On the Signatures of Gravitational Redshift: The Onset of Relativistic Emission Lines

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 10^{5} 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 ~100000, yielding a resolution of ~0.1 Angstroems for optical and near-infrared broad emission lines like Hβ, HeII and Paα, the gravitational redshift can be probed out to approximately 75000 gravitational radii. [abridged]

arXiv comment9 pages, 9 figures, accepted for publication in A&A

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• The optical emission line spectrum of Mark 110
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• Introduction to gravitational redshift of quantum photons propagating in curved spacetime
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• Gravitational Redshift in Kerr-Newman Geometry Using Gravity's Rainbow