Electromagnetic radiation from collapsing stars -- I. The power-series distribution of particles in magnetospheres

This is the first paper in a series in which the dynamics and non-thermal emission of particles in the magnetospheres of collapsing stars, with initial dipole magnetic fields and a particular initial energy distribution of charged particles in the magnetosphere (power-series, relativistic Maxwell and Boltzmann distributions), are considered. When the star magnetosphere compresses during collapse, its magnetic field increases considerably. The cyclic electric field thus produced involves acceleration of charged particles, which generate radiation when moving in the magnetic field. The analysis of particle dynamics and particle emission in the stellar magnetosphere under collapse shows that collapsing stars can be powerful sources of non-thermal radiation, produced by the interaction of charged particles with the magnetic field. The effect can be observed by means of modern instruments. The radiation flux grows with decreasing stellar radius and frequency and can be observed in the form of a radiation pulse with duration equal to the stellar collapse time. This flux depends on the distance to the star, its magnetic field and the particle spectrum in the magnetosphere. In this paper the radiation fluxes are calculated for various collapsing stars with initial dipole magnetic fields and an initial power-series particle energy distribution in the magnetosphere.