Magnetic fields of pulsars surrounded by accretion disks of finite extension

¹ Departamento de Física, Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional, AP 14–740, 07000 México DF, Mexico e-mail: [sibgatullin;aagarcia;vsmanko]@fis.cinvestav.mx
² Faculty of Mechanics and Mathematics, Moscow State University, Moscow 119899, Russia e-mail: sibgat@mech.math.msu.su
³ Institute of Mechanics, Moscow State University, Moscow 119192, Russia e-mail: sibgat@imec.msu.ru

Received: 11 November 2003
Accepted: 29 March 2004

Abstract

The problem of finding the magnetic field of a system consisting of a magnetized neutron star and a perfectly conducting accretion disk of finite extension is reduced to the solution of the integral Fredholm equation of the second kind. Unlike the pioneering works of [CITE], [CITE], we admit that an arbitrary total electric current can flow in the disk with finite outer rim. Having regularized the Fredholm equation, we obtain a convenient method for the construction of the magnetic field. The distribution of the magnetic field along the disk is plotted for different values of the total current and the ratios between the outer and inner radii of the disk.