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Current projects

Grain size evolution in Earth's lower mantle:

Grain size is one of the key factors controlling the rheology and dynamics of the Earth's mantle. The mantle is composed of polycrystalline grains that often deform within the grain size sensitive creep regime, i.e., diffusion creep. Hence, a small change in the grain size can modify the viscosity to a significant extent. However, the effect of grain size-dependent rheology on the dynamics and evolution of the mantle is so far not studied extensively using mantle convection models. Some of the previous studies used grain size evolution data obtained for upper mantle materials. Thus, the dynamics using grain-growth data applicable to the lower mantle remained unconstrained. With more advanced experimental methods, we have now obtained the grain-growth kinetics data for bridgmanite co-existing with ferropericlase, which is equivalent to the lower mantle's composition.
We develop numerical models incorporating composite rheology and grain size kinetics in 2D spherical annulus geometry employing the finite volume code StagYY. For this purpose we impose two kinds of grain growth kinetics in the upper and lower mantle. The combined parameters show faster grain-growth in the upper mantle and a slow grain-growth in the lower mantle. Our preliminary results covering 4.5 Gyrs of evolution suggest that grain size-dependent rheology can potentially stabilise large low shear wave velocity provinces in the lower mantle and provide a suitable viscosity that allows for a change of tectonic mode from squishy-plume lid to mobile lid regime.

Collaborators: J. Paul, T. Katsura, H. Fei / BGI Bayreuth; A. B. Rozel, P. J. Tackley / ETH Zurich

Combined impact and interior evolution models for Mars:

Here we use a coupled SPH-thermochemical approach to first simulate an impact event, and then use the result of this realistic model as the initial condition for the long-term mantle convection model. We find that both the impact scenario and the mantle properties affect the geometry of impact-induced crust and the subsequent state of the interior, and that the impact-induced crust extends beyond the initial magma pond. 
We show that a near head-on impact event with impactor radius of 750 km can best reproduce the southern highlands of Mars with a geometry similar to that of present-day Mars observations.

Collaborators: K. W. Cheng, A. B. Rozel, P. J. Tackley / ETH Zurich, M. Jutzi, H. Ballantyne / Univ. Bern

Probing the viscosity of Venus' mantle:

The Baltis Vallis channel on Venus preserved a record of long-wavelength deformation generated by a convecting mantle, offering a unique window into the planet's geodynamics. We statistically compare the observed dynamic topography of Baltis Vallis with dynamic topography generated by a suite of 3D stagnant-lid mantle convection models. Baltis Vallis' relatively young age and low topography indicate vigorous convection in Venus' mantle, implying a mantle viscosity 1-2 order of magnitude lower than Earth's. This difference may arise from either a water-rich, less degassed interior or a higher-temperature mantle beneath the insulating lid.

Collaborators: N. J. McGregor, F. Nimmo / UC Santa Cruz, C. Gillmann / ETH Zurich, A. M. Plattner / Univ. Alabama, J. W. Conrad / NASA Marshall Spaceflight Center Huntsville

Completed projects

Mantle depletion after martian giant impact:

Previous giant impact models coupled with simulations of mantle convection have shown that the martian crustal dichotomy can be explained by post‐impact melt crystallization that emplaced a thick crust in the southern hemisphere. In this study, we show that the depleted residue left behind by the original post‐impact crustal formation can spread laterally, potentially persisting beneath the northern hemisphere to the present‐day. Such a large‐scale mantle province would concurrently explain both the prevalence of long‐term magmatism on Mars and its strong preference for localized equatorial regions.

K. W. Cheng, A. B. Rozel, G. J. Golabek, H. A. Ballantyne, M. Jutzi and P. J. Tackley (2024). Mars's Crustal and Volcanic Structure Explained by Southern Giant Impact and Resulting Mantle Depletion. Geophys. Res. Lett. 51, e2023GL105910.

Animation:  Movie

Induction heating of planets orbiting white dwarfs:

Recently a number of planets have been discovered that orbit white dwarfs. We investigate whether electromagnetic induction heating due to the extremely strong magnetic fields of some white dwarfs can drive volcanic activity even on small bodies orbiting such white dwarfs on short-period orbits. Our results show that induction heating can indeed rapidly partially melt the mantle of lunar-mass objects orbiting white dwarfs with strong magnetic fields. The related volcanism drives outgassing that could be observed in the future around white dwarfs.

K. G. Kislyakova, L. Noack, E. Sanchis, L. Fossati, G. G. Valyavin, G. J. Golabek and M. Guedel
(2023). Induction heating of planetary interiors in white dwarf systems. Astron. Astrophys. 677, A109, doi:10.1051/0004-6361/202245225.

Investigating the feasibility of an impact-induced Martian Dichotomy:

Most studies attempting to explain the martian dichtomy focus on two theories; either the dichotomy formed solely through geodynamic processes or a giant impact occurred that imprinted the crustal cavity in the northern hemisphere we observe today. Recent work has proved the importance of coupling these hypotheses, introducing a hybrid exogenic-endogenic scenario with crust formation from the impact-generated melt. We model the impact using a suite of SPH simulations that explore a large parameter space. For the outcome of the simulation outcomes we apply a newly developed scheme to estimate the thickness and distribution of new formed or re-distributed post-impact crust.

H. A. Ballantyne, M. Jutzi, G. J. Golabek, L. Mishra, K. W. Cheng, A. Rozel and P. J. Tackley (2023). Investigating the feasibility of an impact-induced Martian dichotomy. Icarus 392, 115395, doi:10.1016/j.icarus.2022.115395.

Fluid flux determination for serpentinites in subduction zones:

We present a new method to determine fluid flux at subduction zone conditions. Orientated drill cores of antigorite starting material were placed into a MgO sleeve. Fluid released upon serpentine dehydration are fixed in the MgO sleeve by the formation of brucite, thus the amount and distribution of brucite in the run product serves as a proxy for fluid flux. The experiments show that dehydration results in an isotropic fluid flux. The timescales of fluid flux indicate that a large fluid pressure can build up during dehydration. Intermediate-depth earthquakes caused by brittle fracturing are thus likely to be caused by dehydration reactions in subducted serpentinites.

L. Eberhard, M. Thielmann, P. Eichheimer, A. Neri, A. Suzuki, M. Ohl, W. Fujita, K. Uesugi, M. Nakamura, G. J. Golabek and D. J. Frost (2022). A new method for determining fluid flux at high pressures applied to the dehydration of subduction zone serpentinites. Geochem. Geophys. Geosyst. 23, e2021GC010062, doi:10.1029/GC2021010062.


Strain-weakening rheology in Earth's lower mantle:

The rheological properties of Earth's lower mantle are key for mantle dynamics and planetary evolution. The main rock-forming minerals in the lower mantle are bridgmanite (Br) and smaller amounts of ferropericlase (Fp). Previous work has suggested that the large differences in viscosity between these minerals greatly affect the bulk rock rheology. The resulting effective rheology becomes highly strain-dependent as weaker Fp minerals become elongated and eventually interconnected. This implies that strain localization may occur in Earth's lower mantle. So far, there have been no studies on global-scale mantle convection in the presence of such strain-weakening rheology. Here, we present 2D numerical models of thermo-chemical convection in spherical annulus geometry including a new strain-dependent rheology formulation for lower mantle materials, combining rheological weakening and healing terms. We find that strain-weakening rheology has several direct and indirect effects on mantle convection. The most notable direct effect is the changing dynamics of weakened plume channels as well as the formation of larger thermochemical piles at the base of the mantle. The weakened plume conduits act as lubrication channels in the mantle and exhibit a lower thermal anomaly. SW rheology also reduces the overall viscosity, notable in terms of increasing convective vigor and core-mantle boundary heat flux. Finally, we put our results into context with existing hypotheses on the style of mantle convection and mixing. Most importantly, we suggest that the new kind of plume dynamics may explain the discrepancy between expected and observed thermal anomalies of deep-seated mantle plumes on Earth.

A. J. P. Guelcher, G. J. Golabek, M. Thielmann, M. D. Ballmer and P. J. Tackley (2022). Narrow, fast and "cool" mantle plumes caused by strain-weakening rheology. Geochem. Geophys. Geosyst. 23, e2021GC010314, doi:10.1029/GC2021010314.

Animations:  Movie1   Movie2   Movie3   Movie4   Movie5

Detailed analysis of main group pallasite slabs:

Olivine aggregates, bodies found in pallasites that consist of olivines with coherent grain boundaries and minor amounts of Fe-Ni and troilite, likely represent well-preserved samples of different mantle regions of pallasite parent bodies (PPBs). We investigated olivine aggregates from the main group pallasites Fukang, Esquel, Imilac, and Seymchan and compare their textures with results from deformation experiments. Our measurements reveal an inverse relationship between the grain size of olivines and the primary metal fraction inside olivine aggregates, which is explained by simultaneous grain growth retarded by Zener pinning in different mantle regions. Textural evidence indicates that the mantle has remained at high temperatures before initial cooling occurred shortly after pallasite formation that was likely caused by an impact. Different degrees of annealing of the deformation textures suggest that the post-collisional cooling occurred in the order Seymchan, Imilac, Esquel, and Fukang. We interpret this observation with an increasing burial depth after the collision. We also demonstrate that the mantle has not been convecting before the impact despite being at high temperature. Using the minimum critical Rayleigh number we estimate PPB radii assuming different core radii. Our results question the recent ferromagmatism hypothesis for pallasite formation and support a multi-stage formation process that includes one or several impacts.

N. P. Walte and G. J. Golabek (2022). Olivine aggregates reveal a complex collisional history of the main group pallasite parent body. Meteorit. Planet. Sci. 57, 1098-1115, doi:10.1111/maps.13810.

Coverage:  FRM News

Scaling laws for the geometry and volume of impact-induced melt:

Growing protoplanets experience a number of impacts during the accretion stage. As large impactors hit the surface of a protoplanet they cause melting. In the resulting magma ocean the impactor's core emulsifies and experiences metal-silicate equilibration with the mantle of the protoplanet while it descends towards its base. This process repeatedly occurs and determines the chemical compositions of both mantle and core of the final terrestrial planet. The partitioning is controlled by parameters such as equilibration pressure and temperature, which are associated with pressure and temperature at the base of the melt region. Both pressure and temperature depend on both the depth and shape of the impact-induced melt because a spatially confined magma ocean, a co-called magma pool, can have a larger equilibration pressure than a radially uniform global magma ocean even if their volumes are the same. We develop scaling laws for the total internal energy gain due to an impact and the heat distribution within the mantle based on more than 100 SPH simulations.

M. Nakajima, G. J. Golabek, K. Wuennemann, D. C. Rubie, C. Burger, H. J. Melosh, L. Manske, S. A. Jacobson and S.D. Hull (2021). Scaling laws for the geometry of an impact-induced magma ocean. Earth Planet. Sci. Lett., 568, 116983, doi:10.1016./j.epsl.2021.116983.

Modification of icy planetesimal interiors by early thermal evolution and collisions:

Comets and small Kuiper belt objects are considered to be among the most primitive objects in the solar system. Early in the solar system evolution the precursors of both groups, the so-called icy planetesimals, were modi ed by both short-lived radiogenic heating and collisional heating. Combining the results of thermal evolution and collision models we estimate under which conditions highly volatile ices like CO, CO2 and NH3 can be retained inside present-day comets and Kuiper belt objects. Our results indicate that for present-day objects derived from the largest post-collision remnant the internal thermal evolution controls the amount of remaining highly volatile ices, while for the objects formed from unbound post-collision material the impact heating is dominant. Finally we apply our results to present-day comets and Kuiper belt objects like 67P/Churyumov-Gerasimenko, C/1995 O1 Hale-Bopp and (486958) Arrokoth.

G. J. Golabek and M. Jutzi (2021). Modification of icy planetesimals by early thermal evolution and collisions: Constraints for formation time and initial size of comets and small KBOs. Icarus 363, 114437, doi:10.1016/j.icarus.2021.114437.

Bifurcation of planetary building blocks during Solar System formation:

Recent astronomical and geochemical evidence point to early spatial and temporal fragmentation of the planet formation process, whose physical origins remain disputed. Here, using a coupled numerical model, we investigate the influence of the build-up of the solar protoplanetary disk on the timing and internal evolution of forming protoplanets. We find that the orbital drift of the water iceline can generate two temporally and spatially distinct bursts of planetesimal formation, which sample different source regions of interstellar materials and experience limited intermixture. Driven by internal radiogenic heating, these planetary reservoirs compositionally evolve in two modes and recover accretion chronology, thermo-chemical pattern, and mass divergence of inner and outer Solar System. Our numerical experiments suggest that the earliest interplay between disk physics and geophysical evolution of accreting planetesimals initiated the present-day observed chemical and isotopic dichotomy of the Solar System planets.

T. Lichtenberg, J. Drążkowska, M. Schoenbaechler, G. J. Golabek and T. O. Hands (2021). Bifurcation of planetary building blocks during Solar System formation. Science 371, 365-370, doi:10.1126/science.abb3091.

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Influence of grain size reduction on transform fault formation:

Numerical models typically struggle to reproduce the strike-slip movement observed along transform faults.
Based on regional visco‐(elasto)‐plastic thermomechanical models it has been demonstrated that a strong strain‐induced weakening of rocks has to be assumed in order to initiate and stabilise the characteristic orthogonal ridge‐transform spreading patterns. However, the physical origin of such intense rheological weakening remains unclear. Employing 3D thermomechanical visco‐plastic models we study the effect of grain size reduction on oceanic transform fault initiation. In our models, transform faults initiate in the brittle crust and propagate downwards, thus indicating a top‐down initiated localisation process. The observed grain size, rheology and strain-rate inside the shear zone of our models agree well with observations in nature; however the longevity of natural examples cannot be reached.

J. Schierjott, M. Thielmann, A. B. Rozel, G. J. Golabek & T. V. Gerya (2020). Can grain size reduction initiate transform faults? - Insights from a 3D numerical study. Tectonics 39, e2019TC005793.

Two-stage formation of angular pallasites revealed by novel high strain-rate deformation experiments:

allasite formation is controversial, either sampling the core-mantle boundary or the shallower mantle of planetesimals that suffered an impact. In order to test this model, we performed high strain-rate deformation experiments employing the analogue system olivine -FeS/Au metal melt. All major textures of angular pallasites, including olivine-metal mush zones and olivine aggregates could be experimentally reproduced. Our results suggest that angular pallasites preserve evidence for a two-stage formation process, including inefficient core-mantle differentiation and an impact causing disruption, core melt injection, and fast cooling. Olivine aggregates are reinterpreted as mantle remnants containing primordial metallic melt pockets not stemming from the impactor.

N. P. Walte, G. F. D. Solferino, G. J. Golabek, D. Silva Souza & A. Bouvier (2020). Two-stage formation of pallasites and the evolution of their parent bodies revealed by deformation experiments. Earth Planet. Sci. Lett. 546, 116419, doi:10.1016/j.epsl.2020.116419.

Coverage:  TUM News   FRM News   Phys.org   EurekAlert!

Numerical and experimental study of microstructure and permeability in porous granular media:

Fluid flow on different scales is of interest for Earth science disciplines like petrophysics, hydrogeology and volcanology. To parameterize fluid flow in large-scale numerical simulations, flow properties on the microscale need to be considered. For this purpose experimental and numerical investigations of flow through porous media over a wide range of porosities are necessary. We sinter glass bead media with various porosities and determine permeability both experimentally and numerically. Using CT scans we investigate the microstructure of the samples. We test different parameterizations for isotropic porous media on their potential to predict permeability by comparing their estimations to computed and experimentally measured values. 

P. Eichheimer, M. Thielmann, W. Fujita, G. J. Golabek, M. Nakamura, S. Okumura, T. Nakatani and M. O. Kottwitz (2020). Combined numerical and experimental study of microstructure and permeability in porous granular media. Solid Earth 11, 1079-1095, https://doi.org/10.5194.se-11-1079-2020.


Effect of water on ringwoodite thermal conductivity and its influence on the thermal evolution of slabs:

Ringwoodite is the most abundant phase in the lowermost mantle transition zone and can host up to 1.5-2 wt% water. We studied the high-pressure thermal conductivity of dry and hydrous ringwoodite. We show that the incorporation of 1.73 wt% of water reduces the ringwoodite thermal conductivity by more than 40% at mantle transition zone pressures. Using simple 1D thermal diffusion models we demonstrate that this effect delays the decomposition of dense hydrous magnesium silicates, thus allowing them to reach Earth's lower mantle.

E. Marzotto, W.-P. Hsieh, T. Ishii, K.-H. Chao, G. J. Golabek, M. Thielmann & E. Ohtani (2020). Effect of water on lattice thermal conductivity of ringwoodite and its implications for the thermal evolution of descending slabs. Geophys. Res. Lett. 47, e2020GL087607.

N-body late accretion models coupled with atmosphere-interior models of Venus:

It remains contentious whether the late accretion after the end of core formation was rich or poor in water and other volatiles. Here we investigate the long-term evolution of Venus using self-consistent numerical simulations of global thermochemical mantle convection coupled with both an atmospheric evolution model and a late accretion N-body delivery model. The results suggest that a preferentially dry composition of the late accretion impactors is most consistent with measurements of atmospheric
H2O, CO2 and N2. We suggest that the late accreted material delivered to Venus was mostly dry enstatite chondrite, consistent with isotopic data for Earth, with less than 2.5% (by mass) wet carbonaceous chondrites. In this scenario, the majority of Venus's and Earth's water would have been delivered during the main accretion phase.

C. Gillmann, G. J. Golabek, S. N. Raymond, M. Schoenbaechler, P. J. Tackley, V. Dehant and V. Debaille (2020). Dry late accretion inferred from Venus's coupled atmosphere and internal evolution. Nat. Geosci. 13, 265-269.

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Microscale deformation of bridgmanite-ferropericlase mixtures:

The mineralogy of the lower mantle can be approximated as a bridgmanite-ferropericlase mixture. Previous work has suggested that the deformation of this mixture might be dramatically affected by the large differences in viscosity between bridgmanite and ferropericlase. We employ numerical models to establish a connection between ferropericlase morphology and the effective rheology of the Earth's lower mantle using a numerical-statistical approach. We link the statistical properties of the two-phase composite to its effective viscosity tensor using analytical approximations. We find that ferropericlase develops elongated structures within the bridgmanite matrix that result in significantly lowered viscosity. We show that significant rheological weakening can thus be already achieved even when ferropericlase does not form an interconnected network. Additionally, the alignment of weak ferropericlase leads to a pronounced viscous anisotropy that develops with total strain, which may have implications for understanding the viscosity structure of Earth's lower mantle as well as for modelling the behaviour of subducting slabs.

M. Thielmann, G. J. Golabek and H. Marquardt (2020). Ferropericlase control of lower mantle rheology: Impact of phase morphology. Geochem. Geophys. Geosyst. 21, e2019GC008688.

Desiccation of planetesimals due to 26Al heating:

Here we demonstrate the power of 26Al, a short-lived radionuclide abundant in the early Solar system, to control the water content of terrestrial exoplanets by rapid dehydration of planetesimals prior to accretion. Using numerical models of planet formation, evolution, and interior structure, we generate synthetic planet populations influenced by varying levels of 26Al heating during accretion. We show that planet bulk water fraction and radius are anti-correlated with initial 26Al levels in the planetesimal-based accretion framework. This yields a system-wide correlation of bulk abundances, consistent with the lack of a clear orbital trend in the water budgets of the TRAPPIST-1 planets.

T. Lichtenberg, G. J. Golabek, R. Burn, M. R. Mayer, Y. Alibert, T. V. Gerya and C. Mordasini (2019).
A water budget dichotomy of rocky protoplanets from 26Al heating. Nat. Astron. 3, 307-313.

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Two-phase flow models of melt evolution in early-formed planetesimals:

Rocky planetesimals in the early solar system melted internally and evolved chemically due to radiogenic heating from 26Al. Here we quantify the parametric controls on magma genesis and transport using a coupled petrological and fluid mechanical model of reactive two-phase flow. We find the mean grain size of silicate minerals to be a key control on magma ascent.
According to our models, the evolution of partially molten planetesimal interiors falls into two categories. In the global magma ocean scenario, the whole interior of a planetesimal experiences nearly complete melting, resulting in turbulent convection and core-mantle differentiation by the rainfall mechanism. In the magma sill scenario, segregating melts gradually deplete the deep interior of the radiogenic heat source. In this case, magma may form melt-rich sills beneath a cool and stable lid, while core formation would proceed by percolation.

T. Lichtenberg, T. Keller, R. F. Katz, G. J. Golabek and T.V. Gerya (2019). Magma ascent in planetesimals: Control by grain size. Earth Planet. Sci. Lett. 507, 154-165.

Animation:  Movie

Formation of mixed-type pallasite meteorites:

The origin of pallasite meteorites remains elusive. Here we test the hypothesis of mixing of olivine fragments with Fe-Ni-S after an impact followed by annealing employing both experimental analogues and numerical models. The experiments show that the addition of sulfur to olivine + Fe-Ni accelerates olivine grain growth, though the growth rate is reduced when Fe-Ni-S is not fully molten. Numerical models satisfying available formation constraints from natural samples indicate that planetesimals with radii ≥200 km are favorable for the formation of rounded olivine-bearing pallasites by annealing of fragments in partially molten Fe-Ni-S. Moreover, early mixing in the planetesimal can form regions containing olivine grains with different grain sizes that could explain the formation of mixed-type pallasites.

G. F. D. Solferino and G. J. Golabek (2018). Olivine grain growth in partially molten Fe-Ni-S: A proxy for the genesis of pallasite meteorites. Earth Planet. Sci. Lett. 504, 38-52.

Animation:  Movie

Constraints on the metal-silicate separation on the IAB parent body:

The short-lived Hf-W decay system is a powerful chronometer for constraining the timing of metal-silicate separation and core formation in planetesimals and planets. Neutron capture effects on W isotopes, however, significantly hamper the application of this tool. In order to correct for neutron capture effects, Pt isotopes have emerged as a reliable in-situ neutron dosimeter. This study applies this method to IAB iron meteorites, in order to constrain the timing of metal segregation on the IAB parent body. Thermal models of the interior evolution that are consistent with the obtained estimates suggest that the IAB parent body underwent metal-silicate separation as a result of internal heating by short-lived radionuclides and accreted at around 1.4 Myr after CAIs with a radius of greater than 60 km.

A. C. Hunt, D. Cook, T. Lichtenberg, P. M. Reger, M. Ek, G. J. Golabek and M. Schoenbaechler (2018). Late metal-silicate separation on the IAB parent asteroid: Constraints from combined W and Pt isotopes and thermal modelling. Earth Planet. Sci. Lett. 482, 490-500.

Formation of chondrules via impact splashes:

Chondrules, mm-sized igneous-textured spherules, are the dominant bulk silicate constituent of chondritic meteorites and originate from highly energetic, local processes during the first million years after the birth of the Sun. So far, an astrophysically consistent chondrule formation scenario explaining major chemical, isotopic and textural features, in particular Fe,Ni metal abundances, bulk Fe/Mg ratios and intra-chondrite chemical and isotopic diversity, remains elusive. Here, we examine the prospect of forming chondrules from impact splashes among planetesimals heated by radioactive decay of short-lived radionuclides using thermomechanical models of their interior evolution. We examine how the observed chemical and isotopic features of chondrules constrain the dynamical environment of accreting chondrite parent bodies by interpreting the meteoritic record as an impact-generated proxy of early solar system planetesimals that underwent repeated collision and reaccretion cycles. Using a coupled evolution-collision model we demonstrate that the vast majority of collisional debris feeding the asteroid main belt must be derived from planetesimals which were partially molten at maximum. Therefore, the precursors of chondrite parent bodies either formed primarily small, from sub-canonical aluminium-26 reservoirs, or collisional destruction mechanisms were efficient enough to shatter planetesimals before they reached the magma ocean phase.

T. Lichtenberg, G. J. Golabek, C. P. Dullemond, M. Schoenbaechler, T. V. Gerya and M. R. Meyer (2018). Impact splash chondrule formation during planetesimal recycling. Icarus 302, 27-43.

Coupled giant impact and longer-term interior evolution models:

Giant impacts have been suggested to explain various characteristics of terrestrial planets and their moons. However, so far in most models only the immediate effects of the collisions have been considered, while the long-term interior evolution of the impacted planets was not studied. We combine 3-D shock physics collision calculations with 3-D thermochemical interior evolution models.
We apply the combined methods to a demonstration example of a giant impact on a Mars-sized body, using typical collisional parameters from previous studies. While the material parameters (equation of state, rheology model) used in the impact simulations can have some effect on the long-term evolution, we find that the impact angle is the most crucial parameter for the resulting spatial distribution of the newly formed crust. The results indicate that a dichotomous crustal pattern can form after a head-on collision, while this is not the case when considering a more likely grazing collision. The results underline that end-to-end 3-D calculations of the entire process are required to study in the future the effects of large-scale impacts on the evolution of planetary interiors.

G. J. Golabek, A. Emsenhuber, M. Jutzi, E. I. Asphaug and T. V. Gerya (2018). Coupling SPH and thermochemical models of planets: Methodology and example of a Mars-sized body. Icarus 301, 235-246.

Animations:  Movie1   Movie2

Formation of the Earth's oldest continental crust:

The global geodynamic regime of early Earth, which operated before the onset of plate tectonics, remains disputed. Geological and geochemical data suggest hotter Archean mantle temperature and more intense juvenile magmatism. Two alternative crust-mantle interaction modes differing in melt eruption efficiency have been proposed: the pipe tectonics regime dominated by volcanism and the squishy lid tectonics regime governed by intrusive magmatism. Both regimes are capable of producing primordial tonalite-trondhjemite-granodiorite (TTG) continental crust, however lithospheric geotherms and crust production rates as well as proportions of various TTG compositions differ significantly. This provides an opportunity to test the heat-pipe and plutonic squishy lid tectonics hypotheses on the basis of natural data. We show that the heat pipe tectonics model results is not able to produce Earth-like primordial continental crust. In contrast, the plutonic squishy lid tectonics regime dominated by intrusive magmatism results is capable of reproducing the observed proportions of various TTG-rocks. The results show that the typical modern eruption efficiency leads to the production of the expected amount of the three main primordial crustal compositions previously reported from field data.

A. B. Rozel, G. J. Golabek, C. Jain, P. J. Tackley & T. Gerya (2017). Continental crust formation on early Earth controlled by intrusive magmatism. Nature 545, 332-335.

Animation:  Movie

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Effect of porosity on the thermo-mechanical evolution of planetesimals:

The thermal history and internal structure of chondritic planetesimals, assembled before the giant impact phase of chaotic growth, potentially yield important implications for the final composition and evolution of terrestrial planets. These parameters critically depend on the internal balance of heating versus cooling, which is mostly determined by the presence of short-lived radionuclides (SLRs) as well as the heat conductivity of the material. The heating by SLRs depends on their initial abundances, the formation time of the planetesimal and its size. It has been argued that the cooling history is determined by the porosity of the granular material, which undergoes dramatic changes via compaction processes and tends to decrease with time. In this study we assess the influence of these parameters on the thermo-mechanical evolution of young planetesimals with both 2D and 3D simulations. Our results indicate that powdery materials lower the threshold for melting and convection in planetesimals, depending on the amount of SLRs present. A subset of planetesimals retains a powdery surface layer which lowers the thermal conductivity and hinders cooling. However, the effect of initial porosity is small compared to those of planetesimal size and formation time, which dominate the thermo-mechanical evolution and are the primary factors for the onset of melting and differentiation.

T. Lichtenberg, G. J. Golabek, T. V. Gerya & M. R. Meyer (2016). The effects of short-lived radionuclides and porosity on the early thermo-mechanical evolution of planetesimals. Icarus 274, 350-365.

Animation:  Movie

Influence of single large impacts on the coupled mantle-atmosphere evolution of Venus:

We investigate the effect of a single large impact during the Late Veneer and Late Heavy Bombardment on the evolution of the mantle and atmosphere of Venus. We use a coupled interior-exterior model. Single vertical impacts are simulated as instant events affecting both the atmosphere and mantle of the planet by (i) eroding the atmosphere, causing atmospheric escape, and (ii) depositing energy in the crust and mantle of the planet. Main impactor parameters include timing, size/mass, velocity and efficiency of energy deposition. We observe that volatile delivery by the impactor and impact erosion of the atmosphere are both minor effects compared to melting and degassing triggered by the energy deposited in the mantle and crust. Small collisions (under 100 km radius) have only local and time-limited effects. Medium-sized impactors (100-400 km) will not have much more consequences unless the energy deposition is enhanced, for example by a fast collision. In that case, it will have comparable effects to the larger category of impacts (400-800 km): a strong thermal anomaly affecting both crust and mantle and triggering melting and a change in mantle dynamics patterns.

C. Gillmann, G. J. Golabek & P. J. Tackley (2016). Effect of a single giant impact on the coupled atmosphere-interior evolution of Venus. Icarus 268, 295-312.

Animation:  Movie

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Appearance of the 'ridge only' regime in mantle convection models with a visco-plastic rheology:

In this study, we report a new convection regime in which a ridge can form without destabilizing the surrounding lithosphere or forming subduction zones. Using simulations in 2D spherical annulus geometry, we show that a depth-dependent yield stress is sufficient to reach this ridge only regime. This regime occurs when the friction coffecient is close to the critical value between mobile lid and stagnant lid regime. The ridge only regime appears for both pure basal heating and mixed heating mode. For basal heating, this regime can occur for all vertical viscosity contrasts, while for mixed heating, a highly viscous deep mantle is required.

A. Rozel, G. J. Golabek, R. Naef & P. J. Tackley (2015). Formation of ridges in a stable lithosphere in mantle convection simulations with visco-plastic rheology. Geophys. Res. Lett. 42, 4770-4777.

Animation:  Movie

Formation of rounded olivine grains in pallasites:

Despite their relatively simple mineralogical composition, the origin of pallasite meteorites remains debated. It has been suggested that catastrophic mixing of olivine fragments with Fe-(Ni)-S followed by various degrees of annealing could explain pallasites bearing solely or prevalently fragmented or rounded olivines. In order to verify this hypothesis, and to quantify the grain growth rate of olivine in a metal matrix, we performed a series of annealing experiments on natural olivine plus synthetic Fe-S mixtures. Olivine grain growth in molten Fe-S is significantly faster than in solid-, sulphur-free metal. We used the experimentally determined grain growth law to model the coarsening of olivine surrounded by Fe-S melt in a 100 to 600 km radius planetesimal. Employing a 1D finite-difference model, annealing depths of up to 50 km allow for (i) average grain sizes consistent with the observed rounded olivine-bearing pallasites, (ii) a remnant magnetization of FeNi olivine inclusions as measured in natural pallasites and (iii) for the metallographic cooling rates derived from FeNi in pallasites. This is valid even if the impact occurs several millions of years after the differentiation of the target body was completed.

G. F. D. Solferino, G. J. Golabek, F. Nimmo & M. W. Schmidt (2015). Fast grain growth of olivine in liquid Fe-S and the formation of pallasites with rounded olivine grains. Geochim. Cosmochim. Acta 162, 259-275.

Is Vesta an intact and pristine protoplanet?

It is difficult to find a Vesta model of iron core, pyroxene and olivine-rich mantle, and HED crust that can match the joint constraints of (a) Vesta's density and core size as reported by the Dawn spacecraft team; (b) the chemical trends of the HED meteorites, including the depletion of sodium, the FeO abundance, and the trace element enrichments; and (c) the absence of exposed mantle material on Vesta's surface, among Vestoid asteroids, or in our collection of basaltic meteorites. These conclusions are based entirely on mass-balance and density arguments, independent of any particular formation scenario for the HED meteorites themselves. We suggest that Vesta either formed from source material with non-chondritic composition or underwent after its formation a radical physical alteration, possibly caused by collisional processes, that affected its global composition and interior structure.

G. J. Consolmagno, G. J. Golabek, D. Turrini, M. Jutzi, S. Sirono, V. Svetsov & K. Tsiganis (2015). Is Vesta an intact and pristine protoplanet? Icarus 254, 190-201.

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Size and formation time of the acapulcoite-lodranite parent body:

The acapulcoite-lodranite meteorites are members of the primitive achondrite class. The observation of partial melting and resulting partial removal of Fe-FeS indicates that this meteorite group could be an important link between achondrite and iron meteorites on the one hand and chondrite meteorites on the other. Thus a better understanding of the thermomechanical evolution of the parent body of this meteorite group can help to improve our understanding of the evolution of early planetesimals. Here we use 2D and 3D finite-difference numerical models to determine the formation time, initial radius of the parent body of the acapulcoite-lodranite meteorites and their formation depth inside the body by applying available geochronological, thermal and textural constraints to our numerical data. Our results indicate that the best fit to the data can be obtained for a parent body with 25-65 km radius, which formed around 1.3 Myr after CAI. The 2D and 3D results considering various initial temperatures and the effect of porosity indicate possible formation depths of the acapulcoite-lodranite meteorites of 9-19 and 14-25 km, respectively. Our data also suggest that other meteorite classes could form at different depths inside the same parent body.

G. J. Golabek, B. Bourdon & T. V. Gerya (2014). Numerical models of the thermomechanical evolution of planetesimals: Application to the acapulcoite-lodranite parent body. Meteorit. Planet. Sci. 49, 1083-1099.

Animation:  Movie

Single-plume state on Enceladus:

The thermal dichotomy of Enceladus suggests an asymmetrical structure in its global heat transfer. So far, most of the models proposed that obtained such a distribution have prescribed an a priori asymmetry, i.e. some anomaly in or below the south polar ice shell. We present here the first set of numerical models of convection that yield a stable single-plume state for Enceladus without prescribed mechanical asymmetry. Using the convection code StagYY in a 2D-spherical annulus geometry, we show that a non-Newtonian ice rheology is sufficient to create a localized, single hot plume surrounded by a conductive ice mantle. We obtain a self-sustained state in which a region of small angular extent has a sufficiently low viscosity to allow subcritical to weak convection to occur due to the stress-dependent part of the rheological law. We find that the single-plume state is very unlikely to remain stable if the rheology is Newtonian, confirming what has been found by previous studies. In a second set of numerical simulations, we also investigate the first-order effect of tidal heating on the stability of the single-plume state. Tidal heating reinforces the stability of the single-plume state if it is generated in the plume itself. Also we show that the likelihood of a stable single-plume state does not depend on the thickness of the ice shell.

A. Rozel, J. Besserer, G. J. Golabek, M. Kaplan and P. J. Tackley (2014). Self-consistent generation of single-plume state for Enceladus using non-Newtonian rheology. J. Geophys. Res. 119, 416-439.

Oligarchic growth of Mars and its implications for Hf-W chronology:

Dauphas and Pourmand (2011) estimated the accretion timescale of Mars to be 0.8 - 2.7 Myr from the W isotopes of Martian meteorites. This timescale was derived assuming perfect metal-silicate equilibration between the impactor and the target's mantle. However, in the case of a small impactor most likely only a fraction of the target's mantle is involved in the equilibration, while only a small part of the impactor's core equilibrates in the case of a giant impact. We examined here the effects of imperfect equilibration using results of high-resolution N-body simulations for the oligarchic growth stage.

Morishima, R., G. J. Golabek and H. Samuel (2013). N-body simulations of oligarchic growth of Mars: Implications for Hf-W chronology. Earth Planet. Sci. Lett. 366, 6-16.

Early thermochemical evolution of asteroid 4 Vesta:

Diogenites are thought to represent mantle rocks formed as cumulates in magma chambers on 4 Vesta. We studied Northwest Africa (NWA) 5480, a harzburgitic diogenite, composed mainly of heterogeneously distributed olivine and orthopyroxene. Electron backscattered diffraction on the olivine grains of NWA 5480 shows that the preferred orientation can be explained neither by cumulate formation, nor by impact reprocessing near the asteroid's surface. Rather, they represent high-temperature solid-state plastic deformation by the pencil-glide slip system, which is well known from dry ultramafic rocks on Earth, typically formed by mantle shear at subsolidus temperatures. Numerical 2D models indicate that these observations may be explained by large-scale downwellings occurring in the asteroid's mantle within the first 50 Myr of Vesta's evolution. Implications include long-lasting enhanced mass exchange occurring in the dynamic interiors of differentiated asteroids.

Tkalcec, B. J, G. J. Golabek and F. E. Brenker (2013). Solid-state plastic deformation in the dynamic interior of a differentiated asteroid. Nature Geosci. 6, 93-97.

Animation:  Movie

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Comparison of numerical surface topography calculations:

Topography is a direct observable of the interaction between the Earth's internal and external dynamics. Therefore, it is important for numerical models of lithospheric deformation to compute topography accurately. Earth's surface is a so-called free surface, which means that both normal and shear stress should vanish at this interface. It has been shown that correct treatment of the Earth's surface as a free surface can have a significant effect in models of lithospheric and mantle dynamics. However, a true free surface is computationally expensive which is why most mantle convection simulations until now treat the surface as a free-slip boundary. For these models, topography is computed directly from normal stresses. A free surface approximation, the so-called 'sticky air', has recently gained interest in the geodynamic community. This method requires the addition of a fluid layer in the model domain while retaining the computational advantage of a free-slip top boundary. The fluid layer is a proxy for air and should, therefore, have a near-zero density and a viscosity, which is several orders of magnitude lower than the lithosphere viscosity. Sufficiently small normal stress at the surface is ensured by the physical properties of the weak layer (i.e., the low values for density and viscosity). We present a theoretical background that provides the physical conditions under which the sticky-air approach is a valid approximation of a true free surface.

Crameri, F., H. Schmeling, G. J. Golabek, T. Duretz, R. Orendt, S. Buiter, D. A. May, B. J. P. Kaus, T. V. Gerya and P. J. Tackley (2012). A comparison of numerical surface topography calculations in geodynamic modelling: an evaluation of the 'sticky air' method. Geophys. J. Int. 189, 38-54.

Formation of the martian crustal dichotomy and long-lived volcanism:

In this project we study the influence of a giant impactor on the evolution of Mars. The crustal dichotomy is the oldest and most striking surface feature on Mars. It is a large difference in elevation and crustal thickness between the southern highlands. It was formed more than 4.1 Ga ago owing to either exogenic or endogenic processes. Based on the geochemical analysis of SNC meteorites it was suggested that a primordial crust with up to 45 km thickness can be formed already during the martian core formation. As the final accretion stage of terrestrial planets is based on stochastically distributed impacts, we suggest that the sinking of the iron core, delivered by a late pre-differentiated giant impactor, induced shear heating-related temperature anomalies in the mantle, which fostered the formation of early asymmetrical primordial crust. In this study, we examine parameter sets that will likely cause an onset of hemispherical low-degree mantle convection directly after, and coupled to, an already asymmetrical core formation. For this purpose we couple 2D cylindrical simulations using the codes I2ELVIS for the core formation and the code StagYY for the long-term mantle convection in series. We apply a temperature, stress- and composition-dependent viscoplastic rheology inside a Mars-sized planet and include radioactive- and shear heating. Results show that low-degree convection can be induced by a giant impact during core formation. Furthermore, the amplitude of shear heating anomalies generally well exceeds the solidus of primitive mantle material. Therefore a hemispherical magma ocean is formed, which can be the source of a dichtomous crust. A degree-1 convective pattern establishes during the long-term evolution with the single upwelling feeding long-term volcanism as observed on Mars.

Golabek, G. J., T. Keller, T. V. Gerya, G. Zhu, P. J. Tackley & J. A. D. Connolly (2011). Origin of the martian dichotomy and Tharsis from a giant impact causing massive magmatism. Icarus 215, 346-357.

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Influence of silicate rheology on core formation:

In this model we simulate the whole planetary body during core formation. The focus lies on the influence of rheological parameters on the mode of core formation. Until now most numerical models of core formation via diapirism were limited to the simulation of the sinking of a single diapir. Here we perform 2D cylindrical simulations using the code I2ELVIS applying the newly developed 'spherical-Cartesian' methodology. It combines finite differences on a fully staggered rectangular Eulerian grid and Lagrangian marker-in-cell technique for solving momentum, continuity and temperature equations as well as the Poisson equation for gravity potential in a self-gravitating planetary body. In the model the planet is surrounded by a low viscosity, massless fluid ('sticky air') to simulate a free surface. We apply a temperature- and stress-dependent viscoplastic rheology inside Mars- and Earth-sized planets and include heat release due to radioactive decay, shear and adiabatic heating. As initial condition we use randomly distributed iron diapirs with random sizes in the range 50 to 100 km radius inside the accreting planet, which represent the iron delivered by predifferentiated impactors. A systematic investigation of the diapir behaviour for different rheological parameters is being performed, and results are being compared to the isotopic time scale of core formation on terrestrial planets. Our results demonstrate that the silicate rheology controls which formation mechanism becomes dominant. We derive scaling laws to predict the mode of core formation for a certain rheology. Our models show that, dependent on the mode of core formation, the heat partitioning between mantle and core can vary considerably. This can affect the onset of mantle convection.

Golabek, G. J., T. V. Gerya, B. J. P. Kaus, R. Ziethe & P. J. Tackley (2009). Rheological controls on the terrestrial core formation mechanism. Geochem. Geophys. Geosyst. 10, Q11007.

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Core formation in slowly accreted planetary bodies:

It has been suggested that the accretion rate is highly dependent on the distance of the accreting planetary body from the sun. As the radiogenic heating by aluminium-26 and iron-60 is short-lived a slow accretion can result in a cold central region of an accreting planetary body. Here we study the core formation in such bodies using 2D cylindrical simulations using both Newtonian and Non-Newtonian rheologies. Results indicate that in some of the cold central protocore can be pushed to the surface of one hemisphere of the planetary body, allowing liquid iron to fill the core. In another scenario, the protocore is fragmented.

Lin, J.-R., T. V. Gerya, P. J. Tackley, D. A. Yuen & G. J. Golabek (2011). Protocore destabilization in planetary embryos formed by cold accretion: Feedbacks from non-Newtonian rheology and energy dissipation. Icarus 213, 24-42.

Lin, J.-R., T. V. Gerya, P. J. Tackley, D. A. Yuen & G. J. Golabek (2009). Numerical modeling of protocore destabilization during planetary accretion: Methodology and results. Icarus 204, 732-748.

Flow channelling instabilities aiding terrestrial core formation:

In this model we assume that the temperature in the central region of an accreting planetary body is too low for silicate melting, but high enough to melt iron partially. We apply Stevenson's stress-induced melt channelling mechanism in the regions surrounding incipient iron diapirs. We perform numerical experiments solving the two-phase, two compositions flow equations within a 2D rectangular box. We apply the Compaction Boussinesq Approximation (CBA) and include a depth-dependent gravity. We use a temperature- and stress-dependent viscosity for the solid phase and melt fraction dependent rheology for the partially molten region around the diapir. As a result we observe for sufficiently small retention numbers the development of iron-rich melt channels within a region of approximately twice the diapir's radius. This leads to an effective draining of the surrounding region. The iron channels propose an effective mechanism to extract iron melt also from deeper parts of the initially central region without the need of substantial silicate melting. This mechanism can enhance the process of iron core formation and affect the metal-silicate equilibration in the deep planetary interior prior the Moon-forming giant impact. Therefore the channelling mechanism could also be interesting for planets like Mars, which probably never experienced complete melting.

Influence of a free surface on subduction:

Numerically modelling the dynamics of a self-consistently subducting lithosphere is a challenging task because of the decoupling problems of the slab from the free surface. We address this problem with a benchmark comparison between various numerical codes (Eulerian and Lagrangian, Finite Element and Finite Difference, with and without markers) as well as a laboratory experiment. The benchmark test consists of three prescribed setups of viscous flow, driven by compositional buoyancy, and with a low viscosity, zero-density top layer to approximate a free surface. Alternatively, a fully free surface is assumed. Our results with a weak top layer indicate that the convergence of the subduction behaviour with increasing resolution strongly depends on the averaging scheme for viscosity near moving rheological boundaries. Harmonic means result in fastest subduction, arithmetic means produces slow subduction and geometric mean results in intermediate behaviour. A few cases with the infinite norm scheme have been tested and result in convergence behaviour between that of arithmetic and geometric averaging. Satisfactory convergence of results is only reached in one case with a very strong slab, while for the other cases complete convergence appears mostly beyond presently feasible grid resolution. Analysing the behaviour of the weak zero-density top layer reveals that this problem is caused by the entrainment of the weak material into a lubrication layer on top of the subducting slab whose thickness turns out to be smaller than even the finest grid resolution. Agreement between the free surface runs and the weak top layer models is satisfactory only if both approaches use high resolution. Comparison of numerical models with a free surface laboratory experiment shows that  Lagrangian-based free surface numerical models can closely reproduce the laboratory experiments provided that sufficient numerical resolution is employed and  Eulerian-based codes with a weak surface layer reproduce the experiment if harmonic or geometric averaging of viscosity is used. The harmonic mean is also preferred if circular high viscosity bodies with or without a lubrication layer are considered. We conclude that modelling the free surface of subduction by a weak zero-density layer gives good results for highest resolutions, but otherwise care has to be taken in handling the associated entrainment and formation of a lubrication layer and choosing the appropriate averaging scheme for viscosity at rheological boundaries.

Constraints on the interconnection threshold in the systems olivine/Fe-S and peridotite/Fe-S from electrical impedance measurements:

The connectivity of FeS melts in olivine and in a fertile peridotite matrix has been addressed through in situ electric impedance spectroscopy measurements at 1 GPa. A first series of experiments used sintered powder samples of a fertile peridotite xenolith mixed with 5-15 vol.% Fe70S30 of eutectic composition. The sheared high-T garnet peridotite with Mg# ≈ 0.90 is composed of 60 vol.% olivine, 15% orthopyroxene, 5.3% clinopyroxene and 19% garnet, the powder grain size was 20-30 μm, similar to the one employed by Yoshino et al. (2003). For a second series, San Carlos olivine aggregates were used as solid matrix and 10-20 vol.% of eutectic Fe70S30 were added. For these, the average grain size was 3 microns, much smaller than in the experiments by Yoshino et al. (2003). The powder mixtures of peridotite + Fe70S30 and olivine aggregates + Fe70S30 were first annealed for 2-5 days in a conventional piston cylinder at 1 GPa and 950-970 degrees C. The electrical conductivity of samples has been measured using the impedance spectroscopy method in a BN-graphite-CaF2 pressure cell with concentric cylindrical electrodes made from Mo- or Re-foil (the estimated oxygen fugacity was close to the IW-buffer). The results indicate that up to 15 vol.% of Fe70S30 the melt phase does not built a stable interconnected network in a peridotite matrix, as indicated by Walte et al. (2007). The percolation threshold for a stable FeS network in olivine matrix lies at 17.5 vol.%, much higher the 6 vol.% found by Yoshino et al. (2003). Our result is in line with the high dihedral angles of typically 70-100 degrees for Fe-S melts in mantle materials. The higher interconnectivity threshold of this study, as compared to previous studies (Yoshino et al., 2003, 2004; Roberts et al., 2007) is a result of our smaller starting grain sizes (for olivine) in combination with much longer run durations. Both these experimental conditions result in enhanced grain growth and thus to a higher degree of textural equilibration, leading to the occurrence of the time depending pinging off of Fe-S melt films in our texturally more mature experiments.

Bagdassarov, N., G. J. Golabek, G. Solferino & M. W. Schmidt (2009). Constraints on the Fe-S melt connectivity in mantle silicates from electrical impedance measurements. Phys. Earth Planet. Int. 177, 139-146.

Constraints on the differentiation time of planetary bodies from centrifuge assisted percolation of Fe-S from partially molten silicates:

The mechanism which segregates molten Fe-S into metallic cores of planetary bodies is still not fully understood. Due to the high interfacial energy and wetting angle between Fe-S melts and silicate mantle minerals, the continuous percolative flow of such melts cannot be efficient for the core segregation in planetary bodies. A series of percolation experiments has been realized on a partially molten fertile garnet peridotite, employing a centrifuging piston cylinder. A high temperature garnet peridotite with Mg# ≈ 0.90 composed of 60 vol.% olivine, 15 vol.% orthopyroxene, 6 vol.% clinopyroxene and 19 vol.% garnet has been used as the silicate matrix. Peridotite powders with the 100-200 or 20-30 μm grain size were mixed with 5-30 vol.% Fe-S of eutectic composition Fe70S30. The aggregates were centrifuged at 500-700 g at temperatures below and above the melting point of the peridotite. The centrifuge experiments revealed a negligible percolation of Fe-S melts through the unmolten peridotite matrix. Only at T >1260 degrees C, i.e. above the solidus of the peridotite, and starting with 5 vol.% of Fe70S30 the vertical melt gradient achieved 1-2 vol.%/mm. In samples with 15 vol.% Fe70S30 the vertical separation achieved 2-2.5 vol.%/mm after 10 h of centrifuging at 500 g. An increase in the degree of partial silicate melting in the peridotite leads to an increase of the Fe-S separation rate from the peridotite matrix. Fe-S contents >10 vol.% cause an increase of the Fe-S melt droplet size and of the effective percolation velocity of Fe-S melt. A threshold dividing fast (>10 cm per year) and slow percolations (<1 mm per year) of Fe-S melt is found around 14-15 vol.% of Fe70S30. The experimentally determined permeabilities of Fe-S melt in the unmolten peridotite with 7-10 vol.% of Fe70S30 melt are 2-3 orders of magnitude lower than the values calculated previously from static experiments. The presence of the silicate melt increases the segregation velocity of Fe-S melt in a partially molten peridotite bymore than one order of magnitude with respect to the unmolten peridotite matrix. This could provide an effective segregation of Fe-S melt in a planetary mantle down to 2.5 vol.% of residual Fe-S melt. The extremely slow percolation of Fe-S melt in the absence of the partial silicate melting precludes a scenario of metallic core formation via percolation before temperatures allow a substantial partial melting of mantle silicates in planetary bodies.

Last updated: April 16, 2024.