Acad Sinica, Inst High Energy Phys, Lab Cosm Ray & High Energy Astrophys, Beijing 100039, Peoples R China
; Peking Univ, Chinese Acad Sci, Beijing Astrophys Ctr, Beijing 100871, Peoples R China
; Univ Sci & Technol China, Ctr Astrophys, Hefei 230026, Peoples R China
; Chinese Acad Sci, Natl Astron Observ, Beijing 100864, Peoples R China
; Chinese Acad Sci, Shanghai Observ, Shanghai 200019, Peoples R China
Recent observations show strong evidence for the presence of Doppler-shifted emission lines in the spectrum of both black hole candidates and active galactic nuclei. These lines are likely to originate from relativistic outflows (or jets) in the vicinity of the central black: hole. Consequently, the profile of such a line should be distorted by strong gravitational effects near the black hole, as well as special relativistic effects. In this paper, we present results from a detailed study on how each process affects the observed line profile. We found that the profile is sensitive to the intrinsic properties of the jets (Lorentz factor, velocity profile, and emissivity law), as well as to the spin of the black hole and the viewing angle (with respect to the axis of the jets). More specifically, in the case of approaching jets, an intrinsically narrow line (blueshifted) is seen as simply broadened at small viewing angles, but it shows a doubly peaked profile at large viewing angles for extreme Kerr black holes (due to the combination of gravitational focusing and Doppler effects); the profile is always singly peaked for Schwarzschild black holes. For receding jets, however, the line profile becomes quite complicated owing to complicated photon trajectories. To facilitate comparison with observations, we searched a large parameter space to derive representative line profiles. We show the results and discuss how to use emission lines as a potential tool for probing the inner region of a black hole jet system.