Analytical Newtonian models of finite thin disks in a magnetic field

Edinson Cardona-Rueda, Gonzalo García-Reyes

Published 2013-12-07, updated 2015-03-10Version 2

Axially symmetric Newtonian thin disks of finite extension in presence of magnetic field are studied based on the well-known Morgan-Morgan solutions. The source of the magnetic field is constructed separating the equation corresponding to the Ampere's law of electrodinamic in spheroidal oblate coordinates. This produces two associated Legendre equations of first order for the magnetic potential and hence that can be expressed as a series of associated Legendre functions of the same order. The discontinuity of its normal derivate across the disk allows us interpreter the source of the magnetic field as a ringlike current distribution extend on the plane of the disk. We also study the motion of charged test particles around of the disks. In particular we analysis the circular speed curves or rotation curve for equatorial circular orbits of particles both inside and outside the disk. The stability of the orbits is analyzed for radial perturbation using a extension of the Rayleigh criterion.