A numerical study of the rotational behavior of the white dwarf in DQ Herculis, II: the turn-over scenario

Abstract

The optical pulsations in DQ Her are universally believed to be due to emission from the magnetic poles of the white dwarf. However, there is no way for a pulsation to be seen if the magnetic axis and the spin axis are aligned; whether the optical pulsation is seen directly from the magnetic poles or as a result of re-processing this beam from sides in an accretion disc, the magnetic and spin axes must be offset. This fact explains why the `oblique rotator' model has been adopted as a standard model for the DQ Her primary. In a recent paper, we have computed several axisymmetric models simulating the DQ Her white dwarf before its `turn-over' (where the term `turn-over' describes the process by which the magnetic axis gets inclining relative to the spin axis at a gradually increasing angle, the so-called `turn-over angle'). For such models, we have found that the moment of inertia along the rotation axis, I33, is less than the moment(s) of inertia along the two other principal axes, I11=I22. The situation I11>I33 is known as `dynamical asymmetry', and can cause a spontaneous turn-over of the magnetic axis with respect to the rotation axis . Consequently, the DQ Her white dwarf is either an oblique rotator undergoing its turn-over phase, or it is already qalmostequal a `perpendicular rotator', i.e., its turn-over angle is almost equal to 90°. Assuming the first case, we study numerically the so-called `turn-over scenario', that is, a scenario on rotational evolution in which the turn-over phase is taken into account. We give emphasis on computations concerning the spin-down time rate of the DQ Her white dwarf due to turn-over (not to be confused with its spin-uptime rate due to accretion) for several possible values of the magnetic field.