Non-Trivial Oblique Spin Equilibria of Super-Earths in Multi-planetary Systems

Abstract

Many Sun-like stars are observed to host close-in super-Earths (SEs) as part of a multiplanetary system. In such a system, the spin of the SE evolves due to spin-orbit resonances and tidal dissipation. In the absence of tides, the planet's obliquity can evolve chaotically to large values. However, for close-in SEs, tidal dissipation is significant and suppresses the chaos, instead driving the spin into various steady states. We find that the attracting steady states of the SE's spin are more numerous than previously thought, due to the discovery of a new class of "mixed-mode" high-obliquity equilibria. These new equilibria arise due to subharmonic responses of the parametrically-driven planetary spin, an unusual phenomenon that arises in nonlinear systems. Many SEs should therefore have significant obliquities, with potentially large impacts on the physical conditions of their surfaces and atmospheres.Introduction. The obliquity of a planet, the angle between the spin and orbital axes, plays an important role in the atmospheric dynamics, climate, and potential habitability of the planet. For instance, the atmospheric circulation of a planet changes dramatically as the obliquity increases beyond 54 • , as the averaged insolation at the poles becomes greater than that at the equator (1, 2). Variations in insolation over long timescales can also affect the habitability of an exoplanet (3, 4). In the Solar System, planetary obliquities range from nearly zero for Mercury and 3.1 • for Jupiter, to 23 • for Earth and 26.7 • for Saturn, to 98 • for Uranus. The obliquities of exoplanets are challenging to measure, and so far only loose constraints have been obtained for the obliquities of faraway planetary-mass companions (5, 6). Nevertheless, there are prospects for better constraints on exoplanetary obliquities in the coming years (7-9). Substantial obliquities are of great theoretical interest for their proposed role in explaining peculiar thermal phase curves of transiting planets (10,11) and various other open dynamical puzzles (12)(13)(14)(15).The obliquity of a planet reflects its dynamical history. Some obliquities could be generated in the earlest phase of planet formation, when/if proto-planetary disks are turbulent and twisted (16,17). Large obliquities are commonly attributed to giant impacts or planet collisions as a result of dynamical instabilities of planetary orbits (18-24). Repeated planet-planet scatterings could also lead to modest obliquities (25,26). Substantial obliquity excitation can be achieved over long (secular) timescales via spin-orbit resonances, when the spin precession and orbital (nodal) precession frequencies of the planet

Stellar obliquities in exoplanetary systems

“…Collisions can lead to large obliquities (Dones & Tremaine 1993;Li & Lai 2020), as can earlier interactions with the protoplanetary or external perturbers (Tremaine 1991;Jennings & Chiang 2021). Nonzero planetary obliquities in exoplanet systems might also lead to important tidal effects (Heller et al 2011;Millholland & Laughlin 2018Su & Lai 2021; see also . A planet's obliquity evolution can be coupled to the properties of its moons, if it has any (Atobe & Ida 2007).…”