We investigate the spatial dependence of high energy electrons and their radiations in pulsar wind nebulae （PWNe）. By assuming a time-dependent broken power-law injection and spatial dependence of convection velocit...We investigate the spatial dependence of high energy electrons and their radiations in pulsar wind nebulae （PWNe）. By assuming a time-dependent broken power-law injection and spatial dependence of convection velocity, magnetic field strength and diffusion coefficient on the radial distance of an expand- ing system, we numerically solve the Fokker-Planck transport equation including convection, diffusion, adiabatic loss and radiative loss in spherical coordinates, and investigate the effects of magnetic field, PWN age, maximum energy of electrons, and diffusion coefficient on electron spectra and non-thermal photon emissions. Our results indicate that （1） electron spectra and the corresponding photon spectra are a function of radial distance r of the expanding system; （2） for a given expansion velocity, the increase of the PWN age causes a slower decrease of the convection velocity （V ∝ r-β） and a more rapid decrease of the magnetic field strength （B ∝ r-1＋β）, but a more rapid increase of the diffusion coefficient （k∝ r1-β） because the index β decreases with the PWN age; and （3） the lower energy part of the electron spectra is dominated by convection and adiabatic loss, but the higher energy part is dominated by the competition between syn- chrotron loss and diffusion, and such a competition is a function of radial distance. Therefore the diffusion effect has an important role in the evolution of electron spectra as well as non-thermal photon spectra in a PWN.展开更多
We present a one-zone homogeneous lepton-hadronic model and obtain steady-state spectra by solving the time-dependent equations to study a plausible origin of hard TeV spectra in PKS 2155-304.In this model,we assume a...We present a one-zone homogeneous lepton-hadronic model and obtain steady-state spectra by solving the time-dependent equations to study a plausible origin of hard TeV spectra in PKS 2155-304.In this model,we assume a steady electron and proton injection rate in the source and solve the non-linear time-dependent kinematic equations that self-consistently consist of proton-photon interaction,synchrotron radiation of electron/positron pairs and proton,inverse Compton scattering,and synchrotron self-absorption.We employ this model to reproduce the multi-wavelength spectrum of PKS 2155-304,then find that the possible bump located at E~1 TeV which may originate from the synchrotron radiation of secondary electrons produced by Bethe-Heitler pair production,resulting in the hard TeV spectrum.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos.11433004 and 11173020)the Top Talents Program of Yunnan Province,the Natural Science Foundation of Yunnan Province (2012FD055 and 2013FB063)the Young Teachers Program of Yuxi Normal University,and the Program for Innovative Research Team (in Science and Technology) in University of Yunnan Province (IRTSTYN)
文摘We investigate the spatial dependence of high energy electrons and their radiations in pulsar wind nebulae （PWNe）. By assuming a time-dependent broken power-law injection and spatial dependence of convection velocity, magnetic field strength and diffusion coefficient on the radial distance of an expand- ing system, we numerically solve the Fokker-Planck transport equation including convection, diffusion, adiabatic loss and radiative loss in spherical coordinates, and investigate the effects of magnetic field, PWN age, maximum energy of electrons, and diffusion coefficient on electron spectra and non-thermal photon emissions. Our results indicate that （1） electron spectra and the corresponding photon spectra are a function of radial distance r of the expanding system; （2） for a given expansion velocity, the increase of the PWN age causes a slower decrease of the convection velocity （V ∝ r-β） and a more rapid decrease of the magnetic field strength （B ∝ r-1＋β）, but a more rapid increase of the diffusion coefficient （k∝ r1-β） because the index β decreases with the PWN age; and （3） the lower energy part of the electron spectra is dominated by convection and adiabatic loss, but the higher energy part is dominated by the competition between syn- chrotron loss and diffusion, and such a competition is a function of radial distance. Therefore the diffusion effect has an important role in the evolution of electron spectra as well as non-thermal photon spectra in a PWN.
基金partially supported by the National Natural Science Foundation of China(Grant Nos.12063006,11803027and 11863007)Yunnan Local Colleges Applied Basic Research Projects(Grant Nos.202001BA070001-031,2017FH001-102,2018FH001-015,2019FH001-012 and2019FH001-076)+1 种基金Science Research Foundation of Yunnan Education Department of China(Grant Nos.2017ZZX177,2018JS422 and 2019J0733)the financial support from the Hundred Talents Program of Yuxi(Grant Nos.2019)。
文摘We present a one-zone homogeneous lepton-hadronic model and obtain steady-state spectra by solving the time-dependent equations to study a plausible origin of hard TeV spectra in PKS 2155-304.In this model,we assume a steady electron and proton injection rate in the source and solve the non-linear time-dependent kinematic equations that self-consistently consist of proton-photon interaction,synchrotron radiation of electron/positron pairs and proton,inverse Compton scattering,and synchrotron self-absorption.We employ this model to reproduce the multi-wavelength spectrum of PKS 2155-304,then find that the possible bump located at E~1 TeV which may originate from the synchrotron radiation of secondary electrons produced by Bethe-Heitler pair production,resulting in the hard TeV spectrum.
