The large obliquity of Saturn explained by the fast migration of Titan

Abstract

The obliquity of a planet is the tilt between its equator and its orbital plane. Giant planets are expected to form with near-zero obliquities [1,2]. After its formation, some dynamical mechanism must therefore have tilted Saturn up to its current obliquity of 26.7 • . This event is traditionally thought to have happened more than 4 Gyrs ago during the late planetary migration [3,4,5] because of the crossing of a resonance between the spin-axis precession of Saturn and the nodal orbital precession mode of Neptune [6]. Here, we show that the fast tidal migration of Titan measured by [7] is incompatible with this scenario, and that it offers a new explanation for Saturn's current obliquity. A significant migration of Titan would prevent any early resonance, invalidating previous constraints on the late planetary migration set by the tilting of Saturn [8,9,10]. We propose instead that the resonance was encountered recently, about 1 Gyr ago, forcing Saturn's obliquity to increase from a small value (possibly less than 3 • ), up to its current state. This scenario suggests that Saturn's normalised polar moment of inertia lies between 0.224 and 0.237. Our findings bring out a new paradigm for the spin-axis evolution of Saturn, Jupiter [11], and possibly giant exoplanets in multiple systems, whereby obliquities are not settled once for all, but continuously evolve as a result of the migration of their satellites.We investigate whether the spin-axis dynamics of Saturn could have been influenced by the migration of its satellites. The torque applied by the sun on Saturn's equatorial bulge produces a precession of its spin axis with a mean frequency ψ = α (1−e 2 ) −3/2 cos ε, where e is the eccentricity of Saturn, ε is its obliquity, and α is called its precession constant [12]. The value of α incorporates the extra torques produced by Saturn's satellites [1,13]. It also depends on Saturn's orbital and physical parameters, among which all are well known except Saturn's normalised polar moment of inertia λ. Estimates found in the literature broadly range in λ ∈ [0.200, 0.240] but they are model-dependent and a proper uncertainty range is hard to define (see Methods). Exploring this whole interval gives a current precession constant α 0 ranging from 0.747 to 0.894 /yr.We take into account the migration of Saturn's satellites by changing their contributions to α. The measurements of [7] unveiled a fast migration for Titan, and a similar tidal timescale t tide = a/ ȧ for all six satellites of Saturn studied. Both these findings support the "resonance locking" tidal 1

The past and future obliquity of Saturn as Titan migrates

“…In our case, Titan largely dominates the satellite's contribution, and it is almost in the close-in regime (L 6 ε). We can therefore use the same trick as Saillenfest et al (2021) and replace Eq. (5) bỹ…”

“…For years, the scenarios that were most successful in reproducing Saturn's current obliquity through this resonance invoked the late planetary migration Boué et al 2009;Vokrouhlický & Nesvorný 2015;Brasser & Lee 2015). However, Saillenfest et al (2021) have recently shown that this picture is incompatible with the fast tidal migration of Titan detected by Lainey et al (2020) in two independent sets of observations -assuming that this migration is not specific to the present epoch but went on over a substantial interval of time. Indeed, satellites affect the spin-axis precession of their host planets (see e.g.…”

“…The same conclusion could also hold for Jupiter (Lainey et al 2009;Lari et al 2020). In fact, Saillenfest et al (2021) have shown that Titan's migration itself is likely responsible for the resonant encounter between Saturn's spin axis and the nodal precession mode of Neptune. Their results indicate that this relatively recent resonant encounter could explain the current large obliquity of Saturn starting from a small value, possibly less than 3 • .…”

“…The findings of Saillenfest et al (2021) have been obtained through backward integrations from Saturn's current spin orientation, and by exploring migration histories for Titan in the vicinity of the nominal scenario of Lainey et al (2020). However, observation uncertainties and our lack of knowledge about the past evolution of Titan's migration rate still allow for a large variety of migration histories, and one can wonder whether the dramatic influence of Titan is a generic result or whether it is restricted to the range of parameters explored by Saillenfest et al (2021). Moreover, even though backward numerical integrations do prove that Titan's migration is able to raise Saturn's obliquity, a statistical picture of the possible trajectories that could have been followed is still missing.…”

“…In Sect. 2, we recall the dynamical model used by Saillenfest et al (2021) and discuss the range of acceptable values for the physical parameters of Saturn and its satellites. Sections 3 and 4 are dedicated to the past spin-axis dynamics of Saturn: after having explored the parameter space and quantified the importance of non-adiabaticity, we perform Monte Carlo experiments to search for the initial conditions of Saturn's spin axis.…”