Origin of eclipsing time variations in Post-Common-Envelope binaries: role of the centrifugal force

Eclipsing time variations (ETVs) in post-common-envelope binaries (PCEBs) were proposed to be due to the time-varying component of the stellar gravitational quadrupole moment. This is suggested to be produced by changes in the stellar structure due to an internal redistribution of angular momentum and the effect of the centrifugal force. We examined this hypothesis and present 3D simulations of compressible magnetohydrodynamics (MHD) performed with the {\sc Pencil Code}. We modeled the stellar dynamo for a solar-mass star with angular velocities of 20 and 30 times solar. We included and varied the strength of the centrifugal force and compared the results with reference simulations without the centrifugal force and with a simulation in which its effect is enhanced. The centrifugal force causes perturbations in the evolution of the numerical model, so that the outcome in the details becomes different as a result of nonlinear evolution. While the average density profile is unaffected by the centrifugal force, a relative change in the density difference between high latitudes and the equator of $\sim10^{-4}$ is found. The power spectrum of the convective velocity is found to be more sensitive to the angular velocity than to the strength of the centrifugal force. The quadrupole moment of the stars includes a fluctuating and a time-independent component, which vary with the rotation rate. As very similar behavior is produced in absence of the centrifugal force, we conclude that it is not the main ingredient for producing the time-averaged and fluctuating quadrupole moment of the star. In a real physical system, we thus expect contributions from both components, that is, from the time-dependent gravitational force from the variation in the quadrupole term and from the spin-orbit coupling that is due to the persistent part of the quadrupole.