2006A&A...456..639G

We study the stability/establishment of dipolar magnetostatic equilibrium configurations in new-born neutron stars (NSs) in dependence on the rotational velocity Ω and on the initial angle α between rotation and magnetic axis. The NS is modeled as a sphere of a highly magnetized (B ∼10¹⁵ G) incompressible fluid of uniform density which rotates rigidly. For the initial dipolar background magnetic field, which defines the magnetic axis, two different configurations are assumed. We solve the 3D non-linear MHD equations by use of a spectral code. The problem in dimensionless form is completely defined by the initial field strength (for a fixed field geometry), the magnetic Prandtl number Pm, and the normalized rotation rate. The evolution of the magnetic and velocity fields is considered for initial magnetic field strengths characterized by the ratio of ohmic diffusion and initial Alfven travel times τ_Ohm/τ_A,0≃1000, for Pmi=0.1, 1, 10, and the ratio of rotation period and initial Alfven travel time, P/τ_A,0=0.012, 0.12, 1.2, 12. We find hints for the existence of a unique stable dipolar magnetostatic configuration for any specific α, independent of the initial field geometry. Comparing NSs possessing the same field structure at the end of their proto-NS phase, it turns out that sufficiently fast rotating NSs (P≲6ms) with α≲45° retain their magnetar field, while the others lose almost all of their initial magnetic energy by transferring it into magnetic and kinetic energy of relatively small-scaled fields and continue their life as radio pulsars with a dipolar surface field of 10^12...13G.