A numerical study of the rotational behavior of the white dwarf in DQ Herculis

Abstract

It is well-known that the optical pulsations in DQ Her are due to emission from the magnetic poles of the white dwarf. As the white dwarf spins on its axis, the magnetic poles sweep into and out of the line of sight due to the fact that the magnetic axis and the spin axis are not aligned, that is, the DQ Her white dwarf is an `oblique rotator'. So, a central question is if an initially axisymmetric model 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 progressively increasing angle, the so-called `turn-over angle') is indeed susceptible to turn-over. For the puprose of resolving this problem, we compute several axisymmetric models of the DQ Her white dwarf. Our results show that, for both the rotation periods proposed on the basis of the observational evidence regarding the optical pulsations of DQ Her (i.e.,71 s or 142 s), the moment of inertia along the rotation axis is less than the corresponding moment of inertia along the remaining two principal axes of the axisymmetric configuration, I 33 > I 11(=I 22). This is because toroidal magnetic field (tending to derive prolate equidensity surfaces) dominates over rotation (tending, in turn, to derive oblate equidensity surfaces), mainly in the interior of the star. The situation I 11 < I 33 is known as `dynamical asymmetry', and can cause a turn-over of the magnetic symmetry axis with respect to the rotation axis, eventually deriving a nonaxisymmetric configuration corresponding to the so-called `perpendicular rotator' with turn-over angle almost equal to 90°. In this view, our results explain why the DQ Her white dwarf is now an oblique rotator.