High energy spatially radiative properties of Vela X pulsar wind nebula

Context. Vela X is a middle-aged pulsar wind nebula (PWN) that has been detected in radio, X-ray, and gamma-ray bands. The observations indicate that that photon index and flux density of the inner regions of the nebula have obvious changes as the radial distance increases in the X-ray band, and the surface brightness has been discovered to decrease with the increase of radial distance in gamma-ray band. Aims. The multi-band photon emission and high energy spatially radiative properties of Vela X are investigated in the framework of a spatially dependent particle transport model. Methods. Electron distribution inside the PWN was described by a spatially dependent particle transport equation and the evolution of the non-thermal photon was described as a photon conservation equation under the assumption of a spherically symmetric system with dynamical evolution. In this model, the dynamical and particle evolution equations were simultaneously solved, and the gamma-ray attenuation by the supernova remnant (SNR) photon fields in the PWN were taken into account. Results. The observed spectral energy distributions of Vela X, including X-ray spectra of the inner regions and gamma-ray spectra observed at GeV and TeV bands, are well reproduced. The radial variations of the photon index in X-ray band and the surface brightness in the TeV energy range as well as the gamma-ray spectra of the inner region and ring extension can also be well reproduced in the framework of our model. The spatial variations of photon indices at GeV and TeV bands are predicted and show that the photon index in GeV band increases with the increase of radial distance while there is only a slight change in the TeV band. Moreover, the modelling results reveal that the gamma-ray attenuation by the SNR photon fields is important for modifying very high energy gamma-ray spectrum of Vela X.