Line profiles from relativistic eccentric rings

We find the existence of closed stationary precessing rings in general relativity, which are composed of particles moving on eccentric orbits around a central black hole. Emission-line profiles radiated by these eccentric rings in a Schwarzschild background are calculated by using a fully relativistic approach. The work is complementary to the recent paper by Eracleous et al., in which line profiles from an eccentric accretion disk are calculated under the weak field approximation, and the results presented in the present paper can be applied directly to some astrophysical systems. It is shown that both the line intensity and the profile from an eccentric ring are sensitive to a number of parameters, i.e., the eccentricity, the semimajor axis, the inclination, and the instantaneous longitude of periastron. Noticeably, the profiles show a large variety. In some cases, they have double peaks within the blue or red peak being higher, and in other cases, they show multiple peaks. These could have impact on the understanding of X-ray emission lines from active galactic nuclei and from X-ray binaries.