A turn-over scenario for rotating magnetic white dwarfs: models with several values of mass, angular momentum, and magnetic field

Abstract

We study a white dwarf with differential rotation and magnetic field, for which the symmetry axis of the toroidal field, the magnetic axis of the poloidal field, and the principal axis I_3 coincide permanently. This common axis, so-called "magnetic symmetry axis", inclines at a small angle relative to the spin axis of the model, the so-called "turn-over angle". Such an almost axisymmetric model undergoes an early evolutionary phase of secular timescale, with moment of inertia along the spin axis, I_{zz}=I_{33}, greater than the moments of inertia along the equatorial axes, I_{11}=I_{22}, since rotation and poloidal field (both deriving oblate configurations) dominate over the toroidal field (deriving prolate configurations). During this phase, the model suffers from secular angular momentum loss due to weak magnetic dipole radiation activated by the poloidal field, leading gradually to "dynamical asymmetry" with I_{11}>I_{33}. However, a dynamically asymmetric configuration tends to turn over spontaneously, i.e., to rotate about axis with moment of inertia greater than I_{33}, with angular momentum remaining invariant. So, the fate of a dynamically asymmetric configuration is to become an oblique rotator and, eventually, a perpendicular rotator. During the so-called "turn-over phase", the turn-over angle increases spontaneously up to 90 degrees on a "turn-over timescale" t_{TOV}. In the present paper, we study numerically the turn-over phase for models of several masses, angular momenta, and magnetic fields.