Fe Kα Lines of MCG-6-30-15: Emission from Thin-torus Particles around a Kerr Black Hole

We investigate the characteristics of monochromatic particles about a Kerr (rotating) black hole (BH) and their contributions to the observed soft X-ray flux of Fe Kα emission lines. We develop a thin-torus model to formulate the particles which are not restricted within the equatorial plane of the BH, but spherically symmetric and extends to both sides of the equatorial plane due to the gravitational frame-dragging effect. A data-fit modeling to the observed line profile of MCG-6-30-15 indicates that (1) The emission originates from the torus at 13.9 ± 0.05rg (rg is the gravitational radius of the BH) with a polar angle of ∼52.20, instead of from a thin disk in the equatorial plane. (2) In addition to the usually accepted two humps in the observed profile, the blue-shifted one at ∼6.4 keV is caused by prograde particles, and the strongly red-shifted one at ∼4.8 keV by retrograde particles, there exists the third one at ∼5.5 keV. (3) The central BH rotates rapidly with α = 0.96 ± 0.005 (α is the dimensionless specific angular momentum of the BH); (4) Relative to the axis of the BH spin, the inclination angle of observation is 28±0.50.