[S-EM13] Geomagnetism, paleomagnetism and rock magnetism

[SEM13-05] Effects of cooling from the CMB on geodynamo with different Rayleigh numbers and inner core radii

*Yuki Nishida¹, Yuto Katoh¹, Hiroaki Matsui², Masaki Matsushima³, Takumi Kera¹, Atsushi Kumamoto¹ (1.Department of Geophysics, Graduate School of Science, Tohoku University, 2.Dept. of Earth and Planetary Sciences, University of California, Davis, 3.Department of Earth and Planetary Sciences, School of Science, Tokyo Institute of Technology)

Keywords:geodynamo, the Rayleigh number, the inner core size, cooling

The geomagnetic field has been sustained for at least 3.5 billion years as revealed by paleomagnetic observations (Biggin et al., 2015; Tarduno et al., 2015). It is generated and maintained by dynamo action driven by convective motions of liquid iron alloy in the outer core. Studies of the thermochemical evolution of the Earth's core suggest that the solid inner core has been growing up for approximately on the last one billion years (Labrosse et al., 2001; Gubbins et al., 2004). Consequently, heat flow in the core has also been changing through the Earth's history (Driscoll and Bercovici, 2014; Patocka et al., 2020). While it is reported that sustained dynamos are dipolar-dominated in cooling from the core-mantle boundary (CMB) with an inner core smaller than the present in numerical dynamo simulations (Hori et al., 2010; Heimpel and Evans, 2013), a question remains how heat flux with relation to different inner core sizes have effects on properties of dynamo. Answers to the question are important to understand a physical state of the past Earth.

In the present study, using a numerical dynamo code Calypso (Matsui et al., 2014), we investigate the effects of cooling from the CMB on numerical dynamos with two inner core sizes. We fix the Ekman, Prandtl, and magnetic Prandtl numbers to be E = 10^-3, Pr = 1, and Pm = 5, respectively, and change the Rayleigh number (Ra) and the radius ratio of the inner core to the outer core, r_i/r_o, to be 0.25 and 0.35. To represent cooling from the CMB, fixed heat flux boundaries are set as different heat flow ratios: Q_i/Q_o = 0.5, 0.75, and 1, where Q_i and Q_o are the heat flow at the inner-core boundary (ICB) and CMB, respectively.

First, we perform numerical simulations of non-magnetic thermal convection to determine the critical Rayleigh number (Ra_crit), which represents the Rayleigh number for the onset of thermal convection, by the same method as Al-Shamali et al. (2004). While critical flux Rayleigh number based on the heat flux at the CMB increases with smaller Q_i/Q_o because of the decreasing the incoming heat flux at the ICB, the conventional critical Rayleigh number, which is based on the temperature difference between the ICB and CMB, is almost the same in various Q_i/Q_o. Property of onset of thermal convection can be understood in the same way regardless of different heat flow ratios in the range of Q_i/Q_o ≧ 0.5 by using the Ra based on the temperature.

Next, we perform dynamo simulations with the three heat flow ratios with changing the flux Ra. We find that kinetic and magnetic energy densities can be lined up based on Ra/Ra_crit. The parameter ranges are 2.4 ≦ Ra/Ra_crit ≦ 11.0 at r_i/r_o = 0.25 and 2.5 ≦ Ra/Ra_crit ≦ 10.5 at r_i/r_o= 0.35. The kinetic energy basically increases with increasing Ra/Ra_crit.The simulation results reveal that the change of the generated magnetic energy by Ra/Ra_crit is similar to the cases in the range of Q_i/Q_o ≧ 0.5. The change of the dipolar dominance by the Ra/Ra_crit is also the same as the behavior that we found in numerical dynamos in the fixed temperature boundary cases at r_i/r_o = 0.25 and 0.35, as we reported at JpGU Meeting 2019. Based on the simulation results and related discussion, in the range of Q_i/Q_o ≧ 0.5, we conclude that the dynamo regime is determined by Ra/Ra_crit regardless of different heat flow ratios.