Vacuum nonlinear electrodynamic effects in hard emission of pulsars and magnetars

The possibilities of observing some nonlinear electrodynamic effects, which can be manifested in hard emission of X-ray, gamma ray pulsars and magnetars by X-ray and gamma ray astronomy methods are discussed. The angular resolution and sensitivity of modern space observatories give the opportunity to study the nonlinear electrodynamic effects, which can occur in very strong magnetic fields of pulsars ($B\sim 10^{12}$ G) and magnetars ($B\sim 10^{15}$ G). Such magnetic field magnitudes are comparable with the typical value of magnetic field induction necessary for manifestation of electrodynamics non-linearity in vacuum. Thus, near a magneticneutron star the electromagnetic emission should undergo nonlinear electrodynamic effects in strong magnetic fields (such as bending of rays, fluxes dispersing, changing of spectra and polarization states). Manifestations of these effects in detected hard emission from magnetic neutron stars are discussed on the base of nonlinear generalizations of the Maxwell equation in vacuum. The dispersion equations for electromagnetic waves propagating in the magnetic dipole field were obtained in the framework of these theories.The possibility of observing the bending of a ray and gamma ray flux dispersing in the neutron star magnetic field are analyzed. The only nonlinear electrodynamicseffect, which can be measured principally, is the effect of gamma ray flux dispersion by the neutron star magnetic field. Studying this effect we can also obtain information on the nonlinear electrodynamics bending of a ray in the source. The main qualitative difference in predictions of different nonlinear electrodynamics theories are discussed.