A Spatially Resolved Turbulent Transport Model of the Spectrum and Extension of the Crab Nebula

Abstract The Crab Nebula is an exceptional astrophysical laboratory for studying the acceleration, transportation, and radiation of ultrarelativistic particles, since its nonthermal emission extends across the entire electromagnetic spectrum up to the PeV γ -rays. Utilizing the latest spectral energy distribution (SED) and energy-dependent morphological measurements, we develop a spatially resolved turbulent transport model that enables us to explore the transport and radiative cooling mechanisms of particles within the Crab Nebula. The model self-consistently links turbulent waves and particles via bidirectional coupling: turbulent scattering regulates particle diffusion escape, while self-generated waves via particle-induced streaming instability mediate turbulent amplification. We simultaneously reproduce the SED and extension of the Crab Nebula, finding the energy-dependent morphologies more favorable to the Kolmogorov-type turbulence. The observed radial shrinkage at both X-ray and TeV γ -ray energies can be attributed to the synchrotron burn-off and particle diffusion escape. Our model predicts a radially increasing diffusion coefficient profile, transitioning from an approximately linear energy dependence in the inner nebula to a quasi-linear regime in outer regions.