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![Snapshots of the radial magnetic field distribution and time-averaged power spectrum with standard deviation at Mercury’s surface. a MESSENGER observation²; b BU1; c TD1; d SL1. The magnetic field is scaled by 2ρμηΩ1∕2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( {2\rho \mu \eta \Omega } \right)^{1/2}$$\end{document} = 0.14 mT, where ρ = 6980 kg m⁻³ is density²⁹, μ = 4π × 10⁻⁷ H m⁻¹ is magnetic permeability in a vacuum, η ~ 1 m2 s⁻¹ is magnetic diffusivity⁴³, and Ω = 1.2 × 10⁻⁶ s⁻¹ is planetary rotation rate. The thickness of the mantle is assumed to be 590 km7, 8, 11. Color scale is reversed in b for the purpose of illustration. The magnetic equator corresponds to where the radial component is zero. e Power spectrum vs. spherical harmonic degree L in units of μT² in cases of observation (black), BU1 (red), TD1 (green), and SL1 (blue). Error bars represent one standard deviation. The close agreement between BU1 and observation up to L = 3 (octupole) component is remarkable. f Power vs. spherical harmonic order M normalized by the M = 0 (axisymmetric) component. The axisymmetric component in BU1 dominates the other components by a factor of at least 1000](publication/330367788/figure/fig4/AS:958979131858946@1605649850512/Snapshots-of-the-radial-magnetic-field-distribution-and-time-averaged-power-spectrum-with.png)
Snapshots of the radial magnetic field distribution and time-averaged power spectrum with standard deviation at Mercury’s surface. a MESSENGER observation²; b BU1; c TD1; d SL1. The magnetic field is scaled by 2ρμηΩ1∕2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left( {2\rho \mu \eta \Omega } \right)^{1/2}$$\end{document} = 0.14 mT, where ρ = 6980 kg m⁻³ is density²⁹, μ = 4π × 10⁻⁷ H m⁻¹ is magnetic permeability in a vacuum, η ~ 1 m2 s⁻¹ is magnetic diffusivity⁴³, and Ω = 1.2 × 10⁻⁶ s⁻¹ is planetary rotation rate. The thickness of the mantle is assumed to be 590 km7, 8, 11. Color scale is reversed in b for the purpose of illustration. The magnetic equator corresponds to where the radial component is zero. e Power spectrum vs. spherical harmonic degree L in units of μT² in cases of observation (black), BU1 (red), TD1 (green), and SL1 (blue). Error bars represent one standard deviation. The close agreement between BU1 and observation up to L = 3 (octupole) component is remarkable. f Power vs. spherical harmonic order M normalized by the M = 0 (axisymmetric) component. The axisymmetric component in BU1 dominates the other components by a factor of at least 1000
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The discovery of Mercury’s unusually axisymmetric, anomalously axially offset dipolar magnetic field reveals a new regime of planetary magnetic fields. The cause of the offset dipole remains to be resolved, although some exotic models have been proposed. Deciphering why Mercury has such an anomalous field is crucial not only for understanding the i...
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... Thin-shell dynamo models with a large solid inner core (of radius greater than about 0.8 core radii, or about 1,600 km) can explain the observed field strength (Heimpel et al., 2005;Stanley et al., 2005). Alternatively, a "deep dynamo" beneath a stably stratified layer would generate a magnetic field similar in morphology and strength to that of Mercury (Christensen, 2006;Takahashi et al., 2019) and would imply an inner core of less than a 1,000 km radius. As discussed, such a stably stratified layer can be the consequence of the core cooling history with a subadiabatic temperature gradient near the core-mantle boundary and a convecting deeper core (Knibbe & Van Hoolst, 2021;Knibbe & van Westrenen, 2018). ...
The three terrestrial planets Mercury, Venus, and Mars (ordered by their distance from the sun) share the same first-order internal structure with the Earth. There is an iron-rich core at the center, overlain by a silicate mantle and a crust that is generated by partial melting of the mantle. But while Mars and Venus have a core with a radius of about half the planetary radius, just as the Earth, the core of Mercury extends to about 80% of the planet’s radius. The interiors of the terrestrial planets are heated by the decay of radioactive elements and cool by removing internal energy. In addition to radiogenic heat, internal energy was deposited during planet formation and early differentiation. Heat transport is dominated by mantle and core convection and volcanic heat transfer although conduction through the lithosphere on top of the mantle matters. The convection powers the planetary heat engine which converts thermal energy into gravitational energy, mechanical (tectonic) work, and magnetic field energy. None of the terrestrial planets has plate tectonics such as the Earth although surface renewal and some form of lithosphere subduction is debated for Venus. The tectonics of Mars and Mercury is best described as stagnant-lid tectonics, with a thick rigid lid overlying the convecting mantle. Both planets show early volcanism, with Mars in particular being locally volcanically active even until a few million years ago. Because of Mercury’s large core, the mantle is comparatively thin, and convection may be sluggish or may even have ceased. Magnetism is another property that the terrestrial planets share with the Earth although it is still not confirmed by data that Venus ever had a magnetic field. A dynamo process driven by buoyancy released through the growth of a solid inner core is producing the present-day magnetic fields of Earth and Mercury, but Mars’ dynamo has likely ceased to be active. Crust units with remanent magnetization testify to the early dynamo. The terrestrial planets have been explored to differing degrees by spacecraft missions which allow a deeper physical understanding of the interiors and their dynamics and evolution.
... It is important to understand the exact nature of the librationally induced flows, as internal fluid motions can influence the magnetic field and rotational dynamics (including libration itself), both of which are used to constrain the properties of Mercury's interior; see, e.g., Wardinski et al. (2021) for the former and Margot et al. (2007) and Van Hoolst et al. (2012) for the latter. Here we consider recent developments in thermal evolution (e.g., Knibbe & van Westrenen 2018;Knibbe & Van Hoolst 2021) and numerical dynamo (e.g., Christensen 2006;Tian et al. 2015;Takahashi et al. 2019) models that indicate the presence of a thick stable layer at the top of Mercury's core that potentially influences the flow near the boundary. This is something that has not been considered in previous experimental (e.g., Aldridge & Toomre 1969;Noir et al. 2009) or numerical (e.g., Calkins et al. 2010Lin & Noir 2020) studies into Mercury's fluid core response to its longitudinal libration or in theoretical studies that estimate that the influence of viscous (e.g., Peale et al. 2002) and electromagnetic (e.g., Peale et al. 2002;Dumberry 2011) coupling on the libration amplitude is negligible based on the rotation and estimated diffusion timescales. ...
Observational constraints on Mercury’s thermal evolution and magnetic field indicate that the top part of the fluid core is stably stratified. Here we compute how a stable layer affects the core flow in response to Mercury’s main 88 day longitudinal libration, assuming various degrees of stratification, and study whether the core flow can modify the libration amplitude through viscous and electromagnetic torques acting on the core–mantle boundary (CMB). We show that the core flow strongly depends on the strength of the stratification near the CMB but that the influence of core motions on libration is negligible with or without a stably stratified layer. A stably stratified layer at the top of the core can, however, prevent resonant behavior with gravito-inertial modes by impeding radial motions and promote a strong horizontal flow near the CMB. The librationally driven flow is likely turbulent and might produce a nonaxisymmetric induced magnetic field with a strength of the order of 1% of Mercury’s dipolar field.
... Knibbe & van Westrenen 2018;Knibbe & Van Hoolst 2021) as well as in numerical dynamo models (e.g. Christensen 2006;Tian et al. 2015;Takahashi et al. 2019) that indicate the presence of a thick stable layer at the top of Mercury's core, which potentially influences the flow near the boundary. This is something that has not been considered in previous experimental (e.g. ...
Observational constraints on Mercury's thermal evolution and magnetic field indicate that the top part of the fluid core is stably stratified. Here we compute how a stable layer affects the core flow in response to Mercury's main 88-day longitudinal libration, assuming various degrees of stratification, and study whether the core flow can modify the libration amplitude through viscous and electromagnetic torques acting on the core-mantle boundary (CMB). We show that the core flow strongly depends on the strength of the stratification near the CMB but that the influence of core motions on libration is negligible with or without a stably stratified layer. A stably stratified layer at the top of the core can however prevent resonant behaviour with gravito-inertial modes by impeding radial motions and promote a strong horizontal flow near the CMB. The librationally driven flow is likely turbulent and might produce a non-axisymmetric induced magnetic field with a strength of the order of 1$\%$ of Mercury's dipolar field.
... While no general consensus has emerged from these, they all point to an inner core that cannot be too large. A limited inner core size is also favored by numerical models of Mercury's dynamo (e.g., Cao et al., 2014;Christensen, 2006;Christensen & Wicht, 2008;Takahashi et al., 2019) and dynamical interpretations of its observed magnetic field (Wardinski et al., 2021). A large inner core (>500 km) also affects the tidal Love numbers k 2 and h 2 (Steinbrügge et al., 2018;Van Hoolst & Jacobs, 2003); a precise determination of these from observations offers then a possible path to detect the presence of an inner core. ...
... This is possible if Mercury's dynamo field is dominated by small length scales components deep in its interior that are filtered by the skin effect from a thermally stratified layer at the top of the core (Christensen, 2006;Christensen & Wicht, 2008). However, other dynamo scenarios have been proposed for which the internal field is not as strong (e.g., Cao et al., 2014;Takahashi et al., 2019;Tian et al., 2015) and an observation of the gravity signal of internal origin may then help to determine which among these are more plausible. ...
In a reference frame rotating with Mercury's mantle and crust, the inner core and fluid core precess in a retrograde sense with a period of 58.646 days. The precession of a triaxial inner core with a different density than the fluid core induces a periodic gravity variation of degree 2, order 1. Elastic deformations from the pressure that the precessing fluid core exerts on the core‐mantle boundary also contribute to this gravity signal. We show that the periodic change in Stokes coefficients ΔC21 and ΔS21 for this signal of internal origin is of the order of 10⁻¹⁰, similar in magnitude to the signal from solar tides. The relative contribution from the inner core increases with inner core radius and with the amplitude of its tilt angle with respect to the mantle. The latter depends on the strength of electromagnetic coupling at the inner core boundary which in turn depends on the radial magnetic field Br; a larger Br generates a larger tilt. The inner core signal features a contrast between ΔC21 and ΔS21 due to its triaxial shape, discernible for an inner core radius >500 km if Br > 0.1 mT, or for an inner core radius >1100 km if Br < 0.01 mT. A detection of this contrast would confirm the presence of an inner core and place constraints on its size and the strength of the internal magnetic field. These would provide key constraints for the thermal evolution of Mercury and for its dynamo mechanism.
... The codensity simplification allows to shorten the modeled scale range and to solve only one evolution equation for the codensity variable, thereby reducing the computational load. Numerical studies of rotating spherical convection that use separate evolution equations for the composition and temperature include Glatzmaier and Roberts (1996), Breuer et al. (2010), Trümper et al. (2012), Takahashi (2014), Takahashi et al. (2019), and Tassin et al. (2021), but all these studies considered "top-heavy" configurations (i.e., the density gradient is unstable to overturning convection). The codensity simplification is clearly not possible in DDC, since the differing diffusivity values is essential to the DDC process. ...
Stably stratified layers may be present at the top of the electrically conducting fluid layers of many planets either because the temperature gradient is locally subadiabatic or because a stable composition gradient is maintained by the segregation of chemical elements. Here we study the double‐diffusive processes taking place in such a stable layer, considering the case of Mercury's core where the temperature gradient is stable but the composition gradient is unstable over a 800 km‐thick layer. The large difference in the molecular diffusivities leads to the development of buoyancy‐driven instabilities that drive radial flows known as fingering convection. We model fingering convection using hydrodynamical simulations in a rotating spherical shell and varying the rotation rate and the stratification strength. For small Rayleigh numbers (i.e., weak background temperature and composition gradients), fingering convection takes the form of columnar flows aligned with the rotation axis and with an azimuthal size comparable with the layer thickness. For larger Rayleigh numbers, the flows retain a columnar structure but the azimuthal size is drastically reduced leading to thin sheet‐like structures that are elongated in the meridional direction. The azimuthal size decreases when the thermal stratification increases, following closely the scaling law expected from the linear planar theory (Stern, 1960, https://doi.org/10.1111/j.2153-3490.1960.tb01295.x). We find that the radial flows always remain laminar with local Reynolds number of order 1–10. Equatorially symmetric zonal flows form due to latitudinal variations of the axisymmetric composition. The zonal velocity exceeds the non‐axisymmetric velocities at the largest Rayleigh numbers. We discuss plausible implications for planetary magnetic fields.
... In particular, the transfer function between topography and gravity, called admittance, provides a powerful method to probe the structure of the lithosphere of a planet. An understanding of the lithosphere can inform us about Mercury's interior structure and temperature distribution, and as such, it provides constraints on the history of thermochemical convection (e.g., Solomon 1976;Michel et al. 2013;Tosi et al. 2013), radial contraction (e.g., Hauck et al. 2013;Byrne et al. 2014), and dynamo generation (e.g., Manthilake et al. 2019;Takahashi et al. 2019). Results from the MESSENGER mission have thus been used to study properties such as lithospheric thickness (e.g., Tosi et al. 2015), crustal thickness (e.g., Padovan et al. 2015;Sori 2018;Beuthe et al. 2020a), and topographic support (e.g., James et al. 2015;Kay & Dombard 2019). ...
We have analyzed the entire set of radiometric tracking data from the MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) mission. This analysis employed a method where standard Doppler tracking data were transformed into line-of-sight accelerations. These accelerations have greater sensitivity to small-scale features than standard Doppler. We estimated a gravity model expressed in spherical harmonics to degree and order 180 and showed that this model is improved, as it has increased correlations with topography in areas where tracking data were collected when the spacecraft altitude was low. The new model was used in an analysis of the localized admittance between gravity and topography to determine properties of Mercury’s lithosphere. Four areas with high correlations between gravity and topography were selected. These areas represent different terrain types: the high-Mg region, the Strindberg crater plus some lobate scarps, heavily cratered terrain, and smooth plains. We employed a Markov Chain Monte Carlo method to estimate crustal density, load density, crustal thickness, elastic thickness, load depth, and a load parameter that describes the ratio between surface and depth loading. We find densities around 2600 kg m ⁻³ for three of the areas, with the density for the fourth area, the northern rise, being higher. The elastic thickness is generally low, between 11 and 30 km.
... The codensity simplification allows to shorten the modelled scale range and to solve only one evolution equation for the codensity variable, thereby reducing the computational load. Numerical studies of rotating spherical convection that use separate evolution equations for the composition and temperature include Glatzmaier and Roberts (1996);Breuer et al. (2010);Trümper et al. (2012); Takahashi (2014); Takahashi et al. (2019); Tassin et al. (2021), but all these studies considered "top-heavy" configurations (i.e. the density gradient is unstable to overturning convection). The codensity simplification is clearly not possible in DDC, since the differing diffusivity values is essential to the DDC process. ...
Stably-stratified layers may be present at the top of the electrically-conducting fluid layers of many planets either because the temperature gradient is locally subadiabatic or because a stable composition gradient is maintained by the segregation of chemical elements. Here we study the double-diffusive processes taking place in such a stable layer, considering the case of Mercury's core where the temperature gradient is stable but the composition gradient is unstable over a 800km-thick layer. The large difference in the molecular diffusivities leads to the development of buoyancy-driven instabilities that drive radial flows known as fingering convection. We model fingering convection using hydrodynamical simulations in a rotating spherical shell and varying the rotation rate and the stratification strength. For small Rayleigh numbers (i.e. weak background temperature and composition gradients), fingering convection takes the form of columnar flows aligned with the rotation axis and with an azimuthal size comparable with the layer thickness. For larger Rayleigh numbers, the flows retain a columnar structure but the azimuthal size is drastically reduced leading to thin sheet-like structures that are elongated in the meridional direction. The azimuthal length decreases when the thermal stratification increases, following closely the scaling law expected from the linear non-rotating planar theory (Stern, 1960). We find that the radial flows always remain laminar with local Reynolds number of order 1-10. Equatorially-symmetric zonal flows form due to latitudinal variations of the axisymmetric composition. The zonal velocity exceeds the non-axisymmetric velocities at the largest Rayleigh numbers. We discuss plausible implications for planetary magnetic fields.
... We consider inner cores ranging from 0 to 1,200 km in radius; the upper bound is based on magnetic field models (Takahashi et al., 2019;Tian et al., 2015). The temperature profile inside the core is prescribed; we choose the present-day temperature profile for the reference thermal evolution scenario of Knibbe and van Westrenen (2018), then evaluate sensitivity to this choice. ...
Plain Language Summary
Mercury's mantle is unusually rich in sulfur relative to the other terrestrial planets. That sulfur is not bound into the silicate rocks, but rather it is expected to take the form of calcium and magnesium‐rich sulfides. We estimate how much sulfide should be present in Mercury's mantle and what the presence of that sulfide means for the density of Mercury's mantle and core. We interpret recent measurements of the moment of inertia (MoI) of Mercury's mantle and of the whole planet in light of the possible sulfide content of Mercury's mantle. We find that if Mercury's mantle contains large amounts of sulfide, but not very much iron (which is what we expect), then the value of Mercury's polar MoI should be low. Alternatively, if Mercury's polar MoI is high, Mercury's mantle must not have much sulfide in it. If Mercury's mantle has little sulfide, either Mercury does not have much sulfur overall, or the sulfur is in Mercury's core. The latter implies that Mercury's interior chemistry (especially the amount of oxygen) is different from what is predicted from the abundance of elements and minerals measured at Mercury's surface.
... Therefore, whether there is a FeS layer is still debatable. On the other hand, since Mercury's magnetic field was found (Anderson et al. 2008(Anderson et al. , 2011(Anderson et al. , 2012, multiple implemented dynamo simulations that are consistent with the field intensity of the magnetic field require the inner core to be smaller than 1200 km (e.g., Cao et al. 2014;Tian et al. 2015;Takahashi et al. 2019). Moreover, as for the core's composition, Knibbe et al. (2020) suggested a series of possible combinations of weight fractions of liquid Fe-Si-C metal alloys that meet the constraints by geodetic measurements and dynamo simulations. ...
... Previous studies implied that Mercury contains a thermally stratified outer core, which results in a sub-adiabatic heat flow at the CMB (e.g., Christensen & Wicht 2008;Dumberry & Rivoldini 2014;Edgington et al. 2019), and such a stratified core would favor an early formation of inner core and a larger size (e.g., Knibbe & van Westrenen 2018). Nevertheless, a precise size of the inner core is still unknown, although several studies suggested that the size is smaller than 1200 km (Steinbrügge et al. 2018;Charlier & Namur 2019;Genova et al. 2019;Takahashi et al. 2019). However, the formation of the inner core has been suggested to be associated with generation of the magnetic field (Laneuville et al. 2014;Rückriemen et al. 2015). ...
... Yet, convective dynamo models almost all assume that composition and temperature have the same diffusivity, while light elements released at the inner-core boundary diffuse several orders of magnitude slower than temperature. The effect of double diffusion, when temperature and composition diffuse at different rates, on the geodynamo has been little studied [174][175][176][177][178] . Further examination of double diffusion could open new avenues for exploring the dynamics of the Earth's core. ...
Earth’s magnetic field is generated by fluid motions in the outer core. This geodynamo has operated for over 3.4 billion years. However, the mechanism that has sustained the geodynamo for over 75% of Earth’s history remains debated. In this Review, we assess the mechanisms proposed to drive the geodynamo (precession, tides and convection) and their ability to match geomagnetic and palaeomagnetic observations. Flows driven by precession are too weak to drive the geodynamo. Flows driven by tides could have been strong enough in the early Earth, before 1.5 billion years ago, when tidal deformation and Earth’s spin rate were larger than they are today. Evidence that the thermal conductivity of Earth’s core could be as high as 250 W m−1 K−1 calls the ability of convection to maintain the dynamo for over 3.4 billion years into question. Yet, convection could supply enough power to sustain a long-lived geodynamo if the thermal conductivity is lower than 100 W m−1 K−1. Exsolution of light elements from the core increases this upper conductivity limit by 15% to 200%, based on the exsolution rates reported so far. Convection, possibly aided by the exsolution of light elements, remains the mechanism most likely to have sustained the geodynamo. The light-element exsolution rate, which remains poorly constrained, should be further investigated. The mechanisms that sustain Earth’s long-lived geodynamo remain under scrutiny. This Review assesses the potential candidates—convection, precession and tides—revealing that convection, possibly helped by the exsolution of light elements, is the most likely scenario. Numerical models of the geodynamo driven by thermo-chemical convection account for most of the observed properties of the present geodynamo.The thermal conductivity in Earth’s core remains debated, with published values ranging between 20 and 250 W m−1 K−1. With a conductivity as high as 250 W m−1 K−1, motionless heat transport would prevail in the core implying that convection would not be able to sustain Earth’s magnetic dynamo for 3.4 billion years (Gyr).Nevertheless, thermo-chemical convection caused by the slow cooling of Earth supplies enough power to the geodynamo when the thermal conductivity is lower than 100 W m−1 K−1. The exsolution of light elements increases this upper conductivity limit only marginally or by up to a factor of three, depending on the exsolution rate.Flows driven by precession are too weak to drive the geodynamo.Flows driven by tides could have been strong enough before 1.5 Gyr ago, when tidal deformation and Earth’s spin rate were larger than today, which calls for further investigation of tidally driven dynamos. Numerical models of the geodynamo driven by thermo-chemical convection account for most of the observed properties of the present geodynamo. The thermal conductivity in Earth’s core remains debated, with published values ranging between 20 and 250 W m−1 K−1. With a conductivity as high as 250 W m−1 K−1, motionless heat transport would prevail in the core implying that convection would not be able to sustain Earth’s magnetic dynamo for 3.4 billion years (Gyr). Nevertheless, thermo-chemical convection caused by the slow cooling of Earth supplies enough power to the geodynamo when the thermal conductivity is lower than 100 W m−1 K−1. The exsolution of light elements increases this upper conductivity limit only marginally or by up to a factor of three, depending on the exsolution rate. Flows driven by precession are too weak to drive the geodynamo. Flows driven by tides could have been strong enough before 1.5 Gyr ago, when tidal deformation and Earth’s spin rate were larger than today, which calls for further investigation of tidally driven dynamos.
