Analytical models of finite thin disks in a magnetic field
arXiv:1312.2110 · doi:10.1007/s12648-015-0786-5
Abstract
Analytical models of axially symmetric thin disks of finite extension in presence of magnetic field are presented based on the well-known Morgan-Morgan solutions. The source of the magnetic field is cons\-tructed separating the equation corresponding to the Ampere's law of electrodynamics in spheroidal oblate coordinates. This produces two asso\-ciated 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 to interpret the source of the magnetic field as a ringlike current distribution extended on all the plane of the disk. We also study the circular speed curves or rotation curve for equatorial circular orbits of charged test particles both inside and outside the disk. The stability of the orbits is analyzed for radial perturbation using a extension of the Rayleigh criterion.
18 pages, 11 figures. Accepted for publication in Indian Journal of Physics
References in corpus (14)
- Evidence for strong extragalactic magnetic fields from Fermi observations of TeV blazars
- EGMF Constraints from Simultaneous GeV-TeV Observations of Blazars
- Magnetic Fields in Dark Cloud Cores: Arecibo OH Zeeman Observations
- Kinetic Theory of Collisionless Self-Gravitating Gases: II. Relativistic Corrections in Galactic Dynamics
- Conformastatic disk-haloes in Einstein-Maxwell gravity
- An Infinite Family of Generalized Kalnajs Disks
- Electrovacuum Static Counterrotating Relativistic Dust Disks
- An Infinite Family of Self-consistent Models for Axisymmetric Flat Galaxies
- Exact relativistic models of thin disks around static black holes in a magnetic field
- General magnetized Weyl solutions: Disks and motion of charged particles
- Monopole and dipole layers in curved spacetimes: formalism and examples
- On the rotation curves for axially symmetric disk solutions of the Vlasov-Poisson system
- Conformastationary disk-haloes in Einstein-Maxwell gravity
- An infinite family of magnetized Morgan-Morgan relativistic thin disks