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

¹ College of Science, Yunnan Agricultural University, Kunming 650201, PR China
² Department of Physics, Yuxi Normal University, Yuxi 653100, PR China
³ Department of Astronomy, Key Laboratory of Astroparticle Physics of Yunnan Province, Yunnan University, Kunming 650091, PR China

^★ Corresponding authors: This email address is being protected from spambots. You need JavaScript enabled to view it. ; This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 21 August 2025
Accepted: 25 March 2026

Abstract

Aims. Recent studies have demonstrated 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 explored the particle slow diffusion mechanism in the frame of a time-dependent spatially uniform model that incorporates both particle advection and diffusion.

Methods. Based on the turbulence theory, we considered the gyroresonant interactions between the particles and turbulent waves, which enabled us to determine the diffusion coefficients of particles within nebulae via the turbulent 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 was produced by the relativistic leptons through synchrotron radiation and inverse Compton process.

Results. The diffusion coefficient increases with the turbulent scale, whereas it decreases with the turbulent-to-ordered magnetic field strength ratio. Meanwhile, effects of the turbulent scale and magnetic field components on spectral energy distributions (SEDs) were analyzed. This model was applied to HESS J1420−607, and the observed spectral energy distribution of photon emission was reproduced well. The results suggest that (1) the particle cooling processes are dominated by adiabatic loss in lower-energy bands, and synchrotron loss dominate for the higher-energy particles, and (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 5.69 × 10²⁶ cm² s⁻¹, and the slow diffusion mechanism may arise from the small-scale turbulence and a relatively strong turbulent magnetic field in HESS J1420−607.