2024ApJ...977..240L

Turbulent transport characteristics of the particles within two Crab-like pulsar wind nebulae (PWNe), 3C58 and G54.1+0.3, are investigated in the framework of a time-dependent turbulent diffusion model. The model takes the gyroresonant interactions between the particles and turbulent waves into account, which enables us to self-consistently determine the energy and spatial coefficients of particles within the nebula via the distributions of turbulent waves. Our application of the model to the multiband emission from 3C58 and G54.1+0.3 reveals the following. (1) The energy and spatial diffusion coefficients seem to follow quasi-linear distributions in the Kolmogorov-type turbulence, but consistent with nonlinear distributions at low energies in the Kraichnan-type turbulence due to the effects of the turbulent scattering. (2) The stochastic acceleration and spatial diffusion processes may play a role in modifying the electron spectrum in the Kolmogorov-type turbulence, whereas in the Kraichnan-type turbulence the energy exchange between the turbulent waves and particles is more efficient, resulting in more significant effects of the stochastic acceleration and spatial diffusion processes on the electron spectrum at the low energies of E_e ≲ 1 TeV. (3) At the high energies of E_e ≳ 1 TeV, the diffusion transport appears to be less effective for the evolution of the particles within 3C58 and G54.1+0.3 because the synchrotron radiative cooling process dominates over the particle transport. These two Crab-like PWNe are expected to be electron PeVatrons in the Galaxy, with a common slow diffusion escape occurring in both 3C58 and G54.1+0.3.