. We conclude that the longstanding discrepancy between the kinematic and nuclear ages for OB associations can be attributed to underestimates of the kinematic age.