Exoplanetary spin-orbit alignment: Results from the ensemble of Rossiter-McLaughlin observations

One possible diagnostic of planet formation, orbital migration, and tidal evolution is the angle ψ between a planet's orbital axis and the spin axis of its parent star. In general, ψ cannot be measured, but for transiting planets one can measure the angle λ between the sky projections of the two axes via the Rossiter-McLaughlin effect. Here, we show how to combine measurements of λ in different systems to derive statistical constraints on ψ. We apply the method to 11 published measurements of λ, using two different single-parameter distributions to describe the ensemble. First, assuming a Rayleigh distribution (or more precisely, a Fisher distribution on a sphere), we find that the peak value is less than 22° with 95% confidence. Second, assuming that a fraction f of the orbits have random orientations relative to the stars, and the remaining fraction (1 - f) are perfectly aligned, we find f < 0.36 with 95% confidence. This latter model fits the data better than the Rayleigh distribution, mainly because the XO-3 system was found to be strongly misaligned while the other 10 systems are consistent with perfect alignment. If the XO-3 result proves robust, then our results may be interpreted as evidence for two distinct modes of planet migration.