The rotation of Mercury is presently captured in a 3/2 spin-orbit resonance with the orbital mean motion. The capture mechanism is well understood as the result of tidal interactions with the Sun combined with planetary perturbations. However, it is now almost certain that Mercury has a liquid core, which should induce a contribution of viscous friction at the core-mantle boundary to the spin evolution. This last effect greatly increases the chances of capture in all spin-orbit resonances, being 100% for the 2/1 resonance, and thus preventing the planet from evolving to the presently observed configuration. Here we show that for a given resonance, as the chaotic evolution of Mercury's orbit can drive its eccentricity to very low values during the planet's history, any previous capture can be destabilized whenever the eccentricity becomes lower than a critical value. In our numerical integrations of 1000 orbits of Mercury over 4 Gyr, the spin ends 99.8% of the time captured in a spin-orbit resonance, in particular in one of the following three configurations: 5/2 (22%), 2/1 (32%) and 3/2 (26%). Although the present 3/2 spin-orbit resonance is not the most probable outcome, we also show that the capture probability in this resonance can be increased up to 55% or 73%, if the eccentricity of Mercury in the past has descended below the critical values 0.025 or 0.005, respectively.
Mercury's crust has a complex structure resulting from a billion years of volcanism. The surface variations in chemical composition have been identified from orbit by the spacecraft MESSENGER. Combining these measurements with laboratory experiments on partial melting, we estimate which variations in surface density and degree of mantle melting are required to produce surface rocks. If the surface density is representative of the deep crustal density, more than one half of crustal thickness variations in the northern hemisphere are explained by lateral variations in mantle melting. The crust i…
We present a model of the Cassini state of Mercury that comprises an inner core, a fluid core and a mantle. Our model includes inertial and gravitational torques between interior regions, and viscous and electromagnetic (EM) coupling at the boundaries of the fluid core. We show that the coupling between Mercury's interior regions is sufficiently strong that the obliquity of the mantle spin axis deviates from that of a rigid planet by no more than 0.01 arcmin. The mantle obliquity decreases with increasing inner core size, but the change between a large and no inner core is limited to 0.015 arc…
We present a new numerical scheme for one-dimensional conduction problems of a spherical shell. The scheme adopts a solution of the conduction equation in each interval of the chosen discretization that is valid if the fluxes at interval boundaries are constant in time. This piece-wise steady flux (PWSF) numerical scheme is continuous and differentiable in the space domain, which is convenient for implementing the numerical scheme in an energy-conserved thermal evolution model of a planetary core in which a conductive stratified layer develops below the core-mantle boundary when the heat flux …
The pathway to forming the iron-rich planet Mercury remains mysterious. Mercury's core makes up 70% of the planetary mass, which implies a significant enrichment of iron relative to silicates, while its mantle is strongly depleted in oxidized iron. The high core mass fraction is traditionally ascribed to evaporative loss of silicates, e.g. following a giant impact, but the high abundance of moderately volatile elements in the mantle of Mercury is inconsistent with reaching temperatures much above 1,000 K during its formation. Here we explore the nucleation of solid particles from a gas of sola…
Origins of Mercury's Big Heart of Iron: Exploring Pathways to Form High Core Mass Fraction (CMF) Planets via N-body Simulations
The Ohio State University（俄亥俄州立大学）；University of Alabama（阿拉巴马大学）；University of Nevada, Las Vegas（内华达大学拉斯维加斯分校）；Flatiron Institute（平顿研究所）；University of Toronto at Scarborough（多伦多大学士嘉堡校区）；University of Toronto（多伦多大学）
We compute predictions of the deviation of Mercury's spin axis from an exact Cassini state caused by tidal dissipation, and viscous and electromagnetic (EM) friction at the core-mantle boundary (CMB) and inner core boundary (ICB). Viscous friction at the CMB generates a phase lead, viscous and EM friction at the ICB produce a phase lag; the magnitude of the deviation depends on the inner core size, kinematic viscosity and magnetic field strength, but cannot exceed an upper bound. For a small inner core, viscous friction at the CMB results in a maximum phase lead of 0.027 arcsec. For a large in…
We present a reanalysis of the K2-106 transiting planetary system, with a focus on the composition of K2-106b, an ultra-short period, super-Mercury candidate. We globally model existing photometric and radial velocity data and derive a planetary mass and radius for K2-106b of $M_{p} = 8.53\pm1.02~M_{\oplus}$ and $R_{p} = 1.71^{+0.069}_{-0.057}~R_{\oplus}$, which leads to a density of $ρ_{p} = 9.4^{+1.6}_{-1.5}$ $\rm g~cm^{-3}$, a significantly lower value than previously reported in the literature. We use planet interior models that assume a two-layer planet comprised of a liquid, pure Fe core…
We present fully three-dimensional equations to describe the rotations of a body made of a deformable mantle and a fluid core. The model in its essence is similar to that used by INPOP (Integration Planétaire de l'Observatoire de Paris), e.g. Viswanathan et al. (2019), and by JPL (Jet Propulsion Laboratory), e.g. Folkner et al. (2014), to represent the Moon. The intended advantages of our model are: straightforward use of any linear-viscoelastic model for the rheology of the mantle; easy numerical implementation in time-domain (no time lags are necessary); all parameters, including those relat…
Nutation Damping from Core-Mantle Boundary Topography
Johns Hopkins University（约翰斯·霍普金斯大学）；Massachusetts Institute of Technology（麻省理工学院）；Earth, Atmospheric and Planetary Science, Massachusetts Institute of Technology（麻省理工学院地球、大气与行星科学系）；Earth and Life Institute, UCLouvain（UCLouvain地球与生活研究所）；Royal Observatory of Belgium（比利时皇家天文台）
The spin axes of the mantle, fluid core and solid inner core of the Moon precess at frequency $Ω_p=2π/18.6$ yr$^{-1}$ though with different orientations, leading to viscous friction at the core-mantle boundary (CMB) and inner core boundary (ICB). Here, we use a rotational model of the Moon with a range of inner core and outer core radii to investigate the relative importance of viscous dissipation at the CMB and ICB, and to show how this dissipation is connected to the phase lead angle ($ϕ_p$) of the mantle ahead of its Cassini state. We show that when the inner core radius is $>80$ km and the…
