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Register a new userEffect of the rotation, tidal dissipation history and metallicity of stars on the evolution of close-in planets
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Since 1995, numerous close-in planets have been discovered around low-mass stars (M to A-type stars). These systems are susceptible to be tidally evolving, in particular the dissipation of the kinetic energy of tidal flows in the host star may modify its rotational evolution and also shape the orbital architecture of the surrounding planetary system. Recent theoretical studies have shown that the amplitude of the stellar dissipation can vary over several orders of magnitude as the star evolves, and that it also depends on the stellar mass and rotation. We present here one of the first studies of the dynamics of close-in planets orbiting low-mass stars (from $0.6~M_odot$ to $1.2~M_odot$) where we compute the simultaneous evolution of the stars structure, rotation and tidal dissipation in its external convective envelope. We demonstrate that tidal friction due to the stellar dynamical tide, i.e. tidal inertial waves (their restoring force is the Coriolis acceleration) excited in the convection zone, can be larger by several orders of magnitude than the one of the equilibrium tide currently used in celestial mechanics. This is particularly true during the Pre Main Sequence (PMS) phase and to a lesser extent during the Sub Giant (SG) phase. Numerical simulations show that only the high dissipation occurring during the PMS phase has a visible effect on the semi-major axis of close-in planets. We also investigate the effect of the metallicity of the star on the tidal evolution of planets. We find that the higher the metallicity of the star, the higher the dissipation and the larger the tidally-induced migration of the planet.
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This is an erratum for the publication Bolmont & Mathis 2016 (Celestial Mechanics and Dynamical Astronomy, 126, 275-296, https://doi.org/10.1007/s10569-016-9690-3). There was a small mistake for the spin integration of our code which we corrected and we take advantage of this erratum to investigate a bit further the influence of a planet on the spin of its host star.
Observations of hot Jupiter type exoplanets suggest that their orbital period distribution depends on the metallicity of their host star. We investigate here whether the impact of the stellar metallicity on the evolution of the tidal dissipation inside the convective envelope of rotating stars and its resulting effect on the planetary migration might be a possible explanation for this observed statistical trend. We use a frequency-averaged tidal dissipation formalism coupled to an orbital evolution code and to rotating stellar evolution models to estimate the effect of a change of stellar metallicity on the evolution of close-in planets. We consider here two different stellar masses: 0.4 and 1.0 $M_{odot}$ evolving from the early pre-main sequence phase up to the red giant branch. We show that the metallicity of a star has a strong effect on the stellar parameters which in turn strongly influence the tidal dissipation in the convective region. While on the pre-main sequence the dissipation of a metal poor Sun-like star is higher than the dissipation of a metal rich Sun-like star, on the main sequence it is the opposite. However, for the $0.4~M_{odot}$ star, the dependence of the dissipation with metallicity is much less visible. Using an orbital evolution model, we show that changing the metallicity leads to different orbital evolutions (e.g., planets migrate farther out from an initially fast rotating metal rich star). By using this model, we qualitatively reproduced the observational trends of the population of hot Jupiters with the metallicity of their host stars. However, more steps are needed to improve our model to try to quantitatively fit our results to the observations. Namely, we need to improve the treatment of the rotation evolution in the orbital evolution model and ultimately we need to consistently couple of the orbital model to the stellar evolution model.
We use the distribution of extrasolar planets in circular orbits around stars with surface convective zones detected by ground based transit searches to constrain how efficiently tides raised by the planet are dissipated on the parent star. We parameterize this efficiency as a tidal quality factor (Q*). We conclude that the population of currently known planets is inconsistent with Q*<10^7 at the 99% level. Previous studies show that values of Q* between 10^5 and 10^7 are required in order to explain the orbital circularization of main sequence low mass binary stars in clusters, suggesting that different dissipation mechanisms might be acting in the two cases, most likely due to the very different tidal forcing frequencies relative to the stellar rotation frequency occurring for star--star versus planet--star systems.
We study the dynamical evolution of the TRAPPIST-1 system under the influence of orbital circularization through tidal interaction with the central star. We find that systems with parameters close to the observed one evolve into a state where consecutive planets are linked by first order resonances and consecutive triples, apart from planets c, d and e, by connected three body Laplace resonances. The system expands with period ratios increasing and mean eccentricities decreasing with time. This evolution is largely driven by tides acting on the innermost planets which then influence the outer ones. In order that deviations from commensurability become significant only on $Gy$ time scales or longer, we require that the tidal parameter associated with the planets has to be such that $Q > sim 10^{2-3}.$ At the same time, if we start with two subsystems, with the inner three planets comprising the inner one, $Q$ associated with the planets has to be on the order (and not significantly exceeding) $10^{2-3}$ for the two subsystems to interact and end up in the observed configuration. This scenario is also supported by modelling of the evolution through disk migration which indicates that the whole system cannot have migrated inwards together. Also in order to avoid large departures from commensurabilities, the system cannot have stalled at a disk inner edge for significant time periods. We discuss the habitability consequences of the tidal dissipation implied by our modelling, concluding that planets d, e and f are potentially in habitable zones.
Tidal dissipation in planets and stars is one of the key physical mechanisms driving the evolution of star-planet and planet-moon systems. Several signatures of its action are observed in planetary systems thanks to their orbital architecture and the rotational state of their components. Tidal dissipation inside the fluid layers of celestial bodies are intrinsically linked to the dynamics and the physical properties of the latter. This complex dependence must be characterized. We compute the tidal kinetic energy dissipated by viscous friction and thermal diffusion in a rotating local fluid Cartesian section of a star/planet/moon submitted to a periodic tidal forcing. The properties of tidal gravito-inertial waves excited by the perturbation are derived analytically as explicit functions of the tidal frequency and local fluid parameters (i.e. the rotation, the buoyancy frequency characterizing the entropy stratification, viscous and thermal diffusivities) for periodic normal modes. The sensitivity of the resulting possibly highly resonant dissipation frequency-spectra to a control parameter of the system is either important or negligible depending on the position in the regime diagram relevant for planetary and stellar interiors. For corresponding asymptotic behaviors of tidal gravito-inertial waves dissipated by viscous friction and thermal diffusion, scaling laws for the frequencies, number, width, height and contrast with the non-resonant background of resonances are derived to quantify these variations. We characterize the strong impact of the internal physics and dynamics of fluid planetary layers and stars on the dissipation of tidal kinetic energy in their bulk. We point out the key control parameters that really play a role and demonstrate how it is now necessary to develop ab-initio modeling for tidal dissipation in celestial bodies.
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