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The top-down solidification of iron asteroids driving dynamo evolution - PubMed

The top-down solidification of iron asteroids driving dynamo evolution

Jerome A Neufeld et al. J Geophys Res Planets. 2019 May.

Abstract

The cores of some small planetesimals, such as asteroid (16) Psyche, are thought to have been exposed through collisions during the early solar system that removed their mantles. These small bodies likely solidified from the top down representing a fundamentally different solidification regime to that of Earth's core. Here we derive simplified models of the downwards solidification of the metallic crust, and consider thermal convection and the potential for viscous delamination of the weak, warm base of the crust to provide a buoyancy flux sufficient to drive a dynamo. Thermal buoyancy is very short lived (~1000 years), and therefore cannot be the source of measured paleomagnetic remanence. In contrast, viscous delamination is found to provide a long-lasting buoyancy flux sufficient to generate an intense, multipolar magnetic field, while not greatly affecting the crustal solidification time. Our results suggest that a Psyche-sized (150 km radius) body solidified in roughly 6.7 - 20 Myr, and that delamination produced a strong magnetic field over much of this time. Finally, including light, insoluble impurities, such as sulfur, results in a partially solid mushy zone at the base of the crust. This further weakens the base of the crust and results in smaller scale delamination events. Despite a significant change in the dynamics of delamination, the time to total solidification and the predicted properties of the magnetic field are broadly comparable to the sulfur-free case, though we argue this may result in observable compositional stratification of the body.

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Figures

Figure 1.
Figure 1.

Schematic diagram for a solidifying planetesimal.

Figure 2.
Figure 2.

In (a) the self-similar profile of temperature with depth through the solid crust and liquid core is shown. In (b) the full implicit solution to (7) for λ, which characterises the solidification rate, is compared against the asymptotic expression (dashed) provided in (8).

Figure 3.
Figure 3.

Profiles of (a) the thermal field (equation 6a), (b) the viscosity μ(T(z)) (equation 17) and (c) the boundary Rayleigh number, Rabl(z), (equation 20) through the crust. The full self-similar solution is given by the solid line, the approximate solution is given by the dashed line (equation 16), and the (approximate) critical boundary layer depth is given by the solid black line (equation 21) in panel (c).

Figure 4.
Figure 4.

Representative numerical solutions in (a) of the crustal thickness, a and core radius, b, and in (b) the superheat, θ, in each case plotted for initial superheat θ0 = 0.1 (red dash-dot), 0.01 (blue dashed), 0.001 (green dotted) and 0.0001 (black solid), and for R = 150 km and representative values as indicated in table 1. Overlain are the asymptotic solutions in (a) for the crustal thickness from (39) (red dots) and the inner core radius from (44) (black dots), and in (b) the asymptotic expression for the superheat from (41) (black dots) calculated for θ0 = 0.1.

Figure 5.
Figure 5.

Reduced model (no superheat, θ = 0) showing the growth of the crust, a(t) (red solid line), and inner core, b(t) (blue dashed line). Also shown for comparison are the asymptotic solutions for the thickness of the crust from equation (39) (solid dots) and the inner core radius from equation (44) (circles).

Figure 6.
Figure 6.

(a) The fractional final crustal thickness as a function of the scaled solidification flux (solid blue) is shown along with approximate expressions for FS≪1 and FS≫1 (dotted black, equation 45) along with a composite expression (dashed red, equation 46). (b) The total time taken for solidification for representative parameter values and as a function of the asteroid radius, R, (solid blue) is shown along with approximate expressions for FS≪1 and FS≫1 (dotted black, 47) along with a composite expression (dashed red, equation 48). The values for a planetesimal with radius R = 150 km are marked with a black dot and are FS=3.31, a∞ = 62.1 km, and t∞ = 6.7 Ma.

Figure 7.
Figure 7.

In (a) the predicted magnetic Reynolds number across the period of solidification. The predicted critical value for small bodies [Rm = 10 [Weiss et al., 2010]] and a Earth-sized bodies [Rm = 40 [Olson and Christensen, 2006]] are included. In (b) the local magnetic Rossby number, Rol (solid blue) is plotted along with the boundary between dipolar and multipolar dynamos (Rol > 0.12, black dashed line).

Figure 8.
Figure 8.

Profiles through the crust of (a) the temperature T, (b) the solid fraction ϕ, and (c) the viscosity μ(T, ϕ) for C¯=0.1 with the profiles (solid blue) and approximate solutions (dashed red) shown. In panel (d) the boundary layer Rayleigh number is shown, which exhibits two maxima at z/a = 0.9997 (dashed) and z/a = 0.83 (solid) corresponding to modes of delamination controlled by the solid fraction variation and thermal structure respectively.

Figure 9.
Figure 9.

In (a) profiles of the Rabl for a sequence of bulk liquid compositions, C¯=0,0.01,0.1,0.5,1,2,5,10,20wt% (C=0.00014,0.0014,0.0069,0.014,0.028,0.069,0.14,0.49), along with the approximate points of maximal Rabl, (δs,Rabl), for the thermal mode (squares) and for the mushy mode of delamination (circles). In (b) the numerically determined boundary layer depth corresponding to the maximal Rabl (points) is plotted with the thermal limit (red), porosity limit (blue), and eutectic limit (green) as given in (63).

Figure 10.
Figure 10.

The magnitude of the solid delamination flux, Fs,ϕ (blue solid), the average solid fraction, ϕ¯ (red dash-dot), the inverse boundary layer thickness, γe (orange dashed), the effective viscosity, μs,e/μs,0 (purple dotted) are plotted as a function of the bulk composition C¯ where, for the values used in this study, C¯=0.14wt% and C¯E=32wt%.

Figure 11.
Figure 11.

In (a) the evolution of the crustal thickness, a(t), (solid) and core radius, b(t), (dashed) for initial bulk liquid compositions C¯(0)=10−4wt%(blue), 10−2 wt% (green), 0.024 wt% (red), 1 wt% (black), 30 wt% (pink). In (b) the evolution of the bulk liquid concentration from the initial value, C¯(0), to the eutectic value, C¯E (indicated by the dashed horizontal lines). Note, C¯→C¯E extremely rapidly, within ~ 400 years, for C¯(0)=30wt%.

Figure 12.
Figure 12.

In (a) the final crustal thickness as a function of the initial bulk concentration, C¯(0), and in (b) the total time for solidification. All calculations are for radius R = 150 km. The colored dots indicate the exemplar solutions for C¯(0)=10−4,10−2,0.024,1,30.

Figure 13.
Figure 13.

In (a) the magnetic Reynolds number is plotted along with the boundaries for magnetic field generation on small (Rm > 10) and large (Rm > 40) bodies and in (b) the local Rossby number is plotted along with the boundary between dipolar and multipolar dynamos (Rol > 0.12, black dashed line), in both figures for initial concentrations C¯(0)=10−4,10−2,0.024,1,30. These results suggest that for all concentrations considered a strong, multipolar magnetic field should be prevalent during the course of planetesimal solidification.

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