Discovery of exoplanetary systems has presented a rather more complex picture of planetary architectures. Transiting exoplanets, those that cross the visible disk of their host stars from our vantage point, permit the measurement of the spin-orbit misalignment between the planetary orbital plane and the stellar equatorial plane that is projected onto the sky, as well as other crucial characteristics (Triaud 2018). This is what is referred to as the sky-projected obliquity angle (λ hereafter). Its measurement is performed through the observations of the Rossiter-McLaughlin effect (Rossiter 1924; McLaughlin 1924). For exoplanets, it entails observations of the stellar radial velocity (RV) during the planetary transit. The anomaly in the measured RV values arises from the deformation of absorption lines from which they are determined, which is caused by the transiting planet occulting either the blue- or red-shifted portion of the spinning stellar disk. The measurement of this effect is possible thanks to precision, high dispersion spectrographs at large telescopes that allow for one to obtain high resolution and large signal-to-noise ratio (S/N) spectra at relatively high temporal sampling. The measurement of λ has been performed for a large number of transiting exoplanets, full details of which can be found in TEPCAT1 (Southworth 2011). These have revealed a surprising diversity in the orbital alignments (for example Queloz et al. 2000; Winn et al. 2005, 2006, 2009; Triaud et al. 2009; Gandolfi et al. 2010; Mancini et al. 2018; Yu et al. 2018; Lendl et al. 2020; Sedaghati et al. 2021), which is in contrast to the Laplacian ideals of planets forming inside a flat disk, coplanar with the stellar equator and staying there (de Laplace 1796). A surprising picture that has emerged is that a significant fraction of those close-in hot-Jupiter regime planets are on misaligned orbits, as is evident in panel b of Fig. 1 (Albrecht et al. 2012; Dawson 2014). Furthermore, the spectral type of the host also appears to play a role, whereby giant planets around hot stars seem to exist on more oblique orbits (panel a of Fig. 1), perhaps pointing to a different, more chaotic formation history, as compared to their cooler counterparts. The relation between the obliquity and the host star temperature was observed by Winn et al. (2010), who placed the boundary between the two regimes at T⋆ = 6250 K (namely theKraft break; Kraft 1967). Hébrard et al. (2011) also point out a lack of planets with masses > 3 MJup on retrograde orbits, the distribution for which is shown in panel c of Fig. 1. Tidal interactions over time with the host star are also expected to realign orbits of close-in, massive planets (Zahn 1977). Attempts have been made to study the impact of stellar age on the obliquity of planetary orbits (for example Safsten et al. 2020; Anderson et al. 2021), with Triaud (2011) finding that hot-Jupiters around younger A stars are more misaligned, setting the age barrier at 2.5 Gyr. However, a lack of precision in the measured stellar ages and the absence of uniform and homogeneous studies estimating those ages have hindered any concrete conclusions being drawn with regard to the impact of stellar ages on planetary orbital alignments. This fact is evident in panel d of Fig. 1.
Citation: Gandolfi et al. 2010
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