### Abstract

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.

Original language | English (US) |
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Pages (from-to) | 1230-1240 |

Number of pages | 11 |

Journal | Astrophysical Journal |

Volume | 696 |

Issue number | 2 |

DOIs | |

State | Published - May 10 2009 |

### All Science Journal Classification (ASJC) codes

- Astronomy and Astrophysics
- Space and Planetary Science

### Keywords

- celestial mechanics
- methods: statistical
- planetary systems
- stars: rotation

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## Cite this

*Astrophysical Journal*,

*696*(2), 1230-1240. https://doi.org/10.1088/0004-637X/696/2/1230