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 Ee ≲ 1 TeV. (3) At the high energies of Ee ≳ 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.

中文翻译：

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脉冲星风云 3C58 和 G54.1+0.3 内粒子的湍流输运特性


在瞬态湍流扩散模型的框架下，研究了粒子在两个蟹状脉冲星云 （PWNe） 3C58 和 G54.1+0.3 内的湍流输运特性。该模型考虑了粒子和湍流波之间的陀螺谐振相互作用，这使我们能够通过湍流波的分布自洽地确定星云内粒子的能量和空间系数。我们将该模型应用于 3C58 和 G54.1+0.3 的多波段发射，揭示了以下内容。（1） 能量和空间扩散系数在 Kolmogorov 型湍流中似乎服从准线性分布，但由于湍流散射的影响，与 Kraichnan 型湍流中低能量下的非线性分布一致。（2） 在 Kolmogorov 型湍流中，随机加速和空间扩散过程可能在改变电子谱方面发挥作用，而在 Kraichnan 型湍流中，湍流波和粒子之间的能量交换更有效，导致随机加速和空间扩散过程在 Ee ≲ 1 TeV 的低能量下对电子谱的影响更显着。（3） 在 Ee ≳ 1 TeV 的高能量下，扩散传输对 3C58 和 G54.1+0.3 内粒子的演化似乎不太有效，因为同步辐射冷却过程主导了粒子传输。这两个类似螃蟹的 PWNe 预计是银河系中的电子 PeVatrons，常见的慢扩散逃逸发生在 3C58 和 G54.1+0.3 中。