An analytic model of a rotating hotspot and kilohertz quasi-periodic oscillations in X-ray binaries

Abstract

To explain kilohertz quasi-periodic oscillations (QPOs) in X-ray binaries, an analytic model of a rotating hotspot is proposed, which is based on the magnetic coupling of a rotating black hole (BH) with its surrounding accretion disc. The hotspot in the inner region of the disc is produced by energy transferred from a spinning BH with non-axisymmetric magnetic field. The frequency and energy band of the hotspot turn out to be related to six parameters, in terms of which the strength and the azimuthal angular region of the bulging magnetic field on the BH horizon, the mass and spin of the BH, and the power-law index of the magnetic field varying with the radial coordinate on the disc are described. In addition, the correlation of the fluctuation of the bulging magnetic field with the widths of QPO frequency is discussed.