ИСТИНА

Among the many hypotheses about the origin of cosmic gamma-ray bursts, a substantial number involves theoretical concepts those are based on consideration of special type supernova explosion in a binary system with a neutron star or other relativistic objects with strong magnetic field. We consider a model of magnetosphere of a neutron star subjected to a strong shock wave from supernova. In this model, a form of magnetosphere’s boundary is determined from the condition of equilibrium between external gas pressure behind the shock and interior magnetic pressure. The field of neutron star is approximated as a point magnetic dipole. The magnetic field is assumed to be potential in a circumstellar space. In the magnetotail there is a reconnecting current layer (RCL) which accumulates an excess of magnetic energy. The model under consideration implies the planar free boundary problem for an analytic function of complex variable. This free boundary problem is reduced to consequent solution of two singular Riemann - Hilbert problems. Solution to the both problems is constructed in analytical form with the help of Appel’s generalized hypergeometric function. The obtained analytic solution, in particular, shows the presence of reverse current in the RCL. The solution is important for the possibility estimation of directional relativistic plasma jets and impulse bursts of gamma-impulses or hard radiation of other kinds. Bibliography: [1] Somov B.V., Plasma Astrophysics, Part II, Reconnection and Flares. Second Edition, Springer SBM, New York, 2013. [2] Bezrodnykh S.I., Somov B.V. Analysis of magnetic field and magnetosphere of neutron star under effect of a shock wave // Advances in Space Research. 2015. V. 56. P. 964-969.