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 Gaussion-like profiles for the BBH-IntDB model at the vertical BLR case. The amplitude of profile variations decreases with increasing offset angles for the BBH-DB scenario, while keeps 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 requires larger mass ratio to generate similar continuum variation than the BBH-DB model.