Variations of Broad Emission Lines from periodicity QSOs under the
  interpretation of supermassive binary black holes with misaligned
  circumbinary broad line regions
  Quasars with periodic light curves are considered as candidates of
supermassive binary black hole (BBH) systems. One way for further confirmations
may be searching for other characteristic signatures, such as those in their
broad emission lines (BELs), if any, which require a thorough understanding on
the response of BELs to the BBH systems. In Ji et al. (2021), we have
investigated the response of circumbinary broad line region (BLR) to the
central active secondary black hole under the relativistic Doppler boosting
(BBH-DB) and intrinsic variation (BBH-IntDB) dominant mechanisms for continuum
variation by assuming the middle plane of the BLR aligned with the BBH orbital
plane. In this paper, we explore how the BEL profiles vary when the BLR is
misaligned from the BBH orbital plane with different offset angles under both
the BBH-DB and BBH-IntDB scenarios. Given a fixed inclination angle of the BBH
orbital plane viewed in edge-on and similar continuum light curves produced by
the two scenarios, increasing offset angles make the initial opening angle of
the circumbinary BLR enlarged due to orbital precession caused by the BBH
system, especially for clouds in the inner region, which result in Lorentz-like
BEL profiles for the BBH-DB model but still Gaussian-like profiles for the
BBH-IntDB model at the vertical BLR case. The amplitude of profile variations
decrease with increasing offset angles for the BBH-DB scenario, while keep
nearly constant for the BBH-IntDB scenario, since the Doppler boosting effect
is motion direction preferred but the intrinsic variation is radiated
isotropically. If the circumbinary BLR is composed of a coplanar and a vertical
components with their number of clouds following the mass ratio of the BBHs,
then the bi-BLR features are more significant for the BBH-IntDB model that
require larger mass ratio to generate similar continuum variation than the
BBH-DB model.
