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Philippe Cardin - One of the best experts on this subject based on the ideXlab platform.
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Subcritical Thermal Convection of Liquid Metals in a Rapidly Rotating Sphere.
Physical review letters, 2017Co-Authors: E. J. Kaplan, Nathanaël Schaeffer, Jérémie Vidal, Philippe CardinAbstract:Planetary Cores consist of liquid metals (low Prandtl number Pr) that convect as the Core cools. Here, we study nonlinear convection in a rotating (low Ekman number Ek) Planetary Core using a fully 3D direct numerical simulation. Near the critical thermal forcing (Rayleigh number Ra), convection onsets as thermal Rossby waves, but as Ra increases, this state is superseded by one dominated by advection. At moderate rotation, these states (here called the weak branch and strong branch, respectively) are smoothly connected. As the Planetary Core rotates faster, the smooth transition is replaced by hysteresis cycles and subcriticality until the weak branch disappears entirely and the strong branch onsets in a turbulent state at Ek
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Subcritical Thermal Convection of Liquid Metals in a Rapidly Rotating Sphere
Physical Review Letters, 2017Co-Authors: E. j. Kaplan, Nathanaël Schaeffer, Jérémie Vidal, Philippe CardinAbstract:Planetary Cores consist of liquid metals (low Prandtl number $Pr$) that convect as the Core cools. Here we study nonlinear convection in a rotating (low Ekman number $Ek$) Planetary Core using a fully 3D direct numerical simulation. Near the critical thermal forcing (Rayleigh number $Ra$), convection onsets as thermal Rossby waves, but as the $Ra$ increases, this state is superceded by one dominated by advection. At moderate rotation, these states (here called the weak branch and strong branch, respectively) are smoothly connected. As the Planetary Core rotates faster, the smooth transition is replaced by hysteresis cycles and subcriticality until the weak branch disappears entirely and the strong branch onsets in a turbulent state at $Ek < 10^{-6}$. Here the strong branch persists even as the thermal forcing drops well below the linear onset of convection ($Ra=0.7Ra_{crit}$ in this study). We highlight the importance of the Reynolds stress, which is required for convection to subsist below the linear onset. In addition, the P\'eclet number is consistently above 10 in the strong branch. We further note the presence of a strong zonal flow that is nonetheless unimportant to the convective state. Our study suggests that, in the asymptotic regime of rapid rotation relevant for Planetary interiors, thermal convection of liquid metals in a sphere onsets through a subcritical bifurcation.
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Subcritical thermal convection of liquid metals in a rotating sphere
arXiv: Geophysics, 2017Co-Authors: E. J. Kaplan, Nathanaël Schaeffer, Jérémie Vidal, Philippe CardinAbstract:Planetary Cores consist of liquid metals (low Prandtl number $Pr$) that convect as the Core cools. The convecting, conductive medium can self-excite and maintain a Planetary magnetic field. Here we study nonlinear convection in a rotating (low, Ekman number $Ek$) Planetary Core using a fully 3D direct numerical simulation. Near the critical thermal forcing (Rayleigh number $Ra$), convection onsets as thermal Rossby waves, but as the $Ra$ increases, this state is superceded by one dominated by advection. At moderate rotation, these states (here called the weak branch and strong branch, respectively) are smoothly connected. As the Planetary Core rotates faster, the smooth transition is replaced by hysteresis cycles and subcriticality until the weak branch disappears entirely and the strong branch onsets in a turbulent state at $Ek < 10^{-6}$. Here the strong branch persists even as the thermal forcing drops well below the linear onset of convection ($Ra=0.7Ra_{crit}$ in this study). We highlight the importance of the P\'eclet number, which is consistently above 10 in the strong branch. We further note the presence of a strong zonal flow that is nonetheless unimportant to the convective state. Our findings suggest that the thermal convection in Planetary Cores may shut down very suddenly, leading to the death of convective motions.
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Quasi-geostrophic kinematic dynamos at low magnetic Prandtl number
2004Co-Authors: Nathanaël Schaeffer, Philippe CardinAbstract:Rapidly rotating spherical kinematic dynamos are computed using the combination of a quasi geostrophic (QG) model for the velocity field and a classical spectral 3D code for the magnetic field. On one hand, the QG flow is computed in the equatorial plane of a sphere and corresponds to Rossby wave instabilities of a geostrophic internal shear layer produced by differential rotation. On the other hand, the induction equation is computed in the full sphere after a continuation of the QG flow along the rotation axis. Differential rotation and Rossby-wave propagation are the key ingredients of the dynamo process which can be interpreted in terms of $\alpha\Omega$ dynamo. Taking into account the quasi geostrophy of the velocity field to increase its time and space resolution enables us to exhibit numerical dynamos with very low Ekman (rapidly rotating) and Prandtl numbers (liquid metals) which are asymptotically relevant to model Planetary Core dynamos.
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Turbulent viscosity measurements relevant to Planetary Core-mantle dynamics
Physics of the Earth and Planetary Interiors, 2004Co-Authors: Daniel Brito, Jonathan M. Aurnou, Philippe CardinAbstract:Abstract Laboratory experiments that combine thermal convection in a rapidly rotating shell with a sudden increase of the shell’s rotation rate (spin-up) enable us to study processes related to turbulent viscous coupling between Planetary fluid Cores and solid mantles. We experimentally measure the large-scale effective viscosity by determining how the synchronisation time between the fluid and the shell (called the spin-up time) is shortened when convective turbulence exists in the bulk of the fluid. Our experiments suggest that viscous Core-mantle coupling in planets may be greater than has been previously estimated using molecular viscosity values.
Hagai B Perets - One of the best experts on this subject based on the ideXlab platform.
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tidal disruption of Planetary bodies by white dwarfs ii debris disc structure and ejected interstellar asteroids
Monthly Notices of the Royal Astronomical Society, 2020Co-Authors: Uri Malamud, Hagai B PeretsAbstract:We make use of a new hybrid method to simulate the long-term, multiple-orbit disc formation through tidal disruptions of rocky bodies by white dwarfs, at high-resolution and realistic semimajor axis. We perform the largest yet suite of simulations for dwarf and terrestrial planets, spanning four orders of magnitude in mass, various pericentre distances, and semimajor axes between 3 and 150 au. This large phase space of tidal disruption conditions has not been accessible through the use of previous codes. We analyse the statistical and structural properties of the emerging debris discs, as well as the ejected unbound debris contributing to the population of interstellar asteroids. Unlike previous tidal disruption studies of small asteroids which form ring-like structures on the original orbit, we find that the tidal disruption of larger bodies usually forms dispersed structures of interlaced elliptic eccentric annuli on tighter orbits. We characterize the (typically power law) size distribution of the ejected interstellar bodies as well as their composition, rotation velocities, and ejection velocities. We find them to be sensitive to the depth (impact parameter) of the tidal disruption. Finally, we briefly discuss possible implications of our results in explaining the peculiar variability of Tabby’s star, the origin of the transit events of ZTF J0139+5245 and the formation of a Planetary Core around SDSS J1228+1040.
L Hennet - One of the best experts on this subject based on the ideXlab platform.
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The formation of nuggets of highly siderophile elements in quenched silicate melts at high temperatures: Before or during the silicate quench?
Earth and Planetary Science Letters, 2015Co-Authors: Valerie Malavergne, E Charon, J Jones, P Cordier, K Righter, D Deldicque, L HennetAbstract:The Highly Siderophile Elements (HSE) are powerful tracers of Planetary differentiation. Despite the importance of their partitioning between silicate and metal for the understanding of Planetary Core formation, especially for the Earth and Mars, there is still a huge discrepancy between conclusions based on different high temperature (HT) experimental studies. These disagreements may be due to the presence of HSE micro and nanonuggets in HT experiments. The formation of these nuggets is still interpreted in different ways. One hypothesis is that these HSE nuggets formed during the quench of the silicate melt, while another hypothesis supposes that these nuggets formed before the quench and represented artefacts of HT experiments. The goal of this work is to clarify whether the presence of HSE nuggets in silicate melts is linked to a quench effect or not. Understanding the formation of these HSE nuggets represents thus a necessary step towards the resolution of the Earth's Core formation scenarios. We performed new HT experiments (1275–2000 • C) at different oxygen fugacities (fO 2), between ambient air up to ∼5 log units below the Iron-Wüstite buffer [IW-5], for two different silicate compositions (synthetic martian and terrestrial basalts) mixed with a metallic mixture of Pt–Au– Pd–Ru. Our 1275–1600 • C experiments were contained in either olivine, diopside or graphite crucible; experiments at 2000 • C were performed using a levitation method, so no capsule was necessary. Our samples contained quenched silicate melts, minerals (olivine, pyroxene, spinel depending on the run), a two-phase metallic bead and nano and micro-nuggets of HSE. Our samples underwent fine textural, structural and analytical characterizations. The distribution of the nuggets was not homogeneous throughout the quenched silicate melt. HSE nuggets were present within crystals. Dendritic textures from the quenched silicate melt formed around HSE nuggets, which could be crystallized, showing that the nuggets acted as nucleation sites during the quench. Thus they predated the quench. Finally, these nuggets also had strong heterogeneities suggesting at least a two-stage formation process under reducing conditions. Consequently, our observations clearly show that these HSE nuggets formed before the quench in the silicate melt. Our results agreed with previous studies, which concluded that HSE abundances in the Earth's mantle require the late accretion of chondritic material subsequent to Core formation. However, the effects of metallic Si, O, H, or the effect of pressure on the HSE partitioning are still not fully understood. Further work to constrain these effects is to be encouraged to understand the Earth's Core formation.
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The formation of nuggets of highly siderophile elements in quenched silicate melts at high temperatures: Before or during the silicate quench?
Earth and Planetary Science Letters, 2015Co-Authors: Valerie Malavergne, E Charon, J Jones, P Cordier, K Righter, D Deldicque, L HennetAbstract:The Highly Siderophile Elements (HSE) are powerful tracers of Planetary differentiation. Despite the importance of their partitioning between silicate and metal for the understanding of Planetary Core formation, especially for the Earth and Mars, there is still a huge discrepancy between conclusions based on different high temperature (HT) experimental studies. These disagreements may be due to the presence of HSE micro and nanonuggets in HT experiments. The formation of these nuggets is still interpreted in different ways. One hypothesis is that these HSE nuggets formed during the quench of the silicate melt, while another hypothesis supposes that these nuggets formed before the quench and represented artefacts of HT experiments. The goal of this work is to clarify whether the presence of HSE nuggets in silicate melts is linked to a quench effect or not. Understanding the formation of these HSE nuggets represents thus a necessary step towards the resolution of the Earth's Core formation scenarios. We performed new HT experiments (1275–2000 • C) at different oxygen fugacities (fO 2), between ambient air up to ∼5 log units below the Iron-Wüstite buffer [IW-5], for two different silicate compositions (synthetic martian and terrestrial basalts) mixed with a metallic mixture of Pt–Au– Pd–Ru. Our 1275–1600 • C experiments were contained in either olivine, diopside or graphite crucible; experiments at 2000 • C were performed using a levitation method, so no capsule was necessary. Our samples contained quenched silicate melts, minerals (olivine, pyroxene, spinel depending on the run), a two-phase metallic bead and nano and micro-nuggets of HSE. Our samples underwent fine textural, structural and analytical characterizations. The distribution of the nuggets was not homogeneous throughout the quenched silicate melt. HSE nuggets were present within crystals. Dendritic textures from the quenched silicate melt formed around HSE nuggets, which could be crystallized, showing that the nuggets acted as nucleation sites during the quench. Thus they predated the quench. Finally, these nuggets also had strong heterogeneities suggesting at least a two-stage formation process under reducing conditions. Consequently, our observations clearly show that these HSE nuggets formed before the quench in the silicate melt. Our results agreed with previous studies, which concluded that HSE abundances in the Earth's mantle require the late accretion of chondritic material subsequent to Core formation. However, the effects of metallic Si, O, H, or the effect of pressure on the HSE partitioning are still not fully understood. Further work to constrain these effects is to be encouraged to understand the Earth's Core formation.
Michael Le Bars - One of the best experts on this subject based on the ideXlab platform.
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Experiments on fragmentation and thermo-chemical exchanges during Planetary Core formation
Physics of the Earth and Planetary Interiors, 2018Co-Authors: Jean-baptiste Wacheul, Michael Le BarsAbstract:The initial thermo-chemical state of telluric planets was largely controlled by mixing following the collision of differentiated proto-planets. Up to now, most models of planet formation simply assume that the iron Core of the impactors immediately broke up to form an "iron rain" within a large-scale magma ocean, leading to the rapid equilibration of the whole metal with the whole mantle. Only recent studies have focused on resolving the fluid mechanics of the problem, with the aim to define more relevant diffusion-advection models of thermal and chemical exchanges within and between the two fluids. Furthermore, the influence of the viscosity ratio on this dynamical process is generally neglected, whilst it is known to play a role in the breakup of the initial iron diapirs and in the shape of the resulting droplets. Here we report the results of analog laboratory experiments matching the dynamical regime of the geophysical configuration. High speed video recording allows us to describe and characterize the fluid dynamics of the system, and temperature measurements allow us to quantify the diffusive exchanges integrated during the fall of the liquid metal. We find that the early representation of this flow as an iron rain is far from the experimental results. The equilibration coefficient at a given depth depends both on the initial size of the metal diapir Preprint submitted to Physics of the Earth and Planetary Interiors May 26, 2017 and on the viscosity of the ambient fluid, whereas the falling speed is only controlled by the initial size. Various scalings for the diffusive exchanges coming from the literature are tested. We find good agreement with the turbulent thermal model developed by Deguen et al. (2014).
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Experiments on fragmentation and thermo-chemical exchanges during Planetary Core formation
Physics of the Earth and Planetary Interiors, 2018Co-Authors: Jean-baptiste Wacheul, Michael Le BarsAbstract:Abstract The initial thermo-chemical state of telluric planets was largely controlled by mixing following the collision of differentiated proto-planets. Up to now, most models of planet formation simply assume that the iron Core of the impactors immediately broke up to form an “iron rain” within a large-scale magma ocean, leading to the rapid equilibration of the whole metal with the whole mantle. Only recent studies have focused on resolving the fluid mechanics of the problem, with the aim to define more relevant diffusion–advection models of thermal and chemical exchanges within and between the two fluids. Furthermore, the influence of the viscosity ratio on this dynamical process is generally neglected, whilst it is known to play a role in the breakup of the initial iron diapirs and in the shape of the resulting droplets. Here we report the results of analog laboratory experiments matching the dynamical regime of the geophysical configuration. High speed video recording allows us to describe and characterize the fluid dynamics of the system, and temperature measurements allow us to quantify the diffusive exchanges integrated during the fall of the liquid metal. We find that the early representation of this flow as an iron rain is far from the experimental results. The equilibration coefficient at a given depth depends both on the initial size of the metal diapir and on the viscosity of the ambient fluid, whereas the falling speed is only controlled by the initial size. Various scalings for the diffusive exchanges coming from the literature are tested. We find good agreement with the turbulent thermal model developed by Deguen et al. (2014).
Valerie Malavergne - One of the best experts on this subject based on the ideXlab platform.
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experimental constraints on the fate of h and c during Planetary Core mantle differentiation implications for the earth
Icarus, 2019Co-Authors: Valerie Malavergne, Helene Bureau, Caroline Raepsaet, Fabrice Gaillard, Melissa Poncet, Suzy Surble, David Sifre, Svyatoslav Shcheka, Chloe Fourdrin, Damien DeldicqueAbstract:Hydrogen (H) and carbon (C) have probably been delivered to the Earth mainly during accretion processes at High Temperature (HT) and High Pressure (HP) and at variable redox conditions. We performed HP (1 – 15 GPa) and HT (1600 – 2300°C) experiments, combined with state-of-the-art analytical techniques to better understand the behavior of H and C during Planetary differentiation processes. We show that increasing pressure makes H slightly siderophile and slightly decreases the highly siderophile nature of C. This implies that the capacity of a growing Core to retain significant amounts of H or C is mainly controlled by the size of the planet: small Planetary bodies may retain C in their Cores while H may have rather been lost in space; larger bodies may store both H and C in their Cores. During the Earth's differentiation, both C and H might be sequestrated in the Core. However, the H content of the Core would remain one or two orders of magnitude lower than that of C since the (H/C)Core ratio might range between 0.04 and 0.27.
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The formation of nuggets of highly siderophile elements in quenched silicate melts at high temperatures: Before or during the silicate quench?
Earth and Planetary Science Letters, 2015Co-Authors: Valerie Malavergne, E Charon, J Jones, P Cordier, K Righter, D Deldicque, L HennetAbstract:The Highly Siderophile Elements (HSE) are powerful tracers of Planetary differentiation. Despite the importance of their partitioning between silicate and metal for the understanding of Planetary Core formation, especially for the Earth and Mars, there is still a huge discrepancy between conclusions based on different high temperature (HT) experimental studies. These disagreements may be due to the presence of HSE micro and nanonuggets in HT experiments. The formation of these nuggets is still interpreted in different ways. One hypothesis is that these HSE nuggets formed during the quench of the silicate melt, while another hypothesis supposes that these nuggets formed before the quench and represented artefacts of HT experiments. The goal of this work is to clarify whether the presence of HSE nuggets in silicate melts is linked to a quench effect or not. Understanding the formation of these HSE nuggets represents thus a necessary step towards the resolution of the Earth's Core formation scenarios. We performed new HT experiments (1275–2000 • C) at different oxygen fugacities (fO 2), between ambient air up to ∼5 log units below the Iron-Wüstite buffer [IW-5], for two different silicate compositions (synthetic martian and terrestrial basalts) mixed with a metallic mixture of Pt–Au– Pd–Ru. Our 1275–1600 • C experiments were contained in either olivine, diopside or graphite crucible; experiments at 2000 • C were performed using a levitation method, so no capsule was necessary. Our samples contained quenched silicate melts, minerals (olivine, pyroxene, spinel depending on the run), a two-phase metallic bead and nano and micro-nuggets of HSE. Our samples underwent fine textural, structural and analytical characterizations. The distribution of the nuggets was not homogeneous throughout the quenched silicate melt. HSE nuggets were present within crystals. Dendritic textures from the quenched silicate melt formed around HSE nuggets, which could be crystallized, showing that the nuggets acted as nucleation sites during the quench. Thus they predated the quench. Finally, these nuggets also had strong heterogeneities suggesting at least a two-stage formation process under reducing conditions. Consequently, our observations clearly show that these HSE nuggets formed before the quench in the silicate melt. Our results agreed with previous studies, which concluded that HSE abundances in the Earth's mantle require the late accretion of chondritic material subsequent to Core formation. However, the effects of metallic Si, O, H, or the effect of pressure on the HSE partitioning are still not fully understood. Further work to constrain these effects is to be encouraged to understand the Earth's Core formation.
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The formation of nuggets of highly siderophile elements in quenched silicate melts at high temperatures: Before or during the silicate quench?
Earth and Planetary Science Letters, 2015Co-Authors: Valerie Malavergne, E Charon, J Jones, P Cordier, K Righter, D Deldicque, L HennetAbstract:The Highly Siderophile Elements (HSE) are powerful tracers of Planetary differentiation. Despite the importance of their partitioning between silicate and metal for the understanding of Planetary Core formation, especially for the Earth and Mars, there is still a huge discrepancy between conclusions based on different high temperature (HT) experimental studies. These disagreements may be due to the presence of HSE micro and nanonuggets in HT experiments. The formation of these nuggets is still interpreted in different ways. One hypothesis is that these HSE nuggets formed during the quench of the silicate melt, while another hypothesis supposes that these nuggets formed before the quench and represented artefacts of HT experiments. The goal of this work is to clarify whether the presence of HSE nuggets in silicate melts is linked to a quench effect or not. Understanding the formation of these HSE nuggets represents thus a necessary step towards the resolution of the Earth's Core formation scenarios. We performed new HT experiments (1275–2000 • C) at different oxygen fugacities (fO 2), between ambient air up to ∼5 log units below the Iron-Wüstite buffer [IW-5], for two different silicate compositions (synthetic martian and terrestrial basalts) mixed with a metallic mixture of Pt–Au– Pd–Ru. Our 1275–1600 • C experiments were contained in either olivine, diopside or graphite crucible; experiments at 2000 • C were performed using a levitation method, so no capsule was necessary. Our samples contained quenched silicate melts, minerals (olivine, pyroxene, spinel depending on the run), a two-phase metallic bead and nano and micro-nuggets of HSE. Our samples underwent fine textural, structural and analytical characterizations. The distribution of the nuggets was not homogeneous throughout the quenched silicate melt. HSE nuggets were present within crystals. Dendritic textures from the quenched silicate melt formed around HSE nuggets, which could be crystallized, showing that the nuggets acted as nucleation sites during the quench. Thus they predated the quench. Finally, these nuggets also had strong heterogeneities suggesting at least a two-stage formation process under reducing conditions. Consequently, our observations clearly show that these HSE nuggets formed before the quench in the silicate melt. Our results agreed with previous studies, which concluded that HSE abundances in the Earth's mantle require the late accretion of chondritic material subsequent to Core formation. However, the effects of metallic Si, O, H, or the effect of pressure on the HSE partitioning are still not fully understood. Further work to constrain these effects is to be encouraged to understand the Earth's Core formation.
