  The possibility to detect circumbinary planets and to study stellar magnetic
fields through binary stars has sparked an increase in the research activity in
this area. In this paper we revisit the connection between stellar magnetic
fields and the gravitational quadrupole moment $Q_{xx}$. We present three
magnetohydrodynamical simulations of solar mass stars with rotation periods of
8.3, 1.2, and 0.8 days and perform a detailed analysis of the magnetic and
density fields using a spherical harmonic decomposition. The extrema of
$Q_{xx}$ are associated with changes of the magnetic field structure. This is
evident in the simulation with a rotation period of 1.2 days. Its magnetic
field has a much more complex behaviour than other models as the large-scale
non-axisymmetric field dominates throughout the simulation and the axisymmetric
component is predominantly hemispheric. This triggers variations in the density
field that follow the magnetic field asymmetry with respect to the equator,
changing the $zz$ component of the inertia tensor, and thus modulating
$Q_{xx}$. The magnetic fields of the other two runs are less variable in time
and more symmetric with respect to the equator such that there are no large
variations in the density, therefore only small variations in $Q_{xx}$ are
seen. If interpreted via the classical Applegate mechanism (tidal locking), the
quadrupole moment variations obtained in the simulations are about two orders
of magnitude below the observed values. However, if no tidal locking is
assumed, our results are compatible with the observed eclipsing time
variations.
