Turbulent magnetic relaxation in pulsar wind nebulae

TL;DR

This paper introduces a turbulent magnetic relaxation model for pulsar wind nebulae that explains magnetic energy dissipation and matches observed features of the Crab Nebula, with implications for astrophysical transients and gamma-ray flares.

Contribution

The model incorporates turbulent magnetic relaxation into MHD equations, providing a self-consistent way to predict magnetic dissipation and electron heating in pulsar wind nebulae, addressing the sigma problem.

Findings

Reproduces Crab Nebula's expansion speed and magnetic field strength

Predicts electron heating rates relevant for particle acceleration

Offers insights into gamma-ray flares and transient phenomena

Abstract

We present a model for magnetic energy dissipation in a pulsar wind nebula. Better understanding of this process is required to assess the likelihood that certain astrophysical transients may be powered by the spin-down of a "millisecond magnetar." Examples include superluminous supernovae, gamma-ray bursts, and anticipated electromagnetic counterparts to gravitational wave detections of binary neutron star coalescence. Our model leverages recent progress in the theory of turbulent magnetic relaxation to specify a dissipative closure of the stationary magnetohydrodynamic (MHD) wind equations, yielding predictions of the magnetic energy dissipation rate throughout the nebula. Synchrotron losses are treated self-consistently. To demonstrate the model's efficacy, we show that it can reproduce many features of the Crab Nebula, including its expansion speed, radiative efficiency, peak photon energy, and mean magnetic field strength. Unlike ideal MHD models of the Crab (which lead to the so-called sigma problem) our model accounts for the transition from ultra to weakly magnetized plasma flow, and for the associated heating of relativistic electrons. We discuss how the predicted heating rates may be utilized to improve upon models of particle transport and acceleration in pulsar wind nebulae. We also discuss implications for the Crab Nebula's gamma-ray flares, and point out potential modifications to models of astrophysical transients invoking the spin-down of a millisecond magnetar.