Arions Generation by Magnetodipole Waves of Pulsars and Magnetars in a Constant Magnetic Field

The influence of the gravitational fields of pulsars and magnetars on the emission of arions (strictly massless pseudoscalar Goldstone particles) during propagation of magnetodipole waves in a constant magnetic field has been evaluated. The solution of the equation was obtained, and the flux of arions emitted by magnetodipole waves during their propagation in a constant magnetic field was found. It has been shown that the amplitude of a created arion wave at a distance from the source of magnetodipole radiation of a pulsar or magnetar, \((r\to\infty)\), in the considered case tends to a constant value. The intensity of arion emission in a solid angle element and the amount of arion energy \(\overline{I}\), emitted in all directions per unit time grow quadratically with increasing distance traveled by the magnetodipole radiation of a pulsar or magnetar in a constant magnetic field. Such growth of the energy is due to the fact that the constant magnetic field is defined in the whole space. In reality, the galactic and intergalactic magnetic fields can exist in this form only in finite regions of space, outside which the force lines of their induction vector are curved. Therefore, it is possible to apply these results only in a region of space for which \(r\leq L_{\textrm{coh}}<\infty\), where \(L_{\textrm{coh}}\) is the coherence length, the distance at which the force lines of the induction vector can be considered to be straight. An estimate for the value of the coupling constant of photons with arions is obtained.