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

TL;DR

This study develops a Monte Carlo method to assess whether stars in young clusters have randomly aligned spin axes, finding no evidence for alignment in the Pleiades and Alpha Per clusters, and refining their distance estimates.

Contribution

It introduces a novel Monte Carlo technique to determine spin-axis alignment in star clusters using sin i measurements, capable of distinguishing aligned from random orientations.

Findings

No evidence for spin-axis alignment in Pleiades and Alpha Per clusters.

Distance estimates for clusters are consistent with previous measurements under random alignment.

The method can discriminate between aligned and random spin axes given certain inclination angles.

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 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.