On the tidal evolution of Hot Jupiters on inclined orbits

By A. Barker, Gordon I. Ogilvie. 2009

190 citations recorded by the source corpus.

Tidal friction is thought to be important in determining the long-term spin-orbit evolution of short-period extrasolar planetary systems. Using a simple model of the orbit-averaged effects of tidal friction, we study the evolution of close-in planets on inclined orbits, due to tides. We analyse the effects of the inclusion of stellar magnetic braking by performing a phase-plane analysis of a simplified system of equations, including the braking torque. The inclusion of magnetic braking is found to be important, and its neglect can result in a very different system history. We then present the results of numerical integrations of the tidal evolution equations, where we find that it is essential to consider coupled evolution of the orbital and rotational elements, including dissipation in both the star and planet, to accurately model the evolution. The main result of our integrations is that for typical Hot Jupiters, tidal friction aligns the stellar spin with the orbit on a similar time as it causes the orbit to decay. This tells us that if a planet is observed to be aligned, then it probably formed coplanar. This reinforces the importance of Rossiter–McLaughlin effect observations in determining the degree of spin-orbit alignment in transiting systems. We apply these results to the only observed system with a spin-orbit misalignment, XO-3, and constrain the efficiency of tidal dissipation (i.e. the modified tidal quality factors Q′) in both the star and the planet in this system. Using a model in which inertial waves are excited by tidal forcing in the outer convective envelope and dissipated by turbulent viscosity, we calculate Q′ for a range of F-star models, and find it to vary considerably within this class of stars. This means that using a single Q′, and assuming that it applies to all stars, is probably incorrect. In addition, we propose an explanation for the survival of two of the planets on the tightest orbits, WASP-12 b and OGLE-TR-56 b, in terms of weak dissipation in the star, as a result of their internal structures and slow rotation periods.

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/ae6753ad8133f583b9ab4e15b7c1351907482777

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In Astronomy and Astrophysics

1. J. Winn
2. D. Lai
3. Jon Fortney
4. J. Johnson
5. F. Rasio
6. G. Chabrier
7. D. Fabrycky
8. J. Southworth

Citations in the corpus

• TIDAL EVOLUTION OF CLOSE-IN PLANETS (2010, methodology): “Comparison with Levrard et al. (2009) Note that, although the stellar-dissipation-driven case (τe ∼ τa) looks similar to the one illustrated by LWC09, there are fundamental differences.”
• HOT STARS WITH HOT JUPITERS HAVE HIGH OBLIQUITIES (2010, methodology): “A third objection, and the hardest to overcome, is that obliquity damping is accompanied by orbital decay, threatening the planet with engulfment (Levrard, Winisdoerffer, & Chabrier 2009, Barker & Ogilvie 2009).”
• On internal wave breaking and tidal dissipation near the centre of a solar-type star (2010, background): “…estimates do not accurately reflect the evolution if the orbit is eccentric, inclined or if the stellar spin is not much slower than the orbit (Barker & Ogilvie 2009), but this estimate shows that this mechanism can be very efficient in contributing to the tidal evolution of hot Jupiters on…”
• Transits and Occultations (2010, background): “Likewise, in most cases one would not expect that enough time has elapsed for tides to modify the star’s spin rate or orientation (Barker & Ogilvie 2009).”
• Tidal dissipation in planet-hosting stars: damping of spin-orbit misalignment and survival of hot Jupiters (2011, methodology): “Many previous works on tidal evolution in hot Jupiter systems (e.g., Rasio et al. 1996; Sasselov 2003; Dobbs-Dixon et al. 2004; Barker & Ogilvie 2009; Jackson et al. 2009; Levrard et al. 2009; Hansen 2010; Matsumura et al. 2010) were based on the weak friction theory of equilibrium tides.”
• The TRAPPIST survey of southern transiting planets. I. Thirty eclipses of the ultra-short period planet WASP-43 b (2012, background): “…with the host star that should lead in most cases to a slow spiral-in of the planet and to a transfer of angular momentum to the star (e.g. Barker & Ogilvie 2009, Jackson et al. 2009, Mastumura et al. 2010), the end result being the planet’s disruption at its Roche limit (Gu et al. 2003).”
• Is tidal heating sufficient to explain bloated exoplanets? Consistent calculations accounting for finite initial eccentricity (2010, methodology): “(19) to rewrite the tidal equation and to keepQ′ constant instead of ∆t as done by, for example, Mardling & Lin (2002), Dobbs-Dixon et al. (2004) and Barker & Ogilvie (2009), one must keep in mind that this procedure is not equivalent either to the constant phase lag (i.e. constant Q) or time lag…”