Particle Transport in Young Pulsar Wind Nebulae

Abstract

The model for pulsar wind nebulae (PWNe) as a result of the magnetohydrodynamic (MHD) downstream flow from a shocked, relativistic pulsar wind has been successful in reproducing many features of the nebulae observed close to central pulsars. However, observations of well-studied young nebulae like the Crab Nebula, 3C 58, and G21.5-0.9 do not show the toroidal magnetic field on a larger scale that might be expected in the MHD flow model; in addition, the radial variation of spectral index due to synchrotron losses is smoother than expected in the MHD flow model. We find that pure diffusion models can reproduce the basic data on nebular size and spectral index variation for the Crab, 3C 58, and G21.5-0.9. Most of our models use an energy-independent diffusion coefficient; power-law variations of the coefficient with energy are degenerate with variation in the input particle energy distribution index in the steady state, transmitting boundary case. Energy-dependent diffusion is a possible reason for the smaller diffusion coefficient inferred for the Crab. Monte Carlo simulations of the particle transport allowing for advection and diffusion of particles suggest that diffusion dominates over much of the total nebular volume of the Crab. Advection dominates close to the pulsar and is likely to play a role in the X-ray half-light radius. The source of diffusion and mixing of particles is uncertain, but may be related to the Rayleigh-Taylor instability at the outer boundary of a young PWN or to instabilities in the toroidal magnetic field structure.

NuSTARSTUDY OF HARD X-RAY MORPHOLOGY AND SPECTROSCOPY OF PWN G21.5–0.9

“…Kennel & Coroniti (1984) assume particle transport by pure advection in a spherical geometry; this situation predicts a roughly uniform nebular spectrum with radius until the (energydependent) nebular edge, where radiative energy losses sharply steepen the spectrum. This behavior is generally inconsistent with observations (Reynolds 2003;Tang & Chevalier 2012), in particular in several objects a fairly uniform spectral steepening with radius is observed (see Bocchino & Bykov 2001).…”

“…When KC84 was used to predict the radial behavior of the spectrum, the resultant spectral photon index has little to no variation from the center of the nebula outward, and begins to vary only toward the PWN periphery (Tang & Chevalier 2012, hereafter TC12, Figure 2). This also does not match the observed behavior of a slowly steepening X-ray spectrum Matheson & Safi-Harb (2005).…”

Closer view of the IGR J11014-6103 outflows

“…Similar profiles for the X-ray photon index have been observed in a few other PWN (e.g. 3C 58, Slane et al 2004;G21.5-0.9, Slane et al 2000;and MSH 15-52, An et al 2014), and have been interpreted in terms of energy-dependent diffusion caused by Rayleigh-Taylor instabilities at the boundaries of the PWN and/or due to instabilities in the nebular magnetic field (Tang 2012;Begelman 1998). A turbulent magnetic field structure may indeed be expected in the strongly perturbed nebula of IGR J11014-6103 given the high proper motion velocity of the system through the ISM.…”

Diffusion in pulsar wind nebulae: an investigation using magnetohydrodynamic and particle transport models

“…The average diffusion coefficientsκ = 1.2×10 26 cm 2 s −1 andκ = 2.5 × 10 25 cm 2 s −1 , corresponding to the KC84(a) and KC84(b) scenarios respectively, are smaller than the valueκ = 2 × 10 27 cm 2 s −1 derived by Tang & Chevalier (2012). The average Péclet numbersξ = 2.0 andξ = 9.7, for the KC84(a) and KC84(b) scenarios respectively, show that convection is the more dominant particle transport process.…”

“…The second is to further investigate the role of diffusion in the evolution of the leptons spectra by extending the results of Tang & Chevalier (2012). These authors focused on modelling the spatial evolution of Γ, while neglecting the corresponding evolution of the X-ray synchrotron flux.…”