Testing compact massive black hole binary candidates through multi-epoch spectroscopy

Emission from two massive black holes (MBHs) bound in a close binary is expected to be modulated by different processes, such as Doppler boost due to the orbital motion, accretion rate variability generated by the interaction with a circumbinary disc, and binary gravitational self-lensing. When the binary is compact enough, the two black holes are thought to be surrounded by a common broad line region that reprocesses the impinging periodically varying ionising flux, creating broad emission lines with variable lineshapes. Therefore, the study of broad emission line variability through multi-epoch spectroscopic campaigns is of paramount importance for the unambiguous identification of a binary. In this work, we study the response of a disc-like broad line region to the Doppler-boosted ionising flux emitted by $\mathrm{sub-milli-pc}$ MBH binaries on a circular orbit and compare it with the response of a broad line region illuminated by a single MBH with a periodically but isotropically varying intrinsic luminosity. We show that in the binary case, the time lags of the blue and red wings of the broad emission lines, arising from diametrically opposite sides of the circumbinary disk, are out of phase by half of the binary's orbital period, as they each respond to the periodic "light-house" modulation from the binary's continuum emission. This asymmetric time-lag represents a new binary signature that can not be mimicked by a single MBH.