Time-dependent Force-free Pulsar Magnetospheres: Axisymmetric and Oblique Rotators

TLDR

Magnetospheres of many astrophysical objects can be accurately described by the low‑inertia (or “force‑free”) limit of MHD. We present a new numerical method for solving force‑free relativistic MHD equations using a finite‑difference time‑domain approach that handles spontaneous current sheet formation. The method enables time‑dependent studies of aligned and oblique pulsar magnetospheres while accounting for current sheet resistivity and reconnection. We confirm the time‑independent solution for aligned rotators, map the 3‑D structure of oblique rotators, and show that the spin‑down luminosity scales as \(L \approx (\mu^{2}\Omega/c^{3})(1+\alpha)\) with magnetic inclination.

Abstract

Magnetospheres of many astrophysical objects can be accurately described by the low-inertia (or "force-free") limit of MHD. We present a new numerical method for the solution of equations of force-free relativistic MHD based on the finite-difference time-domain approach, with a prescription for handling the spontaneous formation of current sheets. We use this method to study the time-dependent evolution of pulsar magnetospheres in both aligned and oblique magnetic geometries. For the aligned rotator, we confirm the general properties of the time-independent solution of Contopoulos et al. For the oblique rotator, we present the three-dimensiional structure of the magnetosphere and compute, for the first time, the spin-down power of pulsars as a function of the inclination of the magnetic axis. We find that the pulsar spin-down luminosity is L ≈ (μ2Ω/c3)(1 + α), where μ is the stellar dipole moment, Ω* is the rotation frequency, and α is the magnetic inclination angle. We also discuss the effects of current sheet resistivity and reconnection on the structure and evolution of the magnetosphere.