Nonlinear Quantum Electrodynamic Vacuum Effects In The Plasmas Of Pulsars

The study of physical processes and effects under extreme fields attracts many peo-ple’s attentions. Firstly, the fundamental physical processes and principles under extreme fields need to be explored. Secondly, new physical processes and effects may emerge un-der extreme fields. Nonlinear quantum electrodynamic (QED) vacuum effect is one of the basic physical effects under the action of extreme fields, in which the vacuum be-haves as a nonlinear medium. If external electric fields approach to the critical field Ecrit～1.32×1016V/cm, electron-positron pairs may be produced spontaneously from vacuum. At present, there are two ways to explore nonlinear QED vacuum effects. The first way is using the intense laser to produce strong electromagnetic fields in the labora-tory. If one wants to observe remarkable QED vacuum effects, the intensity of the laser needs to be1029W/cm2, corresponding to the critical filed. Presently, the capability of generating light with an intensity of1022W/cm2has been demonstrated, and projects to achieve1026W/cm2are underway. The second way is looking for proper stars in the astrophysical regime, such as pulsars. Super-strong electromagnetic fields are in the interior and surface of this kind of stars. They are our natural laboratory to study the strong field physics.In this paper, we study the nonlinear QED vacuum effects in the plasmas of pul-sars. The main contents of this paper are summarized as follows:firstly the probability of electron-positron pair creation out of vacuum under the background of pair plasmas of pulsars is calculated and the effect of the pair production on the emissions of pulsars is also examined; secondly the radiation of electron-positron pairs created from the vacuum of pulsars is discussed; finally the effects of relativistic pair plasmas and vacuum polar-ization on the emissions of pulsars and magnetars are investigated, and the modification of the gravitational redshifts of emissions are obtained.Our main innovational findings are summarized as follows.(1) The probability of electron-positron pair production out of the vacuum of pul-sars is calculated for the first time, and the attenuation of the luminosity of the pulsar radiation resulting from pair production is also examined. Pair production is induced by the super-strong intrinsic magnetic field and the high-energy radiation field. The typical electromagnetic fields near the surface of pulsars are much less than the critical field, so the process of pair creation can be considered as a tunnelling effect in quan-tum mechanics, and the semi-classical WKB approximation can be used to calculate the pair-production possibility. The dependence of the probability on the intensity of elec-tromagnetic fields, the frequency of the electromagnetic radiation and the pair plasma of pulsars is discussed in detail. The results show that the probability of the pair pro-duction increases rapidly with increasing intensities of the magnetic and electric fields. And the electromagnetic radiations with frequencies close to the cyclotron frequency of an electron moving in the magnetized pair plasma play an important role in the pair production. It also turns out that the presence of the plasma background is crucial for the emergence of the pair-creation process, and there is a greater probability in a denser pair plasma. A conclusion is also obtained that only those pulsars with magnetic fields1013G<B*<2Bcrit (where Scrit～*4.4x1013G is the critical magnetic field) and1u-minosities of high-energy radiations L>1035erg/s are the candidates for exploring the pair production out of vacuum (the upper limit of the magnetic field is due to the method of semi-classical WKB approximation).(2) Within the framework of classical electrodynamics and quantum mechanics, the radiation of electron-positron pairs created from vacuum of pulsars is discussed. Electron-positron pairs will be produced from vacuum when high-energy emissions propagate through the magnetized pair plasma in the magnetosphere of a pulsar. These created pairs then move under the action of the strong electromagnetic fields, and emit an electromagnetic radiation. Firstly, the property of the radiation field emitted by the pairs is discussed using Maxwell equations and Boltzmann-Vlasov equation with a source term representing the pair creation rate. It is found that the radiation fields are linearly polarized. Then the quantum character of the pairs created from vacuum is examined, and the frequency and luminosity of the radiation emitted by the pairs are obtained. The thermal radiation property of the electron-positron pairs, when the pairs interact with the emissions of the pulsar and attain to local thermal equilibrium, is also analyzed.(3) The redshift modification of pulsars and magnetars caused by the media is studied. The relativistic plasmas in the magnetospheres of stars and the quantum vacuum are considered together for the first time. The redshifts of emissions from pulsars and magnetars consist of two components:gravitational and non-gravitational redshifts. The latter results from the electromagnetic and kinetic effects of relativistic plasmas, characterized by refractive indices and streaming velocities of the media, respectively. The vacuum polarization effect induced by strong magnetic fields can modify the refractive indices of the media, and thus leads to a modification to the redshifts. The propagation of photons in a moving medium can be described as photons following zero-geodesic lines in a curved space-time characterized by the Gordon metric. Therefore, the Gordon effective metric, generalized to weak-dispersive media, is introduced to study the redshifts of emissions from pulsars and magnetars. The results show that the non-gravitational redshift can be the same magnitude as the gravitational one under certain conditions. And the redshifts caused by the effects of relativistic plasmas and vacuum polarization is related to the wave modes, unlike the gravitational redshift being isotropic.