Entstehung des Erdkerns: Laborexperimente und numerische Modelle zum Perkolationsmechanismus und zum Rayleigh-Taylor Diapirismus

Die vorliegende Arbeit behandelt das Forschungsthema der Entstehung des flüssigen Eisenkerns im Zentrum unseres Planeten. Dieses bislang wenig verstandene Gebiet ist reich an Fragestellungen, sowohl für Experimentatoren als auch für die Geodynamik. Es gibt sehr viele Arbeiten, die den Bildungsprozess experimentell untersuchen, jedoch wurde in den letzten Jahren die numerische Untersuchung in diesem Gebiet kaum vorangetrieben. Der experimentelle Teil der Arbeit stellt sich hierbei der aktuellen Frage nach der Perkolationsschwelle 1 von Eisenschmelze in der Silikatmatrix der Protoerde, während numerisch die Effekte von Potenzgesetzkriechen, Dissipation und Schmelzsegregation beim Absinken eines Eisendiapirs nach Ausbildung eines ersten flachen Magmaozeans in der Protoerde behandelt werden. Die genauen Fragestellungen könnnen dabei im letzten Abschnitt der Einleitung gefunden werden.The diploma thesis 'Formation of Earth's core: Laboratory experiments and numerical models for the percolation mechanism and the Rayleigh-Taylor instability' includes some laboratory experiments and numerical modelling which implement the percolation and Rayleigh-Taylor instability mechanisms. The laboratory experiments have been performed on a fertile peridotite with the addition of iron sulfide by the use of a centrifuge furnace in order to model a percolation flow. In some experiments in-situ performed electrical conductivity measurements have been done in order to access a connectivity of iron sulfide melts. The numerical experiments have been done with the use of a two-dimensional finite difference method applied to the sinking of iron diapirs through a silicate matrix in the case of the temperature and stress-dependent rheology. Peridotite samples containing different amounts of iron sulfide (5-15 vol%) were prepared from powders of the fertile peridotite and chemicals of Fe-FeS of the eutectic composition. They were placed in the centrifuge piston cylinder at the ETH Zürich to determine a percolation velocity of Fe-FeS through the peroditite matrix. It was found that the segregation velocity of Fe-FeS is far too slow in a partially molten silicate matrix to be accounted for the core formation alone. Additionally, the electrical conductivities of samples consisting of fertile peridotite and Fe-FeS were measured in-situ in order to revise the experimental results of Yoshino et al. (2003, 2004). These papers describe an interconnection threshold in a solid silicate matrix at about 5 vol% of iron sulfide. In the present work it was shown that more than 15 vol% Fe-FeS are needed to reach an interconnectivity of Fe-FeS in a peridotite matrix. In the numerical modelling the computer code FDCON was modified and extended to resolve more realistic cases for the evolution of the Rayleigh-Taylor instability at the top of a cold, undifferentiated and less dense protocore. This unstable gravitational configuration was used as a starting point in numerical models. Differing rheologic laws (temperatureindependent, temperature-dependent and power law) were used to explore the parameter space consisting of initial temperature and viscosity of the protocore and the non-dimensional temperature scaling factor of viscosity b to find a realistic scenario in an agreement with the Hf/W isotopic ages of the core in which the core formation is prescribed to be largely completed within the first 33 Ma (Kleine et al., 2002). It was found that only for b <= 10 the iron diapir is able to penetrate fast enough through the protocore and to fullfill the isotopic restrictions. The required central protocore temperature is in an good agreement with the numerical models performed by Merk et al. (2002), which included the heating during the accretion stage and heating due to the radioactive decay of a short-lived isotope 26Al. In a less advanced model without the application of a power law, it is shown that the dissipation plays only a second order role on the sinking depth of a diapir. Numerical experiments including the power law rheology may be useful in order to revise this result for a more realistic case. Finally, it was shown that the introducing of the melt effect in the calculation scheme is relevant to the core formation models due to the intensive development of stress-induced melt channelling in localities surrounding the incipient iron diapir. For simplicity an isothermal model with a temperature independent viscosity of a solid phase and with a rheology depending on a melt-fraction in the partially molten region surrounding a diapir was used. As a result of this model, the intensive development of iron-rich melt channels within a region approximately 2-3 times larger than a diapir size has been observed for sufficiently small melt retention numbers, i.e. the ratio of a Stokes sinking to a Darcy flow velocity. This mechanism enhanced the melt accumulation and accelerated the process of the core formation. The introduction of more realistic temperature profiles, the use of a power-law rheology and a stress-dependent porosity are possible in future numerical models which could lead to a better understanding of the core formation mechanism

Modification of icy planetesimals by early thermal evolution and collisions: Constraints for formation time and initial size of comets and small KBOs

Comets and small Kuiper belt objects are considered to be among the most primitive objects in the solar system as comets like C/1995 O1 Hale-Bopp are rich in highly volatile ices like CO. It has been suggested that early in the solar system evolution the precursors of both groups, the so-called icy planetesimals, were modified by both short-lived radiogenic heating and collisional heating. Here we employ 2D finite-difference numerical models to study the internal thermal evolution of these objects, where we vary formation time, radius and rock-to-ice mass fraction. Additionally we perform 3D SPH collision models with different impact parameters, thus considering both cratering and catastrophic disruption events. Combining the results of both numerical 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

The effects of short-lived radionuclides and porosity on the early 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), such as aluminum-26 and iron-60, 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. Using the code family I2ELVIS/I3ELVIS we have run numerous 2D and 3D numerical finite-difference fluid dynamic models with varying planetesimal radius, formation time and initial porosity. Our results indicate that powdery materials lowered the threshold for melting and convection in planetesimals, depending on the amount of SLRs present. A subset of planetesimals retained a powdery surface layer which lowered the thermal conductivity and hindered cooling. The effect of initial porosity was small, however, compared to those of planetesimal size and formation time, which dominated the thermo-mechanical evolution and were the primary factors for the onset of melting and differentiation. We comment on the implications of this work concerning the structure and evolution of these planetesimals, as well as their behavior as possible building blocks of terrestrial planets.Comment: 19 pages, 11 figures, 5 tables; accepted for publication in Icarus; for associated video files, see http://timlichtenberg.net/2015_porosity.html or http://dx.doi.org/10.1016/j.icarus.2016.03.00

Ferropericlase Control of Lower Mantle Rheology : Impact of Phase Morphology

Abstract The rheological properties of Earth's lower mantle play a key role for global mantle dynamics. 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. Here, 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. Using this 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. While our findings confirm previous endmember models that suggested a change of mantle viscosity due to the formation of interconnected weak layers, 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 modeling the behavior of subducting slabs. We show that to capture the effect of ferropericlase elongation on the effective viscosity tensor (and its anisotropy) in large‐scale mantle convection models, the analytical approximations that have been derived to describe the evolution of the effective viscosity of a two‐phase medium with aligned elliptical inclusions can be used

Coupling SPH and thermochemical models of planets: Methodology and example of a Mars-sized body

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. Here we present a new approach, combining 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. Our 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.Comment: 29 pages, 10 figures, accepted for publication in Icaru

Impact splash chondrule formation during planetesimal recycling

Chondrules 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, remains elusive. Here, we examine the prospect of forming chondrules from planetesimal collisions. We show that intensely melted bodies with interior magma oceans became rapidly chemically equilibrated and physically differentiated. Therefore, collisional interactions among such bodies would have resulted in chondrule-like but basaltic spherules, which are not observed in the meteoritic record. This inconsistency with the expected dynamical interactions hints at an incomplete understanding of the planetary growth regime during the protoplanetary disk phase. To resolve this conundrum, 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 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 aluminum-26 reservoirs, or collisional destruction mechanisms were efficient enough to shatter planetesimals before they reached the magma ocean phase. Finally, we outline the window in parameter space for which chondrule formation from planetesimal collisions can be reconciled with the meteoritic record and how our results can be used to further constrain early solar system dynamics.Comment: 20 pages, 11 figures, 2 tables; accepted for publication in Icarus; associated blog article at goo.gl/5bDqG

Late metal-silicate separation on the IAB parent asteroid: Constraints from combined W and Pt isotopes and thermal modelling

The short-lived $^{182}$Hf-$^{182}$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. The $\epsilon^{182}$W values obtained for the IAB iron meteorites range from -3.61 $\pm$ 0.10 to -2.73 $\pm$ 0.09. Correlating $\epsilon^{\mathrm{i}}$Pt with $^{182}$W data yields a pre-neutron capture $^{182}$W of -2.90 $\pm$ 0.06. This corresponds to a metal-silicate separation age of 6.0 $\pm$ 0.8 Ma after CAI for the IAB parent body, and is interpreted to represent a body-wide melting event. Later, between 10 and 14 Ma after CAI, an impact led to a catastrophic break-up and subsequent reassembly of the parent body. Thermal models of the interior evolution that are consistent with these 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 $\pm$ 0.1 Ma after CAIs with a radius of greater than 60 km.Comment: 11 pages, 8 figures, 2 tables; open access article under the CC BY-NC-ND license (see http://creativecommons.org/licenses/by-nc-nd/4.0/