R. Heller, R. Barnes, and J. Leconte. Habitability of Extrasolar Planets and Tidal Spin Evolution. Origins of Life and Evolution of the Biosphere, 41:539-543, 2011. [ bib | DOI | arXiv | PDF version | ADS link ]
Stellar radiation has conservatively been used as the key constraint to planetary habitability. We review here the effects of tides, exerted by the host star on the planet, on the evolution of the planetary spin. Tides initially drive the rotation period and the orientation of the rotation axis into an equilibrium state but do not necessarily lead to synchronous rotation. As tides also circularize the orbit, eventually the rotation period does equal the orbital period and one hemisphere will be permanently irradiated by the star. Furthermore, the rotational axis will become perpendicular to the orbit, i.e. the planetary surface will not experience seasonal variations of the insolation. We illustrate here how tides alter the spins of planets in the traditional habitable zone. As an example, we show that, neglecting perturbations due to other companions, the Super-Earth Gl581d performs two rotations per orbit and that any primordial obliquity has been eroded.
J. Leconte, D. Lai, and G. Chabrier. Distorted, non-spherical transiting planets: impact on the transit depth and on the radius determination (Corrigendum). Astronomy Astrophysics, 536:C1, 2011. [ bib | DOI | PDF version | ADS link ]
E. Bolmont, S. N. Raymond, and J. Leconte. Tidal evolution of planets around brown dwarfs. Astronomy Astrophysics, 535:A94, 2011. [ bib | DOI | arXiv | PDF version | ADS link ]
Context. The tidal evolution of planets orbiting brown dwarfs (BDs) presents an interesting case study because BDs' terrestrial planet forming region is located extremely close-in. In fact, the habitable zones of BDs range from roughly 0.001 to 0.03 AU and for the lowest-mass BDs are located interior to the Roche limit. <BR /> Aims: In contrast with stars, BDs spin up as they age. Thus, the corotation distance moves inward. This has important implications for the tidal evolution of planets around BDs. <BR /> Methods: We used a standard equilibrium tidal model to compute the orbital evolution of a large ensemble of planet-BD systems. We tested the effect of numerous parameters such as the initial semi-major axis and eccentricity, the rotation period of the BD, the masses of both the BD and planet, and the tidal dissipation factors. <BR /> Results: We find that all planets that form at or beyond the corotation distance and with initial eccentricities smaller than ˜0.1 are repelled from the BD. Some planets initially interior to corotation can survive if their inward tidal evolution is slower than the BD's spin evolution, but most initially close-in planets fall onto the BD. <BR /> Conclusions: We find that the most important parameter for the tidal evolution is the initial orbital distance with respect to the corotation distance. Some planets can survive in the habitable zone for Gyr timescales, although in many cases the habitable zone moves inward past the planet's orbit in just tens to hundreds of Myr. Surviving planets can have orbital periods of less than 10 days (as small as 10 h), so they could be observable by transit.
J. Leconte, D. Lai, and G. Chabrier. Distorted, nonspherical transiting planets: impact on the transit depth and on the radius determination. Astronomy Astrophysics, 528:A41, 2011. [ bib | DOI | arXiv | PDF version | ADS link ]
In this paper, we quantify the systematic impact of the nonspherical shape of transiting planets caused by tidal forces and rotation on the observed transit depth. Such a departure from sphericity leads to a bias in the derivation of the transit radius from the light curve and affects the comparison with planet structure and evolution models, which assume spherical symmetry. As the tidally deformed planet projects its smallest cross section area during the transit, the measured effective radius is smaller than the one of the unperturbed spherical planet (which is the radius predicted by 1D evolution models). This effect can be corrected by calculating the theoretical shape of the observed planet. Using a variational method and a simple polytropic assumption for the gaseous planet structure, we derived simple analytical expressions for the ellipsoidal shape of a fluid object (star or planet) accounting for both tidal and rotational deformations. We determined the characteristic polytropic indexes that describe the structures of irradiated close-in planets within the mass range 0.3 MJ Mp 75 MJ, at different ages, by comparing polytropic models with the inner density profiles calculated with the full evolution code. Our calculations yield a 20% effect on the transit depth, i.e. a 10% decrease in the measured radius, for the extreme case of a 1 MJ planet orbiting a Sun-like star at 0.01 AU, and the effect can be greater for lower mass objects. For the closest planets detected so far ( 0.05 AU), the effect on the radius is of the order of 1 to 10%, by no means a negligible effect, enhancing the puzzling problem of the anomalously large bloated planets. These corrections must thus be taken into account for correctly determining the radius from the transit light curve and when comparing theoretical models with observations. Our analytical expressions can be easily used to calculate these corrections, caused by the nonspherical shape of the planet, on the observed transit depth and thus to derive the planet's real equilibrium radius, the one to be used when comparing models with observations. They can also be used to model ellipsoidal variations in the stellar flux now detected in the CoRoT and Kepler light curves. We also derive directly usable analytical expressions for the moment of inertia and the Love number (k2) of a fluid planet as a function of its mass and, in the case of significant rotation, for its oblateness.Tables B.2 and B.3 are only available in electronic form at <A href=“http://www.aanda.org”>http://www.aanda.org</A>
R. Heller, J. Leconte, and R. Barnes. Tidal obliquity evolution of potentially habitable planets. Astronomy Astrophysics, 528:A27, 2011. [ bib | DOI | arXiv | PDF version | ADS link ]
Context. Stellar insolation has been used as the main constraint on a planet's potential habitability. However, as more Earth-like planets are discovered around low-mass stars (LMSs), a re-examination of the role of tides on the habitability of exoplanets has begun. Those studies have yet to consider the misalignment between a planet's rotational axis and the orbital plane normal, i.e. the planetary obliquity. <BR /> Aims: This paper considers the constraints on habitability arising from tidal processes due to the planet's spin orientation and rate. Since tidal processes are far from being understood we seek to understand differences between commonly used tidal models. <BR /> Methods: We apply two equilibrium tide theories - a constant-phase-lag model and a constant-time-lag model - to compute the obliquity evolution of terrestrial planets orbiting in the habitable zones around LMSs. The time for the obliquity to decrease from an Earth-like obliquity of 23.5deg to 5deg, the “tilt erosion time”, is compared to the traditional insolation habitable zone (IHZ) in the parameter space spanned by the semi-major axis a, the eccentricity e, and the stellar mass Ms. We also compute tidal heating and equilibrium rotation caused by obliquity tides as further constraints on habitability. The Super-Earth Gl581 d and the planet candidate Gl581 g are studied as examples for these tidal processes. <BR /> Results: Earth-like obliquities of terrestrial planets in the IHZ around stars with masses 0.25 M&sun; are eroded in less than 0.1 Gyr. Only terrestrial planets orbiting stars with masses 0.9 M&sun; experience tilt erosion times larger than 1 Gyr throughout the IHZ. Tilt erosion times for terrestrial planets in highly eccentric orbits inside the IHZ of solar-like stars can be 10 Gyr. Terrestrial planets in the IHZ of stars with masses 0.25 M&sun; undergo significant tidal heating due to obliquity tides, whereas in the IHZ of stars with masses 0.5 M&sun; they require additional sources of heat to drive tectonic activity. The predictions of the two tidal models diverge significantly for e 0.3. In our two-body simulations, Gl581 d's obliquity is eroded to 0deg and its rotation period reached its equilibrium state of half its orbital period in 0.1 Gyr. Tidal surface heating on the putative Gl581 g is 150 mW/m2 as long as its eccentricity is smaller than 0.3. <BR /> Conclusions: Obliquity tides modify the concept of the habitable zone. Tilt erosion of terrestrial planets orbiting LMSs should be included by atmospheric modelers. Tidal heating needs to be considered by geologists.