Measuring black hole mass through variable line profiles from accretion disks

Abstract

THE emission lines in the optical spectra of several active galactic nuclei (AGNs) show a broad double-horned profile which is likely to be produced by matter orbiting the central massive black hole in a disk-like geometry^1–3. The unresolved and, sometimes, broad and redshifted Fe K α lines observed in the X-ray spectra of Seyfert galaxies^4–6 and bright X-ray binaries^7–10 might also be dominated by Doppler, transverse and gravitational shifts in a keplerian disk of tens to hundreds of Schwarzschild radii (r_s = 2GM/c²) around the collapsed object^11,12. Line emission from these disks is most likely to be driven by photoionization or Compton heating by radiation from closer to the central object; flux variations in this radiation will cause changes in the disk line emissivity. Here we present detailed calculations of the response of a line from a relativistic keplerian disk to flux variations in the central regions. Two characteristic features form on opposite sides of the line, which, owing to light travel-time effects, gradually drift from the line wings, corresponding to the innermost disk regions, to the blue and red horns. Observations of these line-profile changes could provide the first direct measurement of the mass of the central black hole in AGNs^2,12,13.