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

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.

Spinning stars and cosmic recycling

This chapter considers the relevance of rotating stars as gravitational-wave sources, introducing the notion of a deformed spinning star and estimating the associated gravitational-wave strength through the quadrupole formula. The estimates are compared to the observed spin-down rate for the Crab Pulsar, providing a first idea of how faint these signals are likely to be. Additional physics that must be considered for accreting systems is introduced and a simple model for the spin–orbit evolution of such systems is outlined.

Shape evolution of cometary nuclei via anisotropic mass loss

Context. Breathtaking imagery recorded during the European Space Agency Rosetta mission confirmed the bilobate nature of the nucleus of comet 67P/Churyumov-Gerasimenko. The peculiar appearance of the nucleus is not unique among comets. The majority of cometary cores imaged at high resolution exhibit a similar build. Various theories have been brought forward as to how cometary nuclei attain such peculiar shapes. Aims. We illustrate that anisotropic mass loss and local collapse of subsurface structures caused by non-uniform exposure of the nucleus to solar irradiation can transform initially spherical comet cores into bilobed cores. Methods. We derived a mathematical framework to describe the changes in morphology resulting from non-uniform insolation during the spin-orbit evolution of a nucleus. We solved the resulting partial differential equations that govern the change in the shape of a nucleus subject to mass loss and consequent collapse of depleted subsurface structures analytically for simple insolation configurations and numerically for more realistic scenarios. Results. The proposed mechanism is capable of explaining why a large percentage of periodic comets appear to have peanut-shaped cores and why light-curve amplitudes of comet nuclei are on average larger than those of typical main belt asteroids of the same size.