Confinement of the Crab Nebula with tangled magnetic field by its supernova remnant

TL;DR

This paper extends the standard pulsar wind nebula model by including magnetic field conversion and dissipation effects, explaining the Crab Nebula's slow expansion and magnetic properties.

Contribution

It introduces a phenomenological model incorporating magnetic field conversion and dissipation, addressing the sigma-problem in pulsar wind nebulae.

Findings

Magnetic field conversion significantly decelerates the flow.

Magnetic dissipation mainly influences synchrotron radiation.

The model reproduces Crab Nebula dynamics with finite conversion timescales.

Abstract

A pulsar wind is a relativistic outflow dominated by Poynting energy at its base. Based on the standard ideal magnetohydrodynamic (MHD) model of pulsar wind nebulae (PWNe) with the ordered magnetic field, the observed slow expansion $v_{\rm PWN} \ll c$ requires the wind to be dominated by kinetic energy at the upstream of its termination shock, which conflicts with the pulsar wind theory ($\sigma$-problem). In this paper, we extend the standard model of PWNe by phenomenologically taking into account conversion of the ordered to turbulent magnetic field and dissipation of the turbulent magnetic field. Disordering of the magnetic structure is inferred from the recent three-dimensional relativistic ideal MHD simulations, while magnetic dissipation is a non-ideal MHD effect requiring a finite resistivity. We apply this model to the Crab Nebula and find that the conversion effect is important for the flow deceleration, while the dissipation effect is not. Even for Poynting-dominated pulsar wind, we obtain the Crab Nebula's $v_{\rm PWN}$ by adopting a finite conversion time-scale of $\sim 0.3$ yr. Magnetic dissipation primarily affects the synchrotron radiation properties. Any values of the pulsar wind magnetization $\sigma_{\rm w}$ are allowed within the present model of the PWN dynamics alone, and even a small termination shock radius of $\ll 0.1$ pc reproduces the observed dynamical features of the Crab Nebula. In order to establish a high-$\sigma_{\rm w}$ model of PWNe, it is important to extend the present model by taking into account the broadband spectrum and its spacial profiles.