Abstract
In pulsating X-ray sources a magnetized neutron star is surrounded by an accretion disk whose structure requires a study. In particular, the dipole magnetic field of the star can partially penetrate the disk and, freezing into the matter, can give rise to an induced magnetic field in the disk. The field growth can be limited by its turbulent diffusion. In this paper we calculate such an induced field. The problem is reduced to solving the induction equation in the presence of diffusion. An analytical solution of the equation has been obtained, with the radial and vertical structures of the induced field having been calculated simultaneously. The radial structure is close to the previously predicted dependence on the difference of the angular velocities of the disk and the magnetosphere: \(b\propto\Omega_{\textrm{s}}-\Omega_{\textrm{k}}\), while the vertical structure of the field is close to the linear proportionality between the field and the height above the equator: \(b\propto z\). The possibility of the existence of nonstationary quasi-periodic components of the induced magnetic field is discussed.
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Notes
Only the poloidal field contributes to \(\mathbf{v}\times\mathbf{B}\), and this poloidal field in the model being used is simply the dipolar poloidal component (see Eq. (2)).
This step is needed for the analytical solution of (21), but actually it is easier and faster to solve the boundary value problems for \(B_{n}(r)\) (for an acceptable number \(n\)) numerically. In any case, the analytical solution is useful at least for testing the numerical code.
The boundary conditions at the disk surfaces were not set by the author in an explicit form.
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ACKNOWLEDGMENTS
I thank G.V. Lipunova for the productive discussion of the manuscript.
Funding
This work was supported by the Russian Science Foundation (project no. 21-12-00141).
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Translated by V. Astakhov
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Kuzin, A.V. Induced Magnetic Field in Accretion Disks around Neutron Stars. Astron. Lett. 49, 575–582 (2023). https://doi.org/10.1134/S1063773723100018
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DOI: https://doi.org/10.1134/S1063773723100018