Obliquity evolution of extrasolar terrestrial planets

Abstract

We have investigated the obliquity evolution of terrestrial planets in habitable zones (at ∼1 AU) in extrasolar planetary systems, due to tidal interactions with their satellite and host star with wide varieties of satellite-to-planet mass ratio ( m / M p ) and initial obliquity ( γ 0 ), through numerical calculations and analytical arguments. The obliquity, the angle between planetary spin axis and its orbit normal, of a terrestrial planet is one of the key factors in determining the planetary surface environments. A recent scenario of terrestrial planet accretion implies that giant impacts of Mars-sized or larger bodies determine the planetary spin and form satellites. Since the giant impacts would be isotropic, tilted spins ( sin γ 0 ∼ 1 ) are more likely to be produced than straight ones ( sin γ 0 ∼ 0 ). The ratio m / M p is dependent on the impact parameters and impactors' mass. However, most of previous studies on tidal evolution of the planet–satellite systems have focused on a particular case of the Earth–Moon systems in which m / M p ≃ 0.0125 and γ 0 ∼ 10 ° or the two-body planar problem in which γ 0 = 0 ° and stellar torque is neglected. We numerically integrated the evolution of planetary spin and a satellite orbit with various m / M p (from 0.0025 to 0.05) and γ 0 (from 0° to 180°), taking into account the stellar torques and precessional motions of the spin and the orbit. We start with the spin axis that almost coincides with the satellite orbit normal, assuming that the spin and the satellite are formed by one dominant impact. With initially straight spins, the evolution is similar to that of the Earth–Moon system. The satellite monotonically recedes from the planet until synchronous state between the spin period and the satellite orbital period is realized. The obliquity gradually increases initially but it starts decreasing down to zero as approaching the synchronous state. However, we have found that the evolution with initially tiled spins is completely different. The satellite's orbit migrates outward with almost constant obliquity until the orbit reaches the critical radius ∼ 10 – 20 planetary radii, but then the migration is reversed to inward one. At the reversal, the obliquity starts oscillation with large amplitude. The oscillation gradually ceases and the obliquity is reduced to ∼0° during the inward migration. The satellite eventually falls onto the planetary surface or it is captured at the synchronous state at several planetary radii. We found that the character change of precession about total angular momentum vector into that about the planetary orbit normal is responsible for the oscillation with large amplitude and the reversal of migration. With the results of numerical integration and analytical arguments, we divided the m / M p – γ 0 space into the regions of the qualitatively different evolution. The peculiar tidal evolution with initially tiled spins give deep insights into dynamics of extrasolar planet–satellite systems and discussions of surface environments of the planets.