Abstract
The problem of interaction of the rotating magnetic field, frozen to a star, with a thin well conducting accretion disk is solved exactly. It is shown that a disk pushes the magnetic field lines towards a star, compressing the stellar dipole magnetic field. At the point of corotation, where the Keplerian rotation frequency coincides with the frequency of the stellar rotation, the loop of the electric current appears. The electric currents flow in the magnetosphere only along two particular magnetic surfaces, which connect the corotation region and the inner edge of a disk with the stellar surface. It is shown that the closed current surface encloses the magnetosphere. Rotation of a disk is stopped at some distance from the stellar surface, which is 0.55 of the corotation radius. Accretion from a disk spins up the stellar rotation. The angular momentum transferred to the star is determined.
Highlights
We have shown that the structure of the rotating neutron star magnetic field, interacting with a thin accretion disk, can be exactly solved, and we obtained an analytical solution for this field
We have demonstrated that a disk compresses the stellar magnetic field, pushing it towards a star
The magnetic field is compressed in the region ρ < ρs, where ρs is the inner edge of the disk where it stops rotation in the laboratory frame, ρs = 0.55ρc
Summary
The important characteristics are the electric conductivity of a disk plasma and the neutron star conductivity in the surface layers. The ionized plasma of an accretion disk has the conductivity σ = 1013(Te/1eV)3/2(Λ/10)−1 s−1, which is high enough to consider a disk as an ideal conductor. Te is the temperature of electrons in a disk, which is higher than 10eV; Λ is the Coulomb logarithm (Λ ≃ 20) At such a high conductivity σ the width of the skin layer λsk = (τc2/σ)1/2 is less than the disk width H. A disk tends to exclude the stellar magnetic field, pushing it toward a star. The region of corotation is namely the region where the interaction of an accreting disk with the stellar magnetic field begins. The point of corotation is inside the stellar light cylinder radius RL = c/ωs for all rotating neutron stars: Ps > 3 · 10−5(Ms/M⊙)s. We assume that the axis of a dipole is parallel to the neutron star rotation axis
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