A study of the diffusion mechanism in pulsar wind nebulae: Application to HESS J1420-607

Recent research has indicated the existence of slow diffusion phenomena in pulsar wind nebulae (PWNe), where the diffusion coefficient of particles is significantly smaller than the value considered to be the average in the Galaxy. We aim to explore the particle slow diffusion mechanism in the frame of a time-dependent model with particle advection and diffusion. Based on the turbulence theories, the gyroresonant interactions between the particles and turbulent waves are considered, which enables us to determine the diffusion coefficients of particles within nebulae via the turbulence injection scale and magnetic field components (ordered magnetic field and turbulent magnetic field). Meanwhile, by considering injection, advection, adiabatic loss and radiative loss of particles, the multiband nonthermal emission from a PWN is produced by the relativistic leptons through synchrotron radiation and inverse Compton process. The diffusion coefficient increases with injection scale, whereas it decreases with the turbulent-to-ordered magnetic field strength ratio. Meanwhile, effects of turbulent injection scale and magnetic field components on spectral energy distributions (SEDs) are analyzed. This model is applied to HESS J1420-607, and the observed spectral energy distribution of photon emission is reproduced well. The results suggest that (1) the particle cooling processes are dominated by adiabatic loss in lower-energy bands and IC scattering losses dominate for the higher-energy particles; (2) the advection is the most prominent process to particle transport within this nebula, and the diffusion only plays a role in the high-energy band. More importantly, our model estimates the current diffusion coefficient at an electron energy of 1 TeV 2.6 times 10^ cm^2s^-1, and the slow diffusion mechanism may be caused by the small-scale turbulent injection and relatively ordered magnetic field distribution within HESS J1420-607.