Dynamical tides in exoplanetary systems containing hot Jupiters: confronting theory and observations

Abstract

We study the effect of dynamical tides associated with the excitation of gravity waves in an interior radiative region of the central star on orbital evolution in observed systems containing Hot Jupiters. We consider WASP-43, Ogle-tr-113, WASP-12, and WASP-18 which contain stars on the main sequence (MS). For these systems there are observational estimates regarding the rate of change of the orbital period. We also investigate Kepler-91 which contains an evolved giant star. We adopt the formalism of Ivanov et al. for calculating the orbital evolution.For the MS stars we determine expected rates of orbital evolution under different assumptions about the amount of dissipation acting on the tides, estimate the effect of stellar rotation for the two most rapidly rotating stars and compare results with observations. All cases apart from possibly WASP-43 are consistent with a regime in which gravity waves are damped during their propagation over the star. However, at present this is not definitive as observational errors are large. We find that although it is expected to apply to Kepler-91, linear radiative damping cannot explain this dissipation regime applying to MS stars. Thus, a nonlinear mechanism may be needed.Kepler-91 is found to be such that the time scale for evolution of the star is comparable to that for the orbit. This implies that significant orbital circularisation may have occurred through tides acting on the star. Quasi-static tides, stellar winds, hydrodynamic drag and tides acting on the planet have likely played a minor role. Ivanov et al. (2013) (IPCh) determined the tidal response associated with the excitation of a regular dense spectrum of normal modes, such as provided by the low frequency rotationally modified g modes, by a perturbing tidal potential. They obtained expressions from which the orbital evolution could be obtained. These depend on the amount of dissipation present. Two regimes were highlighted. The regime of moderately large damping (MLD) for which the excited waves are damped before reaching an appropriate boundary, the centre for a radiative core, and the surface for a radiative envelope. In this regime the effect on the orbit is independent of the details of the dissipation process. Note that the same assumption of the validity of MLD regime is implied in the well known theory of dynamical tidal interactions of Zahn (1970) and Zahn (1977) which is ⋆

Star-planet interactions

“…Indeed, for stars with a convective core, Barker & Ogilvie (2010) indicated that dynamical tides in radiative zones may be ineffective, thus dynamical tides in radiative zones are expected to be efficient during the transition phase between the end of the main-sequence and the beginning of the convective Heburning core. This is also supported by the analysis of Chernov et al (2017). Inclusion of dynamical tides in radiative zones may therefore change the bottom part (for distances shorter than about 0.05 au) of the middle and bottom right panels of Fig.…”

“…An obvious uncertainty arises from the complexity of modeling the tidal interactions. We did not account for the effects of dynamical tides in radiative regions (Goodman & Dickson 1998;Ogilvie & Lin 2007;Barker & Ogilvie 2010;Chernov et al 2017;Weinberg et al 2017). In some circumstances (see below), including this type of tides may affect the fate of short-period planets with respect to what we obtained here, while in other circumstances, the effects may be small.…”

Formation of hot Jupiters through disk migration and evolving stellar tides

“…Tidally excited waves in the stellar radiation zones (Goodman & Dickson 1998;Ogilvie & Lin 2007;Chernov et al 2017) or the wave breaking mechanism at the stellar center (Barker & Ogilvie 2010) could trigger additional tidal dissipation beyond the processes in the convective envelope considered in this study. Further refinements of this theory could be achieved through the consistent modeling of the radial profile of the stellar density, the latter of which is assumed to be constant (though different) in both the stellar core and the envelope in our model (Ogilvie 2013).…”

Tidal flows with convection: frequency-dependence of the effective viscosity and evidence for anti-dissipation

“…This mechanism is able to provide the required level of dissipation to explain the decaying orbit of WASP-12 b (e.g. Barker 2011;Chernov et al 2017;Weinberg et al 2017;Bailey & Goodman 2019), if we assume that these waves are fully dissipated. However, uncertainties remain regarding the structure of the star (whether or not it has a radiative core), and whether these waves should in fact be fully damped.…”