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.
