Subcritical thermal convection of liquid metals in a rotating sphere

Planetary cores consist of liquid metals (low Prandtl number $Pr$) that convect as the core cools. The convecting, conductive medium can self-excite and maintain a planetary magnetic field. Here we study nonlinear convection in a rotating (low, Ekman number $Ek$) planetary core using a fully 3D direct numerical simulation. Near the critical thermal forcing (Rayleigh number $Ra$), convection onsets as thermal Rossby waves, but as the $Ra$ increases, this state is superceded by one dominated by advection. At moderate rotation, these states (here called the weak branch and strong branch, respectively) are smoothly connected. As the planetary core rotates faster, the smooth transition is replaced by hysteresis cycles and subcriticality until the weak branch disappears entirely and the strong branch onsets in a turbulent state at $Ek < 10^{-6}$. Here the strong branch persists even as the thermal forcing drops well below the linear onset of convection ($Ra=0.7Ra_{crit}$ in this study). We highlight the importance of the P\'eclet number, which is consistently above 10 in the strong branch. We further note the presence of a strong zonal flow that is nonetheless unimportant to the convective state. Our findings suggest that the thermal convection in planetary cores may shut down very suddenly, leading to the death of convective motions.