The turn-over scenario for white dwarfs and neutron stars

We study numerically the so-called ``turn-over scenario'' for rotating magnetic white dwarfs and neutron stars. According to this scenario, the magnetic symmetry axis of the model inclines at a gradually increasing angle (the so-called ``turn-over angle'') relative to the invariant angular momentum axis. Consequently, the model becomes ``perpendicular rotator'' (i.e., its turn-over angle becomes almost 90 degrees) on a ``turn-over timescale'' calculated to be ~ (a few)x10^6 - (a few)x10^7 yr for the examined white dwarf models and ~ 10^1 - 10^3 yr for the examined neutron star models. Furthermore, the initial differential rotation of the model turns to uniform rotation due to angular momentum mixing caused by hydrodynamic Alfven waves propagating along the poloidal magnetic field lines. Our numerical results show that, during the turn-over phase, the spin-down time rate is large, while the spin-down power remains small; so, the turn-over phase is a characteristic case for which an eventually observed large spin-down time rate should not be interpreted as implying a large spin-down power.