We investigate to what extent the spin axes of stars in young open clusters are aligned. Assuming that the spin vectors lie uniformly within a conical section, with an opening half-angle between lambda=0 (perfectly aligned) and lambda=90 degrees(completely random), we describe a Monte-Carlo modelling technique that returns a probability density for this opening angle given a set of measured sin i values, where i is the unknown inclination angle between a stellar spin vector and the line of sight. Using simulations we demonstrate that although azimuthal information is lost, it is easily possible to discriminate between strongly aligned spin axes and a random distribution, providing that the mean spin-axis inclination lies outside the range 45--75 degrees. We apply the technique to G- and K-type stars in the young Pleiades and Alpha Per clusters. The sin i values are derived using rotation periods and projected equatorial velocities, combined with radii estimated from the cluster distances and a surface brightness/colour relationship. For both clusters we find no evidence for spin-axis alignment: lambda=90 degrees is the most probable model and lambda>40 degrees with 90 per cent confidence. Assuming a random spin-axis alignment, we re-determine the distances to both clusters, obtaining 133+/-7pc for the Pleiades and 182+/-11 pc for Alpha Per. If the assumption of random spin-axis alignment is discarded however, whilst the distance estimate remains unchanged, it has an additional +18/-32 percent uncertainty.
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