LPSC 2014 James#H.#Roberts1 and$Jafar$Arkani+Hamed … · mantle TBL; implicit Euler / tridiagonal...
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C 3. CoreMantle Coupling Mantle Core • Core and mantle initially adiabatic, with thermal boundary layers (TBL) at the surface and CMB (Figure 2, black curve). • Impact raises temperature in mantle and core (Figure 2, red and blue curves). Larger ΔT in outer core than in mantle because the core has lower specific heat and is already molten. • Core stratifies [4] and becomes stable to convection, T varies only with radius. • Mantle convection: Citcom (axisymmetric) [16]; extended Boussinesq approximation [17]; free- slip, temperature boundary conditions; T- and P-dependent viscosity; mixed-mode heating. • Core cooling: 1D parameterized model. Solve the 1D enthalpy equation in core and lower mantle TBL; implicit Euler / tridiagonal matrix algorithm. The process : • At time t, obtain mantle temperature, timestep Δt • Integrate 1D enthalpy equation in core and TBL over Δt, using smaller core timestep, δt • Update T at CMB and in TBL. • Resume mantle convection; Advance to time t+Δt • Iterate until the entire core is adiabatic and convecting Figure 2: Temperature along the impact axis before (black curve) and after (red and blue curves) impact heating. The red curve assuming all the impact heat goes into temperature increase. The blue curve shows the temperature reduced to the solidus wherever melting occurs. C A giant impact on Mars can halt dynamo activity for ~100 My. The core does not become fully convective for ~1Gy. 1. Introduc6on Impact cratering is a fundamental process that modifies planetary surfaces, and is ubiquitous throughout the Solar System. Most bodies have a basin whose diameter approaches the body’s radius. On Mars, over twenty exposed and buried impact basins with diameters over 1000 km have been identified with crater ages in the mid-Noachian, (e.g. [1]). The magnetization strength of the basins correlate with age [2], suggesting that the global magnetic field vanished toward the end of the sequence of basin formation. The impacts may have modified the thermal structure and geodynamics of the interior, and crippled an ancient core dynamo [3-6]. Here, we investigate the coupled thermal evolution of the core and mantle of Mars in response to heating by a giant impact. Heating from the largest impactors can penetrate to the core. Because core cooling is regulated by the vigor of mantle convection, and mantle convection is driven by core heat loss, it is desirable to have a self-consistent model of heat transfer between the core and mantle. The chief difficulty is that the material properties and relevant timescales in each layer are quite different, making a full coupling computationally expensive. We note that the core temperature stratifies after impact heating, largely erasing lateral variations [5]. We exploit this and use a 1-D parameterization of core cooling in conjunction with a finite-element mantle convection model. James H. Roberts 1 and Jafar ArkaniHamed 2 1 Johns Hopkins University Applied Physics Laboratory ([email protected]), 2 Department of Physics, University of Toronto 5. Conclusions 1. A giant basin-forming impact results in stable stratification of the core, insulating the inner core and halting core convection. 2. The shock heating from such an impact increases the short-term vigor of convection in the mantle, forms a hemispheric upwelling beneath the impact site. The hot core creates a low-viscosity channel at the base of the mantle, which funnels the heat from the core into the hemispheric upwelling, allowing the mantle to return to a pre-impact state relatively quickly (tens of My). 3. Dynamo activity may resume after ~100 My. An initially subcritical or weakly supercritical dynamo may not recover. The core does not become fully convective for several hundred My. 2. Shock Hea6ng Figure 1: Temperature perturbation (before taking melting into account) in the core and mantle of Mars resulting from the vertical impact of a rocky projectile 1000 km in diameter at 10 km/s. Plot assumes all waste heat is converted to a temperature increase; in reality latent heat of melting will consume a portion of the mantle heating, moderating the maximum temperature increase. • Collision creates a shock wave that propagates through the body [7-9]. • Passage of shock generates waste heat [10-12] which we compute using the “foundering shock” heating model [13]. • An example of the impact heat distribution is shown in Figure 1. • The energy will actually be partitioned between temperature increase ΔT and melt production (once the solidus is reached) [14]. This is equivalent to instantaneously removing melt to the surface, and ignoring compositional variations between melt residuum and unmelted mantle [15]. References: [1] Frey, H. V. (2008), GRL, 35, L13203. [2] Lillis, R. J., et al. (2008), GRL, 35, L14203. [3] Kuang, W., et al. (2008), GRL 35, L14204. [4] Roberts et al. (2009), JGR, 111, E6013. [5] Arkani-Hamed, J. and Olson, P. (2010), JGR, 115, E07012. [6] Arkani-Hamed, J. (2012), PEPI 196-197, 83-96. [7] O'Keefe, J. D. and Ahrens, T. J. (1977), LPSC, 8, 3357-3374. [8] Melosh, H. J. (1989) Impact cratering, Oxford Univ Press, 253 pp. [9] Cintala, M. J. (1992), JGR, 97, 947-974. [10] Pierazzo, E., et al. (1997), Icarus, 127, 208-223. [11] Reese, C. C., et al. (2002), JGR, 107, 5082. [12] Monteux, J. et al., (2007), GRL, 34, L24201. [13] Watters, W. et al. (2009), JGR, 114, E02001. [14] Roberts, J. H. and Barnouin, O. S. (2012), JGR, 117, E02007. [15] Roberts, J. H. and Arkani-Hamed, J. (2012) Icarus, 218, 278-289. [16] Roberts, J. H. and Zhong, S. (2004) JGR, 109, E03009. [17] Christensen, U. and Yuen, D. A. (1985) JGR , 90, 10,291-10,300. Acknowledgments: This research was supported by grants from NASA’s Mars Fundamental Research program and NSERC. Figure 5: Evolution of viscosity in the lowermost mantle after impact heating. 4. Thermal Evolu6on Pre-Impact Impact 6 ky 300 ky 40 ky 130 ky 1.8 My 500 ky 10 My 900 My 300 My 60 My 130 My Figure 3: Evolution of the temperature structure in the core and mantle immediately before and for up to 900 My after the impact. LPSC 2014 Figure 6: Temperature structure in the lower thermal boundary layer of the mantle 0.5 My after impact. Vertical scale has been exaggerated, and the plot has been mapped into Cartesian geometry to improve visibility. 0-10 ky: Impact Heating • Shock from collision of a 1000-km projectile at 10 km/s heats the mantle and outer core. • Lateral variations in mantle temperature (Figure 3) • Causes large scale buoyancy • Results in hemispheric upwelling • Rapid lateral mixing in core causes stable temperature stratification. Pre-existing dynamo halted • Extremely hot “thermal blanket” at top of core underlain by more modest temperature increases (Figure 4). T > 3000 K just below CMB 10-100 My: Core cooling – Dynamo restoration • Thermal blanket at top of core cools into mantle • Convecting zone develops in outermost core after ~60 My • Magnetic Reynolds number of core increases as convecting shell thickens • Dynamo activity resumes ~100 My after impact 100 My – 1 Gy: Core cooling – Full core convection • Core becomes adiabatic at greater depths. Convecting zone expands downward • Low-viscosity channel in mantle disappears by ~300 My • ~900 My for full restoration of core convection Figure 4: Evolution of temperature in the core and lower thermal boundary layer of the mantle following the impact heating. Panel b focuses on the upper 200 km of the core. CMB is marked by the horizontal line at 1700 km radius. The base of the convecting zone is marked by a star on each curve. 10 ky-1 My: Low-viscosity channel • Heat from core thermal blanket diffuses into lower mantle • Creates low-viscosity channel at base of mantle • Over 10x reduction in viscosity after ~40 ky (Figure 5) • Facilitates efficient mantle cooling • Meso-scale structures on top of low-viscosity channel aid in mixing at depth (Figure 6) 1-10 My: Mantle cooling • Low-viscosity channel serves as lateral conduit; feeds hemispheric upwelling • Upwelling spreads into second thermal blanket beneath stagnant lid. Lasts ~10 My. Figure 7: Evolution of the core properties for five models. a) Depth of the boVom of the convecting outer core. b) Heat flux across the CMB. c) Intensity of the magnetic field in the convecting outer core. d) Magnetic Reynolds number in the convecting outer core. a) d) b) c) Poster 1161
Transcript of LPSC 2014 James#H.#Roberts1 and$Jafar$Arkani+Hamed … · mantle TBL; implicit Euler / tridiagonal...
C 3. Core-‐Mantle Coupling
Mantle
Core
• Core and mantle initially adiabatic, with thermal boundary layers (TBL) at the surface and CMB (Figure 2, black curve).!
• Impact raises temperature in mantle and core (Figure 2, red and blue curves). Larger ΔT in outer core than in mantle because the core has lower specific heat and is already molten.!
• Core stratifies [4] and becomes stable to convection, T varies only with radius.!
• Mantle convection: Citcom (axisymmetric) [16]; extended Boussinesq approximation [17]; free-slip, temperature boundary conditions; T- and P-dependent viscosity; mixed-mode heating. !
• Core cooling: 1D parameterized model. Solve the 1D enthalpy equation in core and lower mantle TBL; implicit Euler / tridiagonal matrix algorithm. !
The process:!• At time t, obtain mantle temperature, timestep Δt!• Integrate 1D enthalpy equation in core and TBL over Δt, using smaller core timestep, δt !• Update !T at CMB and in TBL.!• Resume mantle convection; Advance to time t+Δt!• Iterate until the entire core is adiabatic and convecting!
Figure 2: Temperature along the impact axis before (black curve) and after (red and blue curves) impact heating. The red curve assuming all the impact heat goes into temperature increase. The blue curve shows the temperature reduced to the solidus wherever melting occurs.
C A giant impact on Mars can halt dynamo activity for ~100 My. The core does not become fully convective for ~1Gy.
1. Introduc6on !Impact cratering is a fundamental process that modifies planetary surfaces,
and is ubiquitous throughout the Solar System. Most bodies have a basin whose diameter approaches the body’s radius. On Mars, over twenty exposed and buried impact basins with diameters over 1000 km have been identified with crater ages in the mid-Noachian, (e.g. [1]). The magnetization strength of the basins correlate with age [2], suggesting that the global magnetic field vanished toward the end of the sequence of basin formation. The impacts may have modified the thermal structure and geodynamics of the interior, and crippled an ancient core dynamo [3-6]. Here, we investigate the coupled thermal evolution of the core and mantle of Mars in response to heating by a giant impact.!!Heating from the largest impactors can penetrate to the core. Because core
cooling is regulated by the vigor of mantle convection, and mantle convection is driven by core heat loss, it is desirable to have a self-consistent model of heat transfer between the core and mantle. The chief difficulty is that the material properties and relevant timescales in each layer are quite different, making a full coupling computationally expensive. We note that the core temperature stratifies after impact heating, largely erasing lateral variations [5]. We exploit this and use a 1-D parameterization of core cooling in conjunction with a finite-element mantle convection model. !
James H. Roberts1 and Jafar Arkani-‐Hamed2 1Johns Hopkins University Applied Physics Laboratory ([email protected]), 2Department of Physics, University of Toronto
5. Conclusions 1. A giant basin-forming impact results in stable stratification of the
core, insulating the inner core and halting core convection."!
2. The shock heating from such an impact increases the short-term vigor of convection in the mantle, forms a hemispheric upwelling beneath the impact site. The hot core creates a low-viscosity channel at the base of the mantle, which funnels the heat from the core into the hemispheric upwelling, allowing the mantle to return to a pre-impact state relatively quickly (tens of My).!
3. Dynamo activity may resume after ~100 My. An initially subcritical or weakly supercritical dynamo may not recover. The core does not become fully convective for several hundred My. !
2. Shock Hea6ng
Figure 1: Temperature perturbation (before taking melting into account) in the core and mantle of Mars resulting from the vertical impact of a rocky projectile 1000 km in diameter at 10 km/s. Plot assumes all waste heat is converted to a temperature increase; in reality latent heat of melting will consume a portion of the mantle heating, moderating the maximum temperature increase.
• Collision creates a shock wave that propagates through the body [7-9]. !
• Passage of shock generates waste heat [10-12] which we compute using the “foundering shock” heating model [13].!
• An example of the impact heat distribution is shown in Figure 1. !
• The energy will actually be partitioned between temperature increase ΔT and melt production (once the solidus is reached) [14]. This is equivalent to instantaneously removing melt to the surface, and ignoring compositional variations between melt residuum and unmelted mantle [15]. !
References: [1] Frey, H. V. (2008), GRL, 35, L13203. [2] Lillis, R. J., et al. (2008), GRL, 35, L14203. [3] Kuang, W., et al. (2008), GRL 35, L14204. [4] Roberts et al. (2009), JGR, 111, E6013. [5] Arkani-Hamed, J. and Olson, P. (2010), JGR, 115, E07012. [6] Arkani-Hamed, J. (2012), PEPI 196-197, 83-96. [7] O'Keefe, J. D. and Ahrens, T. J. (1977), LPSC, 8, 3357-3374. [8] Melosh, H. J. (1989) Impact cratering, Oxford Univ Press, 253 pp. [9] Cintala, M. J. (1992), JGR, 97, 947-974. [10] Pierazzo, E., et al. (1997), Icarus, 127, 208-223. [11] Reese, C. C., et al. (2002), JGR, 107, 5082. [12] Monteux, J. et al., (2007), GRL, 34, L24201. [13] Watters, W. et al. (2009), JGR, 114, E02001. [14] Roberts, J. H. and Barnouin, O. S. (2012), JGR, 117, E02007. [15] Roberts, J. H. and Arkani-Hamed, J. (2012) Icarus, 218, 278-289. [16] Roberts, J. H. and Zhong, S. (2004) JGR, 109, E03009. [17] Christensen, U. and Yuen, D. A. (1985) JGR , 90, 10,291-10,300. !
Acknowledgments: This research was supported by grants from NASA’s Mars Fundamental Research program and NSERC.!
Figure 5: Evolution of viscosity in the lowermost mantle after impact heating.
!!
4. Thermal Evolu6on Pre-Impact! Impact! 6 ky!
300 ky!
40 ky! 130 ky!
1.8 My!500 ky! 10 My!
900 My!300 My!
60 My!
130 My!
Figure 3: Evolution of the temperature structure in the core and mantle immediately before and for up to 900 My after the impact.
LPSC 2014
Figure 6: Temperature structure in the lower thermal boundary layer of the mantle 0.5 My after impact. Vertical scale has been exaggerated, and the plot has been mapped into Cartesian geometry to improve visibility.
0-10 ky: ! ! ! !Impact Heating!• Shock from collision of a 1000-km projectile at 10 km/s heats
the mantle and outer core.!• Lateral variations in mantle temperature (Figure 3)!
• Causes large scale buoyancy!• Results in hemispheric upwelling!
• Rapid lateral mixing in core causes stable temperature stratification. Pre-existing dynamo halted!
• Extremely hot “thermal blanket” at top of core underlain by more modest temperature increases (Figure 4). T > 3000 K just below CMB!
10-100 My:! ! !Core cooling – Dynamo restoration !• Thermal blanket at top of core cools into mantle!• Convecting zone develops in outermost core after ~60 My!• Magnetic Reynolds number of core increases as convecting
shell thickens!• Dynamo activity resumes ~100 My after impact!!100 My – 1 Gy: !Core cooling – Full core convection !• Core becomes adiabatic at greater depths. Convecting zone
expands downward!• Low-viscosity channel in mantle disappears by ~300 My!• ~900 My for full restoration of core convection!
Figure 4: Evolution of temperature in the core and lower thermal boundary layer of the mantle following the impact heating. Panel b focuses on the upper 200 km of the core. CMB is marked by the horizontal line at 1700 km radius. The base of the convecting zone is marked by a star on each curve.
10 ky-1 My: ! ! !Low-viscosity channel!• Heat from core thermal blanket diffuses into lower mantle!• Creates low-viscosity channel at base of mantle !
• Over 10x reduction in viscosity after ~40 ky (Figure 5)!• Facilitates efficient mantle cooling!
• Meso-scale structures on top of low-viscosity channel aid in mixing at depth (Figure 6)!
1-10 My: ! ! ! !Mantle cooling!• Low-viscosity channel serves as lateral conduit; feeds
hemispheric upwelling!• Upwelling spreads into second "
thermal blanket beneath "stagnant lid. Lasts ~10 My.!
Figure 7: Evolution of the core properties for five models. a) Depth of the boVom of the convecting outer core. b) Heat flux across the CMB. c) Intensity of the magnetic field in the convecting outer core. d) Magnetic Reynolds number in the convecting outer core.
a)
d)
b)
c)
Poster 1161
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