[SIT22-P32] Study of the required Rayleigh number to sustain geodynamo with various inner core radius
Keywords:geodynamo, the past Earth, the inner core size
The Earth has an intrinsic magnetic field. Paleomagnetic studies suggest that the geomagnetic field has been sustained over 3.5 billion years [e.g., Biggin et al., 2015], and studies of the thermal history of the Earth suggest that the inner core grows to the current size in the last billion years [e.g., O’Rourke & Stevenson, 2016]. The magneto-fluid convection driven by thermal and compositional buoyancy in the outer core is thought to cause geodynamo. While characteristics of magneto-fluid convection have been investigated in detail for the present radius ratio ri/ro=0.35, there have been few simulations for the settings of ri/ro < 0.35, which correspond to the environment of the past Earth. It is important to investigate the dynamo process occurring under the settings of ri/ro < 0.35, so as to examine conditions of the past Earth. Using the numerical dynamo open source code Calypso [Matsui et al., 2014], we perform a series of numerical simulations of the thermal convection and dynamo with the smaller inner core settings than the present inner core. To investigate the characteristics of the convection for dynamo process, we focus on the dependence of dynamo properties on the Rayleigh number, Ra, which is a parameter related to buoyancy, or a driving force of convection. Only Ra is treated as a variable and the other control parameters, the Ekman number E, the Prandtl number Pr, and the magnetic Prandtl number Pm are fixed to be E = 10-3, Pr = 1, and Pm = 5, respectively.
In previous dynamo simulations, the property of Ra around the onset of dynamo action has been revealed for various radius ratios [Heimpel et al., 2005]. The tendency of the dynamo action has also been investigated by previous studies in the present ratio ri/ro = 0.35 [Christensen and Aubert, 2006], but the behavior of dynamo with Ra has not been fully understood with the smaller inner core. We perform dynamo simulations with a range of 1.9 Racrit < Ra < 9.7 Racrit, where Racrit is the critical Rayleigh number, and with the aspect ratio ri/ro = 0.15, 0.25, and 0.35, to quantitatively understand the tendencies with the smaller inner core. The results with ri/ro = 0.25 show that the sustained dipolar dominant dynamo occurs just above the onset of the dynamo action. In the case with larger Ra than that for the dipolar regime, non-dipolar components of the magnetic field is sustained. Finally, dynamo failed in the case with Ra > 8.1 Racrit. The simulation results reveal that the magnetic energy density is largest at the dynamo onset, and becomes smaller at larger Ra. This implies that dynamo is not likely to be sustained in intense convection under the assumed setting. The results of ri/ro = 0.25 and 0.35 imply that the revealed tendency revealed by the present study can be applied to ri/ro = 0.15. Comparing the simulation results in the same Ra/Racrit(= 3.6), the magnetic dipole moment becomes smaller with the smaller inner core. This suggests a possibility that the convection favorable for the dipolar dominant dynamo is difficult to occur with the smaller inner core. We also find that the Ra range of the dipolar dominant cases becomes narrower with the smaller inner core, implying that Ra was very selective at the past Earth. To interpret the simulation results with the real physical quantities, the average temperature difference between the core-mantle boundary and the inner core boundary, ΔT, is estimated. ΔT in ri/ro = 0.25 is larger than that in ri/ro = 0.35, so required buoyancy to sustain a dipolar dominant dynamo is larger with the smaller inner core.
In previous dynamo simulations, the property of Ra around the onset of dynamo action has been revealed for various radius ratios [Heimpel et al., 2005]. The tendency of the dynamo action has also been investigated by previous studies in the present ratio ri/ro = 0.35 [Christensen and Aubert, 2006], but the behavior of dynamo with Ra has not been fully understood with the smaller inner core. We perform dynamo simulations with a range of 1.9 Racrit < Ra < 9.7 Racrit, where Racrit is the critical Rayleigh number, and with the aspect ratio ri/ro = 0.15, 0.25, and 0.35, to quantitatively understand the tendencies with the smaller inner core. The results with ri/ro = 0.25 show that the sustained dipolar dominant dynamo occurs just above the onset of the dynamo action. In the case with larger Ra than that for the dipolar regime, non-dipolar components of the magnetic field is sustained. Finally, dynamo failed in the case with Ra > 8.1 Racrit. The simulation results reveal that the magnetic energy density is largest at the dynamo onset, and becomes smaller at larger Ra. This implies that dynamo is not likely to be sustained in intense convection under the assumed setting. The results of ri/ro = 0.25 and 0.35 imply that the revealed tendency revealed by the present study can be applied to ri/ro = 0.15. Comparing the simulation results in the same Ra/Racrit(= 3.6), the magnetic dipole moment becomes smaller with the smaller inner core. This suggests a possibility that the convection favorable for the dipolar dominant dynamo is difficult to occur with the smaller inner core. We also find that the Ra range of the dipolar dominant cases becomes narrower with the smaller inner core, implying that Ra was very selective at the past Earth. To interpret the simulation results with the real physical quantities, the average temperature difference between the core-mantle boundary and the inner core boundary, ΔT, is estimated. ΔT in ri/ro = 0.25 is larger than that in ri/ro = 0.35, so required buoyancy to sustain a dipolar dominant dynamo is larger with the smaller inner core.