Interplay of Tidal Evolution and Stellar Wind Braking in the Rotation of Stars Hosting Massive Close-in Planets

Abstract

This paper deals with the application of the creep tide theory (Ferraz-Mello) to the study of the rotation of stars hosting massive close-in planets. The stars have nearly the same tidal relaxation factors as gaseous planets and the evolution of their rotation is similar to that of close-in hot Jupiters: they tidally evolve toward a stationary solution. However, stellar rotation may also be affected by stellar wind braking. Thus, while the rotation of a quiet host star evolves toward a stationary attractor with a frequency ( e 1 6 2 + ) times the orbital mean motion of the companion, the continuous loss of angular momentum in an active star displaces the stationary solution toward slower values: active host stars with big close-in companions tend to have rotational periods longer than the orbital periods of their companions. The study of some hypothetical examples shows that, because of tidal evolution, the rules of gyrochronology cannot be used to estimate the age of one system with a large close-in companion, no matter if the star is quiet or active, if the current semimajor axis of the companion is smaller than 0.03-0.04 AU. Details on the evolution of the systems: CoRoT LRc06E21637, CoRoT-27, Kepler-75, CoRoT-2, CoRoT-18, CoRoT-14 and on hypothetical systems with planets of mass 1-4 M Jup in orbit around a star similar to the Sun are given.

Transiting exoplanets from the CoRoT space mission

“…This relatively old system shows an eccentric orbit; the study of the tidal evolution of this system (Ferraz-Mello et al 2015) shows that because of the distance between the brown dwarf and the star (0.0626 AU), an existing initial eccentricity is not damped to zero during the stellar lifetime, however, the presently observed rotational period of the star cannot be explained without taking the interplay between magnetic braking of the star and tidal forces into account.…”

“…Several factors concur to make this system one of the best suitable for the study of the interplay of magnetic braking and tidal evolution: the high mass of CoRoT-33b, the short distance from it to the star, and the age of the system. The simulations done by Ferraz-Mello et al (2015) show that in a system like CoRoT-33, the magnetic braking may be very efficient in the beginning and this drives the rotational period to a value somewhat larger than the current observed stellar rotational period, when braking and tidal evolution equilibrate themselves. Subsequently, the system evolves losing energy, and the companion orbit spirals down toward the star and both the orbital period of the companion and the rotation period of the star slowly decrease for the remaining life of the system, and it can possibly reach such commensurability just by chance.…”

EPIC 219388192b—An Inhabitant of the Brown Dwarf Desert in the Ruprecht 147 Open Cluster

“…The eccentric, short-period orbit with well-known age also makes EPIC 219388192b an excellent-and unique-candidate to check the theories of star-BD tidal interactions in the presence of magnetic stellar winds (cf. Ferraz-Mello et al 2015).…”

Rotation of Planet-Hosting Stars

“…The spin-up of a Sun-like star by a companion of 1 Jupiter mass is expected to be negligible if their initial separation is larger than 0.04 -0.08 AU (Ferraz-Mello et al 2015), i.e., initial periods longer than 3 -8 days, where the uncertainty in this estimate is dominated by the assumed value of Q . Tides are much weaker for stars with smaller radii so the spin-up of low mass stars (M-dwarfs) by planetary companions is expected to be negligible if the planet survives the initial contraction onto the main sequence (Bolmont et al 2012).…”