The impact of short-lived radionuclides and initial …...The impact of short-lived radionuclides...
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The impact of short-lived radionuclides and initial porosity on the thermomechanical evolution of early-formed planetesimals Tim Lichtenberg a,b , Gregor J. Golabek b,c , Taras V. Gerya b & Michael R. Meyer a a Institute for Astronomy, ETH Zürich, Switzerland b Institute of Geophysics, ETH Zürich, Switzerland c Bayerisches Geoinstitut, University of Bayreuth, Germany [email protected] | timlichtenberg.net The impact of short-lived radionuclides and initial porosity on the thermomechanical evolution of early-formed planetesimals Tim Lichtenberg a,b , Gregor J. Golabek b,c , Taras V. Gerya b & Michael R. Meyer a a Institute for Astronomy, ETH Zürich, Switzerland b Institute of Geophysics, ETH Zürich, Switzerland c Bayerisches Geoinstitut, University of Bayreuth, Germany [email protected] | timlichtenberg.net Introduction The thermal history and internal struc- ture of chondritic planetesimals can have a crucial impact on the formation, evolution, and final composition of terrestrial planets. These critically depend on the internal bal- ance of heating versus cooling, which are mostly determined by the presence of short- lived radionuclides (SLRs), such as 26 Al and 60 Fe, as well as the heat conductivity of the material. The heating by SLRs depends on the for- mation time of the planetesimal and its size. It is often argued that the cooling history via heat conduction is determined by the porosity of the granular material, which un- dergoes dramatic changes via compaction processes. In this study we assess the combined effect of radiogenic heating by SLRs and initial porosity on the thermomechanical evolu- tion of young planetesimals and the impli- cations for terrestrial planet formation via 2D and 3D numerical simulations. Model setup • 2D & 3D finite-difference code family I 2 ELVIS / I 3 ELVIS [1]. • Fluid dynamics conservation equations solved on fully staggered Eulerian grid. • Use extended Boussinesq approximation to account for creeping flows with thermal and chemical buoyancy forces. • Energy equation advanced using La- grangian marker-in-cell technique. • Parameter space: R p = 20 - 200 km, t form = 0.1 - 1.75 Myr, φ init =0.0 - 0.75. • Spherical planetesimals composed of pure silicate layers with dry olivine rheology [5], surrounded by sticky-air [2, 6] with T space = 290 K. • Time-dependent radioactive heating by 26 Al and 60 Fe, 40 K, 235 U, 238 U and 232 Th. 26 Al/ 27 Al =5.85 · 10 -5 [7]. • Box dimensions: 500 2 / 500 3 km (2D/3D) on a 501 2 (2D) / 261 3 (3D) grid. Porosity implementation Based on the study by [3] we incorporate the porosity via changes to the material density ρ Si-por (c,P,T,φ)= ρ Si-sol (c, P, T ) · (1 - φ), and the effective thermal conductivity [4] k eff ,por = k 1 = k · e -φ/φ 0 : φ< 0.2, k 3 =(k 4 1 + k 4 2 ) 1/4 :0.2 ≤ φ ≤ 0.4, k 2 = k · e a-φ/φ 1 : φ> 0.4. The initial porous state decreases via cold isostatic pressing [4] φ(P )=0.42 + 0.46 · P P 0 ! 1.72 +1 -1 . The material compaction is sensitive to creep processes in the heated material lat- tice by sintering effects via ∂φ ∂t = A(1 - φ) σ 3/2 < 3 · exp " -E 0 a RT # . With experientally determined parameters: a =1.2, φ 0 =0.08, φ 1 =0.167, P 0 =0.13 bar, A =4 · 10 -5 , E 0 a = 85 kcal mol -1 [4]. 2D composition model grid 3D analogues Fig. 2: Density isocontours with corresponding temperatures in a 3D mixing model. Comparison of model types Solid Melt Deformation Mixing Fig. 3: Composition (top ) and density (bottom) for different model types of Figure 1. Composition codes: 5/6 - solid silicates, 25/26 - molten silicates. Thermal evolution Fig. 5: Evolution of peak temperature for radius (left ) and formation time (right ) isolines. The dashed lines show the solidus and liquidus temperatures. Porous shells and inclusions Fig. 6: Retained porous shell (left ) and porous inclusions (right ), which isolate the planetesimal interior. Conclusions • Porosity lowers threshold for melt- ing and convective processes. • Porosity effects negligible com- pared to those of planetesimal size and formation time. • Subset of models retains porous shells (Fig. 6) or porosity inclu- sions, both lower thermal conduc- tivity and decrease cooling. • Models show non-axisymmetric geometries, which are inaccessi- ble with 1D calculations. • Internal structures and porous lay- ers potentially important for later impacts during collisional growth. References [1] T. V. Gerya and D. A. Yuen. Phys. Earth Planet. Inter., 163:83–105, 2007. [2] A. Ghosh and H. Y. McSween. Icarus, 134:187–206, 1998. [3] G. J. Golabek et. al. Meteorit. Planet. Sci, 49, 1083–1099, 2014. [4] S. Henke et. al. A&A, 537:A45, January 2012. [5] G. Ranalli. Rheology of the earth, 413 pp, 1995. [6] H. Schmeling et. al. Phys. Earth Planet. Inter., 171(1):198–223, 2008. [7] K. Thrane et. al. ApJL, 646(2):L159, 2006. Videos and more!
Transcript of The impact of short-lived radionuclides and initial …...The impact of short-lived radionuclides...
The impact of short-lived radionuclides and initial porosity on thethermomechanical evolution of early-formed planetesimals
Tim Lichtenberga,b, Gregor J. Golabekb,c, Taras V. Geryab & Michael R. Meyera
a Institute for Astronomy, ETH Zürich, Switzerland b Institute of Geophysics, ETH Zürich, Switzerlandc Bayerisches Geoinstitut, University of Bayreuth, Germany
[email protected] | timlichtenberg.net
The impact of short-lived radionuclides and initial porosity on thethermomechanical evolution of early-formed planetesimals
Tim Lichtenberga,b, Gregor J. Golabekb,c, Taras V. Geryab & Michael R. Meyera
a Institute for Astronomy, ETH Zürich, Switzerland b Institute of Geophysics, ETH Zürich, Switzerlandc Bayerisches Geoinstitut, University of Bayreuth, Germany
[email protected] | timlichtenberg.net
Introduction
The thermal history and internal struc-ture of chondritic planetesimals can havea crucial impact on the formation, evolution,and final composition of terrestrial planets.These critically depend on the internal bal-ance of heating versus cooling, which aremostly determined by the presence of short-lived radionuclides (SLRs), such as 26Aland 60Fe, as well as the heat conductivity ofthe material.The heating by SLRs depends on the for-mation time of the planetesimal and its size.It is often argued that the cooling historyvia heat conduction is determined by theporosity of the granular material, which un-dergoes dramatic changes via compactionprocesses.In this study we assess the combined effectof radiogenic heating by SLRs and initialporosity on the thermomechanical evolu-tion of young planetesimals and the impli-cations for terrestrial planet formation via 2Dand 3D numerical simulations.
Model setup
• 2D & 3D finite-difference code familyI2ELVIS/I3ELVIS [1].•Fluid dynamics conservation equations
solved on fully staggered Eulerian grid.•Use extended Boussinesq approximation
to account for creeping flows with thermaland chemical buoyancy forces.•Energy equation advanced using La-
grangian marker-in-cell technique.•Parameter space: Rp = 20− 200 km, tform =
0.1− 1.75 Myr, φinit = 0.0− 0.75.•Spherical planetesimals composed of pure
silicate layers with dry olivine rheology [5],surrounded by sticky-air [2, 6] with Tspace =290 K.•Time-dependent radioactive heating by
26Al and 60Fe, 40K, 235U, 238U and 232Th.26Al/27Al = 5.85 · 10−5 [7].•Box dimensions: 5002 / 5003 km (2D/3D) on
a 5012 (2D) / 2613 (3D) grid.
Porosity implementation
Based on the study by [3] we incorporate theporosity via changes to the material density
ρSi−por(c, P, T, φ) = ρSi−sol(c, P, T ) · (1− φ),
and the effective thermal conductivity [4]
keff,por =
k1 = k · e−φ/φ0 : φ < 0.2,
k3 = (k41 + k4
2)1/4 : 0.2 ≤ φ ≤ 0.4,
k2 = k · ea−φ/φ1 : φ > 0.4.
The initial porous state decreases via coldisostatic pressing [4]
φ(P ) = 0.42 + 0.46 ·
(PP0
)1.72
+ 1
−1
.
The material compaction is sensitive tocreep processes in the heated material lat-tice by sintering effects via∣∣∣∣∣∂φ∂t
∣∣∣∣∣ = A(1− φ)σ3/2
<3· exp
[−E ′aRT
].
With experientally determined parameters: a = 1.2, φ0 = 0.08, φ1 = 0.167, P0 = 0.13 bar,
A = 4 · 10−5, E ′a = 85 kcal mol−1 [4].
2D composition model grid 3D analogues
Fig. 2: Density isocontours with corresponding temperatures in a 3D mixing model.
Comparison of model types
Solid Melt Deformation Mixing
Fig. 3: Composition (top) and density (bottom) for different model types of Figure 1. Composition codes: 5/6 - solid silicates, 25/26 - molten silicates.
Thermal evolution
Fig. 5: Evolution of peak temperature for radius (left) and formation time (right) isolines. The dashed lines
show the solidus and liquidus temperatures.
Porous shells and inclusions
Fig. 6: Retained porous shell (left) and porous inclusions (right), which isolate the planetesimal interior.
Conclusions
•Porosity lowers threshold for melt-ing and convective processes.•Porosity effects negligible com-
pared to those of planetesimal sizeand formation time.•Subset of models retains porous
shells (Fig. 6) or porosity inclu-sions, both lower thermal conduc-tivity and decrease cooling.•Models show non-axisymmetric
geometries, which are inaccessi-ble with 1D calculations.• Internal structures and porous lay-
ers potentially important for laterimpacts during collisional growth.
References
[1] T. V. Gerya and D. A. Yuen. Phys. Earth Planet. Inter., 163:83–105, 2007.
[2] A. Ghosh and H. Y. McSween. Icarus, 134:187–206, 1998.
[3] G. J. Golabek et. al. Meteorit. Planet. Sci, 49, 1083–1099, 2014.
[4] S. Henke et. al. A&A, 537:A45, January 2012.
[5] G. Ranalli. Rheology of the earth, 413 pp, 1995.
[6] H. Schmeling et. al. Phys. Earth Planet. Inter., 171(1):198–223, 2008.
[7] K. Thrane et. al. ApJL, 646(2):L159, 2006.
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