Efficiency of Magnetic to Kinetic Energy Conversion in a Monopole Magnetosphere

Abstract

Unconfined relativistic outflows from rotating, magnetized compact objects are often well modeled by assuming that the field geometry is approximately a split-monopole at large radii. Earlier work has indicated that such an unconfined flow has an inefficient conversion of magnetic energy to kinetic energy. This has led to the conclusion that ideal magnetohydrodynamical (MHD) processes fail to explain observations of, e.g., the Crab pulsar wind at large radii where energy conversion appears efficient. In addition, as a model for astrophysical jets, the monopole field geometry has been abandoned in favor of externally confined jets since the latter appeared to be generically more efficient jet accelerators. We perform time-dependent axisymmetric relativistic MHD simulations in order to find steady-state solutions for a wind from a compact object endowed with a monopole field geometry. Our simulations follow the outflow for 10 orders of magnitude in distance from the compact object, which is large enough to study both the initial “acceleration zone” of the magnetized wind as well as the asymptotic “coasting zone.” We obtain the surprising result that acceleration is actually efficient in the polar region, which develops a jet despite not being confined by an external medium. Our models contain jets that have sufficient energy to account for moderately energetic long and short gamma-ray burst (GRB) events (∼1051–1052 erg), collimate into narrow opening angles (opening half-angle θj ≈ 0.03 rad), become matter-dominated at large radii (electromagnetic energy flux per unit matter energy flux σ < 1), and move at ultrarelativistic Lorentz factors (γj ∼ 200 for our fiducial model). The simulated jets have γj θj ∼ 5–15, so they are in principle capable of generating “achromatic jet breaks” in GRB afterglow light curves. By defining a “causality surface” beyond which the jet cannot communicate with a generalized “magnetic nozzle” near the axis of rotation, we obtain approximate analytical solutions for the Lorentz factor that fit the numerical solutions well. This allows us to extend our results to monopole wind models with arbitrary magnetization. Overall, our results demonstrate that the production of ultrarelativistic jets is a more robust process than previously thought.