Planetary migration

Planetary migration changes a planet's orbital semimajor axis through torques from a disc or exchanges of energy and angular momentum with other bodies, often followed by tidal dissipation. Short-period giant planets, eccentric progenitors, resonant architectures, and stellar obliquity provide complementary constraints rather than one unique migration diagnostic.

The stellar obliquity is the angle between a star's spin and a planet's orbital angular momentum. The Rossiter-McLaughlin effect constrains the angle $\lambda$ between the sky projections of those two axes, rather than a component of $\psi$. If the orbital and stellar-spin inclinations to the line of sight are $i_{\mathrm{orb}}$ and $i_{\ast }$, then $\cos \psi =\cos i_{\ast }\cos i_{\mathrm{orb}}+\sin i_{\ast }\sin i_{\mathrm{orb}}\cos \lambda$; $\lambda$ alone generally does not determine $\psi$. Large misalignments constrain formation and planetary migration, but can also reflect a tilted birth disc.

A transiting body hides different velocity regions of a rotating stellar disc and causes an anomalous measured Doppler shift. Its time dependence constrains the sky-projected spin-orbit angle, which is not generally the full stellar obliquity.