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

¹ Università degli Studi di Milano-Bicocca, Piazza della Scienza 3, 20126 Milano, Italy
² INAF – Osservatorio Astronomico di Brera, Via Brera 20, I-20121 Milano, Italy
³ INFN, Sezione di Milano-Bicocca, Piazza della Scienza 3, I-20126 Milano, Italy
⁴ Como Lake Centre for AstroPhysics (CLAP), DiSAT, Università dell’Insubria, Via Valleggio 11, 22100 Como, Italy
⁵ Space Telescope Science Institute, 3700 San Martin Dr., Baltimore, MD 21218, USA
⁶ Department of Physics and Astronomy, Johns Hopkins University, 3400 North Charles Street, Baltimore, MD 21218, USA
⁷ Niels Bohr International Academy, Niels Bohr Institute, Blegdamsvej 17, DK-2100 Copenhagen Ø, Denmark
⁸ Department of Astronomy and Astrophysics, Penn State University, 525 Davey Lab., 251 Pollock Road, University Park, PA 16802, USA
⁹ Department of Astronomy, Columbia University, New York, NY 10027, USA
¹⁰ Department of Physics, Columbia University, New York, NY 10027, USA
¹¹ Institute of Science and Technology Austria (ISTA), Am Campus 1, Klosterneuburg, 3400, Austria

^⋆ Corresponding author: l.bertassi@campus.unimib.it

Received: 17 March 2025
Accepted: 17 August 2025

Abstract

Emission from two massive black holes (MBHs) bound in a close binary is expected to be modulated by different processes, such as the 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 line shapes. 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 sub-milliparsec 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 disc, are out of phase by half of the binary’s orbital period, as they each respond to the periodic ‘lighthouse’ modulation from the binary’s continuum emission. This asymmetric time lag represents a new binary signature that cannot be mimicked by a single MBH.