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 \(\psi \).
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Notes
- 1.
We would like to emphasize the efforts made by Lund M. N. and his collaborators for their work on HAT-P-7. This system turned out to be studied simultaneously and independently by our respective teams.
- 2.
Since the pressure gradient supports the gravity, \((1/\rho )(p/R_\star ) \sim c^2/R_\star \sim GM_\star /R_\star ^2\) or \(c/R_\star \sim \sqrt{G\rho _\star }\).
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Masuda, K. (2018). Three-Dimensional Stellar Obliquities of HAT-P-7 and Kepler-25 from Joint Analysis of Asteroseismology, Transit Light Curve, and the Rossiter–McLaughlin Effect. In: Exploring the Architecture of Transiting Exoplanetary Systems with High-Precision Photometry. Springer Theses. Springer, Singapore. https://doi.org/10.1007/978-981-10-8453-9_4
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