Relativistic Expansion of Magnetic Loops at the Self-similar Stage

Abstract

We obtained self-similar solutions of relativistically expanding magnetic loops taking into account the azimuthal magnetic fields. We neglect stellar rotation and assume axisymmetry and a purely radial flow. As the magnetic loops expand, the initial dipole magnetic field is stretched into the radial direction. When the expansion speed approaches the light speed, the displacement current reduces the toroidal current and modifies the distribution of the plasma lifted up from the central star. Since these self-similar solutions describe the free expansion of the magnetic loops, i.e., $Dv/Dt=0$, the equations of motion are similar to those of the static relativistic magnetohydrodynamics. This allows us to estimate the total energy stored in the magnetic loops by applying the virial theorem. This energy is comparable to that of the giant flares observed in magnetars.

arXiv comment23 pages, 36 figures, accepted for publication in MNRAS. We revised our manuscript in equation (67). This change does not affect any other equations nor figures

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Cited by in corpus (5)

• Magnetic field configurations of a magnetar throughout its interior and exterior -- core, crust and magnetosphere
• Coexistence of oppositely flowing multi-$\phi$-currents: Key to large toroidal magnetic fields within stars
• Relativistic expansion of a magnetized fluid
• Special Relativistic Magnetohydrodynamic Simulation of Two-Component Outflow Powered by Magnetic Explosion on Compact Stars
• Relativistic Expansion of Magnetic Loops at the Self-similar Stage II: Magnetized outflows interacting with the ambient plasma