A method to identify the boundary between rocky and gaseous exoplanets from tidal theory and transit durations

Abstract

The determination of an exoplanet as rocky is critical for the assessment of planetary habitability. Observationally, the number of small-radius, transiting planets with accompanying mass measurements is insufficient for a robust determination of the transitional mass or radius. Theoretically, models predict that rocky planets can grow large enough to become gas giants when they reach *10 M Earth , but the transitional mass remains unknown. Here I show how transit data, interpreted in the context of tidal theory, can reveal the critical radius that separates rocky and gaseous exoplanets. Standard tidal models predict that rocky exoplanets' orbits are tidally circularized much more rapidly than gaseous bodies', suggesting the former will tend to be found on circular orbits at larger semi-major axes than the latter. Well-sampled transits can provide a minimum eccentricity of the orbit, allowing a measurement of this differential circularization. I show that this effect should be present in the data from the Kepler spacecraft, but is not apparent. Instead, it appears that there is no evidence of tidal circularization at any planetary radius, probably because the publicly-available data, particularly the impact parameters, are not accurate enough. I also review the bias in the transit duration towards values that are smaller than that of planets on circular orbits, stressing that the azimuthal velocity of the planet determines the transit duration. The ensemble of Kepler planet candidates may be able to determine the critical radius between rocky and gaseous exoplanets, tidal dissipation as a function of planetary radius, and discriminate between tidal models.

Tidal locking of habitable exoplanets

“…The CPL and CTL models predict qualitatively similar behavior for the orbital evolution of close-in exoplanets when rotational effects are ignored, e.g. (Jackson et al 2009;Levrard et al 2009;Barnes et al 2013;Barnes 2015).…”

“…The governing equations are calculated with a 4th order Runge-Kutta integrator (although Euler's method works surprisingly well), with an adaptive timestep determined by the most rapidly evolving parameter. This software package and its variants have been used on a wide range of binary systems, including exoplanets Barnes 2015), binary stars (Gómez Maqueo Chew et al 2012, brown dwarfs (Fleming et al 2012;Ma et al 2013), and exomoons . For the simulations presented below, I used the Runge-Kutta method with a timestep that was 1% of the shortest dynamical time (x/(dx/dt), where x is one of the 6 independent variables), and assumed a planet became tidally locked if its rotation period reached 1% of the equilibrium rotation period.…”

“…where X = log(M * /M ⊙ ). The star's k 2 , Q, and τ values are set to 0.5, 10 6 , and 0.01 s for all cases, similar to previous studies (Rasio et al 1996;Jackson et al 2008;Matsumura et al 2010;Barnes 2015). For the CPL model, the initial values of the phase lags are determined by the initial rotational and orbital frequencies as described in Eq.…”

Chemo-kinematic Ages of Eccentric-planet-hosting M Dwarf Stars

“…Rocky planets have low Q p values around 10-200 (Goldreich & Soter 1966;Murray & Dermott 2000;Lainey et al 2007;Henning et al 2009). Because of the large separation between gas giant and terrestrial Q p values, they can be used to differentiate between rocky and gaseous planets (Barnes 2015). Since we can only provide a lower bound on Q p , we cannot place strict constraints on the composition of these planets, though a high minimum Q p might suggest the planet is more like a gas-giant than a rocky planet.…”

Comparative Habitability of Transiting Exoplanets

“…where R * is the stellar radius and b is the impact parameter. Barnes (2015) introduced a convenient parameter ∆, the "transit duration anomaly" (see also Plavchan et al 2014),…”