Variation of Broad Emission Lines from QSOs with Optical/UV Periodicity to Test the Interpretation of Supermassive Binary Black Holes

Periodic quasars have been suggested to host supermassive binary black holes (BBHs) in their centers, and their optical/UV periodicities are interpreted as caused by either the Doppler-boosting (DB) effect of continuum emission from the disk around the secondary black hole (BH) or intrinsic accretion rate variation. However, no other definitive evidence has been found to confirm such a BBH interpretation(s). In this paper, we investigate the responses of broad emission lines (BELs) to the continuum variations for these quasars under two BBH scenarios, and check whether they can be distinguished from each other and from that of a single BH system. We assume a simple circumbinary broad-line region (BLR) model, compatible with BLR size estimates, with a standard $\Gamma$ distribution of BLR clouds. We find that BELs may change significantly and periodically under the BBH scenarios due to (1) the position variation of the secondary BH and (2) the DB effect, if significant, and/or intrinsic variation, which is significantly different from the case of a single BH system. For the two BBH scenarios, the responses of BELs to (apparent) continuum variations, caused by the DB effect or intrinsic rate variation, are also significantly different from each other, mainly because the DB effect has a preferred direction along the direction of motion of the secondary BH, while that due to intrinsic variation does not. Such differences in the responses of BELs from different scenarios may offer a robust way to distinguish different interpretations of periodic quasars and to identify BBHs, if any, in these systems.