Tidal dissipation and eccentricity pumping: Implications for the depth of the secondary eclipse of 55 Cancri e

Abstract

Aims. We use the super Earth 55 Cnc e as a case study to address an observable effect of tidal heating. This transiting short-period planet belongs to a compact multiple system with massive planets. We investigate whether planet-planet interactions can force the eccentricity of this planet to a level affecting the eclipse depth observed with Spitzer. Methods. Using the constant time lag tidal model, we first calculate the observed planet flux as a function of albedo and eccentricity, for different tidal dissipation constants and for two extreme cases: a planet with no heat redistribution and a planet with full heat redistribution. We derive the values of albedo and eccentricity that match the observed transit depth. We then perform N-body simulations of the planetary system including tides and general relativity to follow the evolution of the eccentricity of planet e. We compare the range of eccentricities given by the simulations with the eccentricities required to alter the eclipse depth. Results. Using our nominal value for the dissipation constant and the most recent estimates of the orbital elements and masses of the 55 Cnc planets, we find that the eccentricity of planet e can be large enough to contribute at a measurable level to the thermal emission measured with Spitzer. This affects the constraints on the albedo of the planet, which can be as high as 0.9 (instead of 0.55 when ignoring tidal heating). We also derive a maximum value for the eccentricity of planet e directly from the eclipse depth: e < 0.015 assuming Earth's dissipation constant. Conclusions. Transiting exoplanets in multiple planet systems -like 55 Cancri -are exceptional targets for testing tidal models because their tidal luminosity may be observable. Future multi-wavelengths observations of eclipse depth and phase curves (for instance with EChO and JWST) should allow us to better resolve the temperature map of these planets and break the degeneracy between albedo and tidal heating that remains for single band observations. In addition, an accurate determination of the eccentricity will make it possible to constrain the dissipation rate of the planet and to probe its internal structure.

The effect of rotation and tidal heating on the thermal lightcurves of super Mercuries

“…This damping timescale is calculated according to Leconte et al (2010, Eq. (6)) assuming no forcing from planetary companions but perturbations from massive or eccentric planets in the same system could maintain a high eccentricity for longer Beust et al (2012); Bolmont et al (2013). This criterion is therefore conservative and the observability domain could be extended to higher eccentricities in multiple systems.…”

“…To do this we approximate the stellar radiation by a blackbody at the effective temperature of the star. When considering a specific stellar system or a comparison with real observations it is more appropriate to use a more realistic spectral density obtained from a model and/or observations, as we did in a separate study dedicated to 55 Cnc e (Bolmont et al 2013). …”

“…Lightcurves of multiplanet systems have been modeled by Kane et al (2011) and Kane & Gelino (2013). Bolmont et al (2013) investigated the influence of tidal heating on the thermal emission and phase curve of 55 Cnc e.…”

Variability in the super-Earth 55 Cnc e

“…55 Cnc e is one of the largest members of known USP planets. Owing to its close proximity to the parent star, 55 Cnc e has an equilibrium temperature of ∼2400 K and may experience intense tidal heating (Bolmont et al 2013). With V∼6, 55 Cnc is the brightest star known to host a transiting exoplanet, and has led to measurements of the planet's radius at exquisite precision in the visible as well as in the Spitzer 4.5 µm IRAC band (Demory et al 2011;Winn et al 2011;.…”

On the potentially dramatic history of the super-Earth ρ 55 Cancri e

“…If this is the case, 55 Canc e may originally have been a Neptune-mass planet, more similar to other known members of the system, such as 55 Canc c and 55 Canc f, suggesting migration as a chain of giant planets and failed cores. Residual heating may still make a contribution to the amplitude of the secondary eclipse (Bolmont et al 2013) if the eccentricity is in the range ∼ 0.001 − 0.01.…”