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