Constraining tidal dissipation in F-type main-sequence stars: the case of CoRoT-11

¹ INAF-Osservatorio Astrofisico di Catania, via S. Sofia 78, 95123 Catania, Italy
e-mail: nuccio.lanza@oact.inaf.it
² Research and Scientific Support Department, European Space Agency, Keplerlaan 1, 2200AG, Noordwijk, The Netherlands

Received: 15 November 2010
Accepted: 18 February 2011

Abstract

Context. Tidal dissipation in late-type stars is presently poorly understood and the study of planetary systems hosting hot Jupiters can provide new observational constraints to test proposed theories.

Aims. We focus on systems with F-type main-sequence stars and find that the recently discovered system CoRoT-11 is presently the best suited for this kind of investigation.

Methods. A classic constant tidal lag model is applied to reproduce the evolution of the system from a plausible nearly synchronous state on the zero-age main sequence (ZAMS) to the present state, thus putting constraints on the average modified tidal quality factor $\mathrm{⟨}{\mathit{Q}}_{\mathrm{s}}^{\mathrm{\prime }}\mathrm{⟩}$ of its F6V star.Initial conditions with the stellar rotation period longer than the orbital period of the planet can be excluded on the basis of the presently observed state in which the star spins faster than the planet orbit.

Results. It is found that $\mathrm{4}\mathrm{\times }{\mathrm{10}}^{\mathrm{6}}{}_{\stackrel{\mathit{<}}{\mathrm{~}}}\mathrm{⟨}{\mathit{Q}}_{\mathrm{s}}^{\mathrm{\prime }}\mathrm{⟩}{}_{\stackrel{\mathit{<}}{\mathrm{~}}}\mathrm{2}\mathrm{\times }{\mathrm{10}}^{\mathrm{7}}$, if the system started its evolution on the ZAMS close to synchronization, with an uncertainty related to the constant tidal lag hypothesis and the estimated stellar magnetic braking within a factor of  ≈5–6.For a non-synchronous initial state of the system, $\mathrm{⟨}{\mathit{Q}}_{\mathrm{s}}^{\mathrm{\prime }}\mathrm{⟩}{}_{\stackrel{\mathit{<}}{\mathrm{~}}}\mathrm{4}\mathrm{\times }{\mathrm{10}}^{\mathrm{6}}$ implies an age younger than  ~1 Gyr, while $\mathrm{⟨}{\mathit{Q}}_{\mathrm{s}}^{\mathrm{\prime }}\mathrm{⟩}{}_{\stackrel{\mathit{>}}{\mathrm{~}}}\mathrm{2}\mathrm{\times }{\mathrm{10}}^{\mathrm{7}}$ may be tested by comparing the theoretically derived initial orbital and stellar rotation periods with those of a sample of observed systems. Moreover, we discuss how the present value of ${\mathit{Q}}_{\mathrm{s}}^{\mathrm{\prime }}$ can be measured by a timing of the mid-epoch and duration of the transits as well as of the planetary eclipses to be observed in the infrared with an accuracy of  ~0.5–1 s over a time baseline of  ~25 yr.

Conclusions. CoRoT-11 is a highly interesting system that potentially allows us a direct measure of the tidal dissipation in an F-type star as well as the detection of the precession of the orbital plane of the planet that provides us with an accurate upper limit for the obliquity of the stellar equator. If the planetary orbit has a significant eccentricity ($\mathit{e}{}_{\stackrel{\mathit{>}}{\mathrm{~}}}\mathrm{0.05}$), it will be possible to also detect the precession of the line of the apsides and derive information on the Love number of the planet and its tidal quality factor.