2012ApJ...761...83M

GJ 581d is a potentially habitable super-Earth in the multiple system of exoplanets orbiting a nearby M dwarf. We investigate this planet's long-term dynamics with an emphasis on its probable final rotation states acquired via tidal interaction with the host. The published radial velocities for the star are re-analyzed with a benchmark planet detection algorithm to confirm that there is no evidence for the recently proposed two additional planets (f and g). Limiting the scope to the four originally detected planets, we assess the dynamical stability of the system and find bounded chaos in the orbital motion. For the planet d, the characteristic Lyapunov time is 38 yr. Long-term numerical integration reveals that the system of four planets is stable, with the eccentricity of the planet d changing quasi-periodically in a tight range around 0.27, and with its semimajor axis varying only a little. The spin-orbit interaction of GJ 581d with its host star is dominated by the tides exerted by the star on the planet. We model this interaction, assuming a terrestrial composition of the mantle. Besides the triaxiality-caused torque and the secular part of the tidal torque, which are conventionally included in the equation of motion, we also include the tidal torques' oscillating components. It turns out that, depending on the mantle temperature, the planet gets trapped into the 2:1 or an even higher spin-orbit resonance. It is very improbable that the planet could have reached the 1:1 resonance. This improves the possibility of the planet being suitable for sustained life.