Spin-orbit angle distribution and the origin of (mis)aligned hot Jupiters

Abstract

Context. For 61 transiting hot Jupiters, the projection of the angle between the orbital plane and the stellar equator (called the spinorbit angle) has been measured. For about half of them, a significant misalignment is detected, and retrograde planets have been observed. This challenges scenarios of the formation of hot Jupiters. Aims. In order to better constrain formation models, we relate the distribution of the real spin-orbit angle Ψ to the projected one β. Then, a comparison with the observations is relevant. Methods. We analyse the geometry of the problem to link analytically the projected angle β to the real spin-orbit angle Ψ. The distribution of Ψ expected in various models is taken from the literature, or derived with a simplified model and Monte Carlo simulations in the case of the disk-torquing mechanism.Results. An easy formula to compute the probability density function (PDF) of β knowing the PDF of Ψ is provided. All models tested here look compatible with the observed distribution beyond 40 degrees, which is so far poorly constrained by only 18 observations. But only the disk-torquing mechanism can account for the excess of aligned hot Jupiters, provided that the torquing is not always efficient. This is the case if the exciting binaries have semi-major axes as large as ∼10 4 AU. Conclusions. Based on comparison with the set of observations available today, scattering models and the Kozai cycle with tidal friction models can not be solely responsible for the production of all hot Jupiters. Conversely, the presently observed distribution of the spin-orbit angles is compatible with most hot Jupiters having been transported by smooth migration inside a proto-planetary disk, itself possibly torqued by a companion.

Highly inclined and eccentric massive planets

“…In this frame, the observed misalignment of approximately half of the hot Jupiters with respect to the stellar equator could be the result of a misalignment between the old disc midplane and the present stellar equator (see for instance Crida & Batygin 2014).…”

Detecting the spin-orbit misalignment of the super-Earth 55 Cancri e

“…Whereas first observed systems revealed aligned, prograde orbits (e.g., Queloz et al 2000;Winn et al 2005;Loeillet et al 2008), first misaligned systems were reported with the cases of XO-3 (Hébrard et al 2008;Winn et al 2009c;Hirano et al 2011) and HD 80606 (Moutou et al 2009;Pont et al 2009;Winn et al 2009a;Hébrard et al 2010). About thirty misaligned systems have been identified today over more than eighty measured systems 1 (Albrecht et al 2012;Crida & Batygin 2014), including some with retrograde or nearly polar orbits (e.g., Winn et al 2009b;Narita et al 2010;Triaud et al 2010;Hébrard et al 2011). These unexpected results favor scenarios where close-in massive planets have been brought in by planet-planet (or planet-star) scattering, Kozai migration, and/or tidal friction, rather than more standard scenarios implying disk migration that are expected to conserve the initial alignment between the angular momentums of the disk and of the planetary orbits (see, e.g., Fabrycky & Tremaine 2007;Guillochon et al 2011), although some models show that the initial misalignment of a planet can be maintained through its interactions with the disk (Teyssandier et al 2013).…”

The Imprint of Exoplanet Formation History on Observable Present-Day Spectra of Hot Jupiters

“…These mechanisms take place after the dispersal of the protoplanetary disk and can lead to highly inclined planets. To date, it is debated whether disk migration or scattering/Kozai is the dominant mechanism leading to close-in planets (e.g., Crida & Batygin 2014). …”