Mercury's Internal Structure

We describe the current state of knowledge about Mercury's interior structure. We review the available observational constraints, including mass, size, density, gravity field, spin state, composition, and tidal response. These data enable the construction of models that represent the distribution of mass inside Mercury. In particular, we infer radial profiles of the pressure, density, and gravity in the core, mantle, and crust. We also examine Mercury's rotational dynamics and the influence of an inner core on the spin state and the determination of the moment of inertia. Finally, we discuss the wide-ranging implications of Mercury's internal structure on its thermal evolution, surface geology, capture in a unique spin-orbit resonance, and magnetic field generation.Comment: 36 pages, 11 figures, in press, to appear in "Mercury - The View after MESSENGER", S. C. Solomon, B. J. Anderson, L. R. Nittler (editors), Cambridge University Pres

A machine-learning-based surrogate model of Mars' thermal evolution

Constraining initial conditions and parameters of mantle convection for a planet often requires running several hundred computationally expensive simulations in order to find those matching certain ‘observables’, such as crustal thickness, duration of volcanism, or radial contraction. A lower fidelity alternative is to use 1-D evolution models based on scaling laws that parametrize convective heat transfer. However, this approach is often limited in the amount of physics that scaling laws can accurately represent (e.g. temperature and pressure-dependent rheologies or mineralogical phase transitions can only be marginally simulated). We leverage neural networks to build a surrogate model that can predict the entire evolution (0–4.5 Gyr) of the 1-D temperature profile of a Mars-like planet for a wide range of values of five different parameters: reference viscosity, activation energy and activation volume of diffusion creep, enrichment factor of heat-producing elements in the crust and initial temperature of the mantle. The neural network we evaluate and present here has been trained from a subset of ∼10 000 evolution simulations of Mars ran on a 2-D quarter-cylindrical grid, from which we extracted laterally averaged 1-D temperature profiles. The temperature profiles predicted by this trained network match those of an unseen batch of 2-D simulations with an average accuracy of 99.7per cent⁠

Machine learning inference of the interior structure of low-mass exoplanets

We explore the application of machine learning based on mixture density neural networks (MDNs) to the interior characterization of low-mass exoplanets up to 25 Earth masses constrained by mass, radius, and fluid Love number $k_2$. We create a dataset of 900$\:$000 synthetic planets, consisting of an iron-rich core, a silicate mantle, a high-pressure ice shell, and a gaseous H/He envelope, to train a MDN using planetary mass and radius as inputs to the network. For this layered structure, we show that the MDN is able to infer the distribution of possible thicknesses of each planetary layer from mass and radius of the planet. This approach obviates the time-consuming task of calculating such distributions with a dedicated set of forward models for each individual planet. While gas-rich planets may be characterized by compositional gradients rather than distinct layers, the method presented here can be easily extended to any interior structure model. The fluid Love number $k_2$ bears constraints on the mass distribution in the planets' interior and will be measured for an increasing number of exoplanets in the future. Adding $k_2$as an input to the MDN significantly decreases the degeneracy of the possible interior structures.Comment: 14 pages, 7 figures, accepted for publication in Ap

Mercury's Internal Structure

We describe the current state of knowledge about Mercury's interior structure. We review the available observationalconstraints, including mass, size, density, gravity eld, spin state, composition, and tidal response. These data enablethe construction of models that represent the distribution of mass inside Mercury. In particular, we infer radial prolesof the pressure, density, and gravity in the core, mantle, and crust. We also examine Mercury's rotational dynamicsand the inuence of an inner core on the spin state and the determination of the moment of inertia. Finally, we discussthe wide-ranging implications of Mercury's internal structure on its thermal evolution, surface geology, capture in aunique spin-orbit resonance, and magnetic eld generation

Mercury's Moment of Inertia from Spin and Gravity Data

Earth-based radar observations of the spin state of Mercury at 35 epochs between 2002 and 2012 reveal that its spin axis is tilted by (2.04 plus or minus 0.08) arc min with respect to the orbit normal. The direction of the tilt suggests that Mercury is in or near a Cassini state. Observed rotation rate variations clearly exhibit an 88-day libration pattern which is due to solar gravitational torques acting on the asymmetrically shaped planet. The amplitude of the forced libration, (38.5 plus or minus 1.6) arc sec, corresponds to a longitudinal displacement of ∼450 m at the equator. Combining these measurements of the spin properties with second-degree gravitational harmonics (Smith et al., 2012) provides an estimate of the polar moment of inertia of MercuryC/MR2 = 0.346 plus or minus 0.014, where M and R are Mercury's mass and radius. The fraction of the moment that corresponds to the outer librating shell, which can be used to estimate the size of the core, is Cm/C = 0.431 plus or minus 0.025

GJ 367b: A dense, ultrashort-period sub-Earth planet transiting a nearby red dwarf star

Ultrashort-period (USP) exoplanets have orbital periods shorter than 1 day. Precise masses and radii of USP exoplanets could provide constraints on their unknown formation and evolution processes. We present the work from Lam et al. 2021 (Science, 374, 1271) and report the detection and characterization of the USP planet GJ 367b using high-precision photometry and radial velocity observations. GJ 367b orbits a bright (V-band magnitude of 10.2), nearby, and red (M-type) dwarf star every 7.7 hours. GJ 367b has a radius of 0.718 ± 0.054 Earth-radii and a mass of 0.546 ± 0.078 Earth-masses, making it a sub-Earth planet. The corresponding bulk density is 8.106 ± 2.165 grams per cubic centimeter - close to that of iron. An interior structure model predicts that the planet has an iron core radius fraction of 86 ± 5%, similar to that of Mercury's interior

Investigation of the interior of Mercury through the study of its gravity, topography, and tidal response

With the goal of furthering our understanding of the interior structure of Mercury, this work tries to answer the following two questions. What can the response of the planet to solar tides reveal about the interior structure? What is the thickness of the crust and what are the implications for the interior?By comparing the models developed here for the tidal response of Mercury with the response measured by the MErcury Surface Space ENvironment GEochemistry and Ranging spacecraft (MESSENGER), the rheology of the mantle of the innermost planet is investigated.The measured tidal deformation indicates that, unless the rigidity of mantle materials is unexpectedly high, the mantle is relatively cold. Geochemical arguments based on the composition of the surface of Mercury as measured by MESSENGER have been used to put forward the hypothesis of the existence of a solid FeS layer at the bottom of the mantle.The tidal modeling indicates that the presence of the FeS layer is unlikely.To further constrain the interior structure of Mercury the thickness of the crust is calculated by computing geoid-to-topography ratios over the surface of the planet. The inferred crustal thickness, $35\pm18$ km, has three interesting implications.First, this relatively thin crust allows for the possibility that basin-forming events excavated mantle material from Mercury's mantle. If this material is still exposed on the surface it can potentially be observed by instruments onboard MESSENGER and future missions at Mercury.Second, the volume of silicate materials present in the crust of Mercury represents about 10\% of the total silicate materials in the planet, the largest value among the terrestrial planets. This implies that Mercury had the highest efficiency of crustal production.Finally, by combining the estimate of the crustal thickness with the measured abundances of heat-producing elements on the surface of Mercury a lower bound can be placed on the amount of heat production in the mantle at a time following the accretion and differentiation of the planet, approximately 4.45 Ga ago.This information is useful for future models of the thermochemical evolution of the innermost planet