Effects of the centrifugal force in stellar dynamo simulations

Abstract: The centrifugal force is often omitted from simulations of stellar convection either for numerical reasons or because it is assumed to be weak compared to the gravitational force. However, it might be an important factor in rapidly rotating stars, such as solar analogs, due to its $\Omega^2$ scaling, where $\Omega$ is the rotation rate of the star. We study the effects of the centrifugal force in a set of 21 semi-global stellar dynamo simulations with varying rotation rates. Included in the set are three control runs aimed at distinguishing the effects of the centrifugal force from the nonlinear evolution of the solutions. We decomposed the magnetic field into spherical harmonics and studied the migration of azimuthal dynamo waves (ADWs), the energy of different large-scale magnetic modes, and differential rotation. In the regime with the lowest rotation rates, $\Omega = 5-10\Omega_\odot$, where $\Omega_\odot$ is the rotation rate of the Sun, we see no marked changes in either the differential rotation or the magnetic field properties. For intermediate rotation, $\Omega = 20-25\Omega_\odot$, we identify an increase in the differential rotation as a function of centrifugal force. The axisymmetric magnetic energy tends to decrease with centrifugal force, while the non-axisymmetric one increases. The ADWs are also affected, especially in the propagation direction. In the most rapidly rotating set with $\Omega=30\Omega_\odot$, these changes are more pronounced, and in one case the propagation direction of the ADW changes from prograde to retrograde. The control runs suggest that the results are a consequence of the centrifugal force and not due to the details of the initial conditions or the history of the run. We find that the differential rotation and the ADWs only change as a function of the centrifugal force when rotation is rapid enough.