Magnetic Braking by a Stellar Wind--III: The Oblique Rotator with a Quasi-Radial Field

Abstract

It is known that if a rotating magnetic star emits a stellar wind during part of its lifetime, the consequent magnetic torque not only brakes the star, but in general causes the instantaneous axis of rotation to precess through the star, in particular altering the angle χ between the rotation and magnetic axes. This suggests that the same magnetic coupling may be responsible for both the abnormally slow rotations of the magnetic variables and for the large values of χ required if the oblique rotator model is to account for field reversal. In this paper, the magnitude and sign of the precessional torque component are computed for the special case with the magnetic field outside the star the sum of a basic, split monopole field, with radial field-lines and an equatorial current-sheet, a perturbation field, of order ϵ, due to a small angle-dependent flux distribution over the stellar surface, and further perturbations due to the stellar rotation α , of order α and ϵα respectively. The field of order α yields a braking torque, but has too much symmetry to yield a precessional component, which results only from the part of order αϵ . If the surface flux distribution is symmetric about the magnetic axis, the precessional torque vanishes when χ is either o or π/2; while if the flux has a non-axisymmetric part, and in addition is not completely antisymmetric in the magnetic equator, then the precessional torque vanishes for two orthogonal values of χ, with |$\left| \chi - \pi/2 \right| \lessgtr \pi/4$| respectively. The details of the photospheric flux distribution also determine whether χ approaches the larger or the smaller value. When the flux distribution is axisymmetric, then for the most important cases computed the magnetic and rotation axes tend to align when the perturbation flux is more concentrated to the magnetic poles, and to become orthogonal when there is less flux at the poles than at the equator. The flux distribution actually present is presumably determined by internal stellar hydromagnetics. With this assumed external field structure, it is found that the ratio of the precessional and braking torques is usually too small for a sizeable change in χ to be associated with a reasonable degree of braking. However, if the field outside the star has the type of structure discussed in Paper I of this series, we may expect this torque ratio to be big enough for the process to be significant.