Tidal evolution of exoplanetary systems hosting potentially habitable exoplanets. The cases of LHS-1140 b-c and K2-18 b-c

Abstract

ABSTRACT We present a model to study secularly and tidally evolving three-body systems composed by two low-mass planets orbiting a star, in the case where the bodies rotation axes are always perpendicular to the orbital plane. The tidal theory allows us to study the spin and orbit evolution of both stiff Earth-like planets and predominantly gaseous Neptune-like planets. The model is applied to study two recently discovered exoplanetary systems containing potentially habitable exoplanets (PHE): LHS-1140 b-c and K2-18 b-c. For the former system, we show that both LHS-1140 b and c must be in nearly circular orbits. For K2-18 b-c, the combined analysis of orbital evolution time-scales with the current eccentricity estimation of K2-18 b allows us to conclude that the inner planet (K2-18 c) must be a Neptune-like gaseous body. Only this would allow for the eccentricity of K2-18 b to be in the range of values estimated in recent works (e = 0.20 ± 0.08), provided that the uniform viscosity coefficient of K2-18 b is greater than 2.4 × 1019 Pa s (which is a value characteristic of stiff bodies) and supposing that such system has an age of some Gyr.