Are the spin axes of stars randomly aligned within a cluster?

Abstract

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 λ= 0° (perfectly aligned) and λ= 90° (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°. 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: λ= 90° is the most probable model and λ >40° with 90 per cent confidence. Assuming a random spin-axis alignment, we redetermine the distances to both clusters, obtaining 133 ± 7 pc 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 per cent uncertainty.