Investigation of the Iron-56 Kα Spectral Line Profile in Kerr Black Hole Accretion Disks

We present a systematic numerical investigation of the relativistic spectral line profile of the iron-56 (⁵⁶Fe) Kα emission at a rest-frame energy of E_* = 6.4 keV originating from geometrically thin and optically thick accretion disks surrounding Kerr black holes. Employing the ray-tracing transfer-function formalism following the approach of Yang, Ayzenberg & Bambi [1], we compute the observed photon count distribution N(E_obs) by integrating the redshifted local emission over the disk surface from the innermost stable circular orbit (ISCO) to a sufficiently large outer radius. The relativistic redshift factor g = E_obs/E_*, encoding both gravitational redshift and Doppler boosting due to the orbital motion of disk material, is derived analytically from the Kerr metric in Boyer–Lindquist coordinates for the equatorial plane. We systematically study the dependence of the N(E) profile on the dimensionless black hole spin parameter a_* ∈ {0, 0.5, 0.9, 0.998} at inclination angles ι = 30° and ι = 45°. Our results demonstrate that increasing spin shifts the broad red wing of the iron line to lower energies, consistent with the progressive shrinkage of the ISCO and the deepening of the gravitational potential well. The characteristic asymmetric double-peaked morphology of the photon count profile carries unambiguous information about the black hole spin.

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