Tilman Spohn

Magnetism and thermal evolution of the terrestrial planets

Of the terrestrial planets, Earth and probably Mercury possess substantial intrinsic magnetic fields generated by core dynamos, while Venus and Mars apparently lack such fields. Thermal histories are calculated for these planets and are found to admit several possible present states, including those which suggest simple explanations for the observations; while the cores of Earth and Mercury are continuing to freeze, the cores of Venus and Mars may still be completely liquid. The models assume whole mantle convection, which is parameterized by a simple Nusselt-Rayleigh number relation and dictates the rate at which heat escapes from the core. It is found that completely fluid cores, devoid of intrinsic heat sources, are not likely to sustain thermal convection for the age of the solar system but cool to a subadiabatic, conductive state that can not maintain a dynamo. Planets which nucleate an inner core continue to sustain a dynamo because of the gravitational energy release and chemically driven convection that accompany inner core growth. The absence of a significant inner core can arise in Venus because of its slightly higher temperature and lower central pressure relative to Earth, while a Martian core avoids the onset of freezing if the abundance of sulfur in the core is ⪆15% by mass. All of the models presented assume that (I) core dynamos are driven by thermal and/or chemical convection; (ii) radiogenic heat production is confined to the mantle; (iii) mantle and core cool from initially hot states which are at the solidus and superliquidus, respectively; and (iv) any inner core excludes the light alloying material (sulfur or oxygen) which then mixes uniformly upward through the outer core. The models include realistic pressure and composition-dependent freezing curves for the core, and material parameters are chosen so that the correct present-day values of heat outflow, upper mantle temperature and viscosity, and inner core radius are obtained for the earth. It is found that Venus and Mars may have once had dynamos maintained by thermal convection alone. Earth may have had a completely fluid core and a dynamo maintained by thermal convection for the first 2 to 3 by, but an inner core nucleates and the dynamo energetics are subsequently dominated by gravitational energy release. Complete freezing of the Mercurian core is prohibited if it contains even a small amount of sulfur, and a dynamo can be maintained by chemical convection in a thin, fluid shell.

The interior structure of Mars: Implications from SNC meteorites

Two end-member models of Mars present interior structure are presented: the first model is optimized to satisfy the geochemical data derived from the SNC meteorites in terms of the bulk chondritic ratio Fe/Si = 1.71, while the second model is optimized to satisfy the most probable maximum value C = 0.366 x M p r p 2 of the polar moment of inertia factor. Hydrostatic equilibrium and stationary heat transfer are assumed, and the basic differential equations for the mechanical and thermal structure are solved numerically together with an isothermal Murnaghan-Birch type equation of state truncated in Eulerian strain at forth order. We obtain the radial distribution of mass, hydrostatic pressure, gravity, temperature, and heat flow density along with the corresponding density stratification, viscosity profiles, and the global seismic velocity structure of model Mars. The first model being consistent with the geochemical requirement produces C = 0.357 x M p r p 2 , whereas the second model commensurate with the geophysical constraint gives Fe/Si = 1.35. The calculated central pressure is about 40 GPa in both models, and the central temperature is in the 2000 to 2200 K range. The model calculations suggest a Fe-Ni-FeS core a little less than one half of the planetary radius in size surrounded by a silicate mantle subdivided into lower spinel and upper olivine layers and overlain by a 100- to 250-km thick basaltic crust and a surface heatflow density of 25 to 30 mW m -2 . In both models the pressure in the mantle is not sufficient for the spinel to perovskite transition to occur. The present thermal lithosphere is estimated to be about 500 km thick and to be subdivided into a 300-km-thick outermost rheological lithosphere and an underlying thermal boundary layer of mantle convection. Given the core sulfur content of 14 wt% as derived from SNC meteorites, the Martian core is found to be entirely molten, implying the nonoperation of a self-sustained dynamo due to the absence of sufficiently vigorous convection.

Oceans in the icy Galilean satellites of Jupiter

Abstract Equilibrium models of heat transfer by heat conduction and thermal convection show that the three satellites of Jupiter—Europa, Ganymede, and Callisto—may have internal oceans underneath ice shells tens of kilometers to more than a hundred kilometers thick. A wide range of rheology and heat transfer parameter values and present-day heat production rates have been considered. The rheology was cast in terms of a reference viscosity ν0 calculated at the melting temperature and the rate of change A of viscosity with inverse homologous temperature. The temperature dependence of the thermal conductivity k of ice I has been taken into account by calculating the average conductivity along the temperature profile. Heating rates are based on a chondritic radiogenic heating rate of 4.5 pW kg−1 but have been varied around this value over a wide range. The phase diagrams of H2O (ice I) and H2O + 5 wt% NH3 ice have been considered. The ice I models are worst-case scenarios for the existence of a subsurface liquid water ocean because ice I has the highest possible melting temperature and the highest thermal conductivity of candidate ices and the assumption of equilibrium ignores the contribution to ice shell heating from deep interior cooling. In the context of ice I models, we find that Europa is the satellite most likely to have a subsurface liquid ocean. Even with radiogenic heating alone the ocean is tens of kilometers thick in the nominal model. If tidal heating is invoked, the ocean will be much thicker and the ice shell will be a few tens of kilometers thick. Ganymede and Callisto have frozen their oceans in the nominal ice I models, but since these models represent the worst-case scenario, it is conceivable that these satellites also have oceans at the present time. The most important factor working against the existence of subsurface oceans is contamination of the outer ice shell by rock. Rock increases the density and the pressure gradient and shifts the triple point of ice I to shallower depths where the temperature is likely to be lower then the triple point temperature. According to present knowledge of ice phase diagrams, ammonia produces one of the largest reductions of the melting temperature. If we assume a bulk concentration of 5 wt% ammonia we find that all the satellites have substantial oceans. For a model of Europa heated only by radiogenic decay, the ice shell will be a few tens of kilometers thinner than in the ice I case. The underlying rock mantle will limit the depth of the ocean to 80–100 km. For Ganymede and Callisto, the ice I shell on top of the H2O–NH3 ocean will be around 60- to 80-km thick and the oceans may be 200- to 350-km deep. Previous models have suggested that efficient convection in the ice will freeze any existing ocean. The present conclusions are different mainly because they are based on a parameterization of convective heat transport in fluids with strongly temperature dependent viscosity rather than a parameterization derived from constant-viscosity convection models. The present parameterization introduces a conductive stagnant lid at the expense of the thickness of the convecting sublayer, if the latter exists at all. The stagnant lid causes the temperature in the sublayer to be warmer than in a comparable constant-viscosity convecting layer. We have further modified the parameterization to account for the strong increase in homologous temperature, and therefore decrease in viscosity, with depth along an adiabat. This modification causes even thicker stagnant lids and further elevated temperatures in the well-mixed sublayer. It is the stagnant lid and the comparatively large temperature in the sublayer that frustrates ocean freezing.

Mantle differentiation and thermal evolution of Mars, Mercury, and Venus

Abstract Thermal evolution models for the terrestrial planets Mars, Mercury, and Venus with core and mantle chemical differentiation, lithosphere growth, and volcanic heat transfer have been calculated. The mantle differentiates by forming a crust and the core differentiates by inner core solidification. Continued volcanic activity for billions-of-years is found to be possible even on small terrestrial planets if crust growth is limited by lithosphere growth during the early evolution. Later, crust formation may be limited by the declining vigor of mantle convection. The thicknesses of the crust and lithosphere are found to depend mainly on planet size, on the bulk concentration of radiogenic elements in the planet, and on the ratio between volcanic and conductive heat transfer through the lithosphere. Two end-member models have been calculated and the concentration of radiogenics in the planet has been varied. In the first model, heat transfer from the mantle to the surface occurs via heat conduction through the lithosphere, while in the second model, mantle heat is advected via volcanic vents. Geologic evidence for volcanism on Mars and Mercury for at least 3.5 Ga and up to 1 Ga, respectively, the absence of a magnetic field on Mars, and the presence of such a field on Mercury suggest that heat transfer in these planets was dominated by heat conduction through the lithosphere for most of their thermal history. The present crust of Mercury is estimated to be a few tens of kilometers thick and about 10% of the mantle initial inventory of heat sources is fractionated into the crust. The Martian crust may be 50–100 km thick, possibly constituting more than a third of the lithosphere. Volcanic heat piping may have been an important heat transfer mechanism on Venus and volcanic activity may continue to the present day. Venus may have a crust that may constitute almost the entire lithosphere but crustal thickness may be limited by the basalt-eclogite phase transformation to 60 to 80 km. It is estimated that the present mantles of Mars and Venus are similarly depleted of about 20 to 40% of their initial heat source inventory.

The landing(s) of Philae and inferences about comet surface mechanical properties

The Philae lander, part of the Rosetta mission to investigate comet 67P/Churyumov-Gerasimenko, was delivered to the cometary surface in November 2014. Here we report the precise circumstances of the multiple landings of Philae, including the bouncing trajectory and rebound parameters, based on engineering data in conjunction with operational instrument data. These data also provide information on the mechanical properties (strength and layering) of the comet surface. The first touchdown site, Agilkia, appears to have a granular soft surface (with a compressive strength of 1 kilopascal) at least ~20 cm thick, possibly on top of a more rigid layer. The final landing site, Abydos, has a hard surface.

Interior structure models and tidal Love numbers of Titan

[1]xa0Interior models of a differentiated Titan with an internal ammonia-water ocean and chondritic radiogenic heat production in an undifferentiated rock + iron core have been calculated. We assume thermal and mechanical equilibrium and calculate the structure of the interior as a function of the thickness of an ice I layer on top of the ocean as well as the moment of inertia factor and the tidal Love numbers for comparison with Cassini gravity data. The Love numbers are linearly dependent on the thickness of the ice I shell at constant rheology parameters but decrease by one order of magnitude in the absence of an internal ocean. Ice shell thicknesses are between 90 and 105 km for models with 5 wt.% ammonia and for core densities between 3500 and 4500 kg m−3. For 15 wt.% ammonia, the shell is 65 to 70 km thick. We use a strongly temperature-dependent viscosity parameterization of convective heat transport and find that the stagnant lid comprises most of the ice I shell. Tidal heating in the warm convective sublayer is of minor importance. The internal ocean is several hundred kilometers thick, and its thickness decreases with increasing thickness of the ice shell. Core sizes vary from 1500 to 1800 km radius with associated moment of inertia factors of 0.30 ± 0.01.

The interior structure of Mercury: what we know, what we expect from BepiColombo

Abstract The BepiColombo mission is planned to very accurately measure the gravity field, the topography, and the tidal Love numbers of Mercury. In this paper, we review our present knowledge of the interior structure and show how the data from BepiColombo can be used to improve on our knowledge. We show that our present estimates of the core mass and volume depend mostly on our confidence in cosmochemically constrained values of the average silicate shell and core densities. The moment of inertia (MOI) C about the rotation axis will be determined very accurately from the degree 2 components of the gravity field and from measurements of the obliquity and the libration frequency of the rotation axis. The ratio Cm/C between the MOI of the solid planet to the MOI of the planet, both about the rotation axis, will additionally be obtained. If the core is liquid or if there is a liquid outer core, Cm/C will be around 0.5. In this case, Cm can be identified with the MOI of the silicate shell. If the core is solid, Cm/C will be about 1. The MOI C can be used to test and refine present models but will most likely not per se help to increase the confidence in the two-layer model beyond the present level, at least if there is a substantial inner core. C and Cm/C can be used to calculate the inner core radius and the outer core density, assuming the silicate shell density and the inner core density are given by cosmochemistry. The accuracy of the outer core density estimate depends largely on the confidence in the cosmochemical data. The inner core radius can be determined to the accuracy of the densities if the inner core radius is greater than 0.5 core radii. These values can be checked against the Love number of the planet. The higher order components of the gravity field can be used to estimate core–mantle boundary undulations and crust thickness variations. The former will dominate the gravity field at long wavelength, while the latter will dominate at short wavelengths.

The NetLander very broad band seismometer

Abstract The interior of Mars is today poorly known, in contrast to the Earth interior and, to a lesser extent, to the Moon interior, for which seismic data have been used for the determination of the interior structure. This is one of the strongest facts motivating the deployment on Mars of a network of very broad band seismometers, in the framework of the 2007 CNES-NASA joint mission. These seismometers will be carried by the Netlanders, a set of 4 landers developed by a European consortium, and are expected to land in mid-2008. Despite a low mass, the seismometers will have a sensitivity comparable to the present Very Broad Band Earth sensors, i.e. better than the past Apollo Lunar seismometers. They will record the full range of seismic and gravity signals, from the expected quakes induced by the thermoelastic cooling of the lithosphere, to the possible permanent excitation of the normal modes and tidal gravity perturbations. All these seismic signals will be able to constrain the structure of Mars’ mantle and its discontinuities, as well as the state and size of the Martian core, shortly after for the centennial of the discovery of the Earth core by Oldham (Quart. J. Geol. Soc. 62(1906) 456–475).

Three dimensional models of Martian mantle convection with phase transitions

We have employed a three-dimensional compressible convection model to study the dynamics of phase transitions in the Martian mantle. A large core model with two exothermic phase transitions, the olivine to β-spinel and the β- to γ-spinel transition, and a small core model including also the endothermic spinel to perovskite transition have been considered. The two exothermic transitions create ‘thermal barriers’ for small upwellings due to the latent heat consumption from the phase change. Upwelling plumes lose part or all of their buoyancy, which causes the formation of one stable area full of plumes. This tendency for the merging of plumes increases with internal heating. This type of convective planform is consistent with the relatively few large volcanic centers. The presence of a 175 km thick perovskite layer above the core-mantle boundary (CMB) yields a similar flow pattern, albeit with an even smaller number of plumes. However, the excess temperatures of the plumes and the mantle flow velocities in the lower mantle are smaller than those found in models without perovskite layer. The phase transitions cause an increase of temperature near the CMB, which prevents the lower mantle and the core from extensive cooling. A model with a perovskite layer decreasing in thickness with time can account for a peak in volcanic and magnetic activity early in the Martian history.

PHASE TRANSITIONS IN THE MARTIAN MANTLE : IMPLICATIONS FOR PARTIALLY LAYERED CONVECTION

Abstract Numerical simulations of mantle convection in Mars, using an axisymmetric spherical-shell model, show partial layering caused by the two exothermic olivine-spinel (α-β, β-γ) phase transitions. An extended Boussinesq approximation has been used in which viscous dissipation, adiabatic heating and cooling, and latent heat are included. The Rayleigh number (Ra) has been varied between 5 × 105 and 108. The partial layering with the vertical velocity at the exothermic phase transitions varying strongly in space and time is the result of two opposing effects: the enhanced buoyancy of the phase boundaries by thermal anomalies and the impeding influences from the latent heat release (or consumption). The effect of the latent heat is stronger in Mars than the Earth because of the comparatively low pressure gradient in the Martian mantle and the smaller excess temperature of upwellings and downwellings. The time-series of the mean vertical mass transport across the phase transitions show oscillations between blocking and acceleration of the flow. The amplitude and the oscillations in the time-series increase with increasingRa. Because of the partial layering, the planet will cool more slowly and less uniformly than suggested by thermal evolution models with parameterized convection. In addition, the number of strong mantle plumes is reduced to only a few upwellings. Such a pattern is suggested for Mars by the existence of two pronounced volcanic centers, Tharsis and Elysium. This could also cause a strong time dependence in the Martian volcanic activity. The latent heat release causes the mantle temperature to increase across each transition by about 50 K and produces a hot lower mantle and a liquid core. We have tested the case of a 85–350 km thick perovskite layer at the core-mantle boundary. A layer thicker than about 300 km would convect separately, and induce leaking to the mantle above at a significantly smaller rate compared to the layers induced by the olivine-spinel phase boundaries. For a perovskite layer smaller than about 300 km, the convective vigor near the core-mantle boundary decreases with the layer thickness.