Variations of light curves and broad emission lines for periodic QSOs from co-rotating supermassive binary black holes in elliptical orbits

Context. Periodic quasi-stellar objects (QSOs) are considered as candidates of supermassive binary black hole (BBH) systems in galactic centers. The periodicity of their light curves can be interpreted as being due to the Doppler boosting caused by the rotation of the two black holes (BHs). Further confirmation of these candidates may require different lines of observational evidence. Aims. Assuming the Doopler boosting scenario, in this paper we investigate the (coherent) variations of broad emission lines (BELs) and continuum light curves for active BBH systems surrounded by a circumbinary broad-line region (cBLR) and focus on their dependence on the eccentric orbital configuration. Methods. We calculated the variation of continuum light according to the motion of BBHs on elliptical orbits, with simplified orbital orientation for demonstration, the Doppler enhanced or weakened photoionization of each BLR cloud by the central BBH sources and its variation by assuming a shifted Gamma-distribution of BLR clouds for a simple BLR geometry, and finally obtain the coherent variation of the continuum and the BELs. Results. We find that the amplitude and variation pattern of the continuum light curves and the evolution of the BEL profiles both sensitively depend on the eccentric orbital configuration of BBH systems, especially when the eccentricity is high. If only the secondary BH is active, the variation amplitudes of continuum light curves and BELs both increase with increasing BBH inclination angles and orbital eccentricities, but decrease with increasing BBH mass ratio. If both BHs are active, the asymmetry in the ionization of BLR clouds at different areas caused by the Doppler boosting effect of the secondary BH is weakened due to that of the primary BH at the opposite direction, which leads to systematically smaller variation amplitudes of both continuum light curves and BELs compared with those in the cases where only secondary the BH is activated. Conclusions. The coherent variations of the BEL profiles with the continuum light for those periodic QSOs provide an important way to confirm the existence of BBHs in their center. Future joint analysis of the light curves and multi-epoch observed BEL profiles for periodic QSOs may lead to the identification of a number of BBH systems.