On the signatures of gravitational redshift: the onset of relativistic emission lines

¹ Max-Planck-Institut für Extraterrestrische Physik, PO box 1312, 85741 Garching, Germany e-mail: amueller@mpe.mpg.de
² European Southern Observatory, Karl-Schwarzschild-Strasse 2, 85748 Garching, Germany

Received: 16 May 2006
Accepted: 9 June 2006

Abstract

Aims.We quantify the effect of gravitational redshift on emission lines to explore the transition region from the Newtonian to the Einsteinian regime. With the emitting region closer to the Kerr black hole, lines are successively subjected to a stronger gravitationally induced shift and distortion. Simulated lines are compared to broad, optical emission lines observed in Mrk 110.

Methods.We simulate relativistic emission line profiles by using Kerr ray tracing techniques. Emitting regions are assumed to be thin equatorial rings in stationary Keplerian rotation.
The emission lines are characterised by a generalized Doppler factor or redshift associated with the line core.

Results.With decreasing distance from the black hole, the gravitational redshift starts to smoothly deviate from the Newtonian Doppler factor: 
shifts of the line cores reveal an effect at levels of 0.0015 to 60% at gravitational radii ranging from 10⁵ to 2. This corresponds to fully relativistic Doppler factors of 0.999985 to 0.4048. 
The intrinsic line shape distortion by strong gravity i.e. very asymmetric lines occur at radii smaller than roughly ten gravitational radii.

Conclusions.Due to the asymptotical flatness of black hole space-time, GR effects are ubiquitous and their onset can be tested observationally with sufficient spectral resolution. With a resolving power of , yielding a resolution of ≈0.1 Å for optical and near-infrared broad emission lines like Hβ, HeII and Paα, the gravitational redshift can be probed out to approximately 75 000 gravitational radii. In general, gravitational redshift is an important indicator of black hole mass and disk inclination as recently demonstrated by observations of optical lines in Mrk 110. Comparing our simulated lines with this observations, we independently confirm an inclination angle of 30 degrees for the accretion disk. Redshift deviations induced by black hole spin can be probed only very close to the black hole e.g. with X-ray iron lines.