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Spectral line broadening in magnetized black holes

We consider weakly magnetized non-rotating black holes. In the presence of a regular magnetic field the motion of charged particles in the vicinity of a black hole is modified. As a result, the position of the innermost stable circular orbit (ISCO) becomes closer to the horizon. When the Lorentz force is repulsive (directed from the black hole) the ISCO radius can reach the gravitational radius. In the process of accretion charged particles (ions) of the accreting matter can be accumulated near their ISCO, while neutral particles fall down to the black hole after they reach $6M$ radius. The sharp spectral line Fe K$α$, emitted by iron ions at such orbits, is broadened when the emission is registered by a distant observer. In this paper we study this broadening effect and discuss how one can extract information concerning the strength of the magnetic field from the observed spectrum.