  One possible diagnostic of planet formation, orbital migration, and tidal
evolution is the angle psi between a planet's orbital axis and the spin axis of
its parent star. In general, psi cannot be measured, but for transiting planets
one can measure the angle lambda between the sky projections of the two axes
via the Rossiter-McLaughlin effect. Here, we show how to combine measurements
of lambda in different systems to derive statistical constraints on psi. We
apply the method to 11 published measurements of lambda, 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 degrees with 95% confidence.
Second, assuming 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.
