An analytic model of rotating hot spot and kHz QPOs in X-ray binaries

An analytic model of rotating hot spot is proposed to explain kilohertz quasi-periodic oscillations (kHz QPO) in X-ray binaries, which is based on the magnetic coupling (MC) of a rotating black hole (BH) with its surrounding accretion disc. The hot spot 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 hot spot turns out to be related to six parameters, by 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.