Three-Dimensional Stellar Obliquities of HAT-P-7 and Kepler-25 from Joint Analysis of Asteroseismology, Transit Light Curve, and the Rossiter–McLaughlin Effect

Abstract

Measurements of stellar obliquities for transiting systems are usually two-dimensional: either the sky-projection \(\lambda \) of the true obliquity, or the difference between orbital inclination (almost \(90 ^\circ \)) and stellar inclination \(i_\star \), is used to infer the degree of the spin–orbit misalignment. In this chapter, we develop a methodology for determining true stellar obliquity \(\psi \), combining the analyses of asteroseismology, transit light curves, and the Rossiter–McLaughlin effect. We demonstrate the power of such a joint analysis by applying it for the first time to two real systems, HAT-P-7 hosting a hot Jupiter and Kepler-25 with two transiting planets and another non-transiting one. We also show that the joint analysis allows for an accurate and precise determination of the numerous parameters characterizing the planetary system, in addition to \(\psi \).