The onset of General Relativity: Gravitationally redshifted emission lines

Abstract

We study and quantify gravitational redshift by means of relativistic ray tracing simulations of emission lines. The emitter model is based on thin, Keplerian rotating rings in the equatorial plane of a rotating black hole. Emission lines are characterised by a generalized fully relativistic Doppler factor or redshift associated with the line core. Two modes of gravitational redshift, shift and distortion, become stronger with the emitting region closer to the Kerr black hole. Shifts of the line cores reveal an effect at levels of 0.0015 to 60 % at gravitational radii ranging from 100000 to 2. The corresponding Doppler factors range from 0.999985 to 0.4048. Line shape distortion by strong gravity, i.e. very skewed and asymmetric lines occur at radii smaller than roughly ten gravitational radii. Gravitational redshift decreases with distance to the black hole but remains finite due to the asymptotical flatness of black hole space-time. The onset of gravitational redshift can be tested observationally with sufficient spectral resolution. Assuming a resolving power of ~100000, yielding a resolution of ~0.1 Angstroms for optical and near-infrared broad emission lines, the gravitational redshift can be probed out to approximately 75000 gravitational radii. In general, gravitational redshift is an indicator of black hole mass and spin as well as for the inclination angle of the emitter, e.g. an accretion disk. We suggest to do multi-wavelength observations because all redshifted features should point towards the same central mass.