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

TL;DR

This work addresses the challenge of identifying sub-parsec MBHBs by proposing a spectroscopic reverberation-mapping test that leverages Doppler-boosted, anisotropic ionising flux from a circular MBHB illuminating a disc-like BLR. By constructing BELs from a non-axisymmetric BLR emissivity and simulating blue/red wing light curves, the authors show that the red and blue wing delays relative to the continuum are out of phase by about half the orbital period, a signature quantified by the statistic $\chi$. The method remains robust to damped random walk AGN variability and realistic signal-to-noise for unequal-mass binaries with $q\lesssim 0.3$, though equal-mass binaries and misaligned BLRs pose challenges. The proposed approach provides a concrete, spectroscopic pathway to confirm MBHB candidates in upcoming time-domain surveys and reverberation-mapping campaigns, with extensions to more complex dynamics and lensing effects planned.

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.

Figures (15)

• Figure 1: Upper panel: Binary period for binaries with different total mass and separations. The horizontal dashed red line indicates where the period is $\rm{P}=1 \ \rm{yr}$. Middle panel: Coalescence time of the binaries with different masses (see the colours in the upper panel) and mass ratios, $q$. The solid lines show binaries with $q=0.1$, dashed lines show binaries with $q=0.25$, and finally, dash-dotted lines show binaries with $q=1$. The horizontal dashed red line indicates where the coalescence time due to GW emission is $\tau_{\rm{coal}}=100 \ \rm{yr}$. Lower panel: Ratio between the characteristic radius of the BLR and the binary separation for different masses. In all three panels, the segments of the lines that meet the conditions of interest in this work (binaries with total masses of around $10^6-10^7 \rm{M_{\odot}}$, an orbital period of $\rm{P}<1 \ \rm{yr}$, and a coalescence time due to GW emission of $\tau_{\rm{coal}}> 100 \ \rm{yr}$) are drawn with a thicker line. In the middle panel, only the case of $q=0.1$ has a thick segment to maintain readability.
• Figure 2: Illustration of the emission patterns in two scenarios. In the binary scenario (left), the emission from the accretion disc is beamed along the direction of motion, while in the single MBH scenario (right) the emission is the same in all directions.
• Figure 3: Illustration of the BLR geometry. Here $R_{\mathrm{in}}$ and $R_{\mathrm{out}}$ are the inner and outer radii of the BLR, while $R_{\mathrm{BLR}}$ is its characteristic radius. $\textbf{L}$ is the angular momentum of the system, l.o.s is the line of sight to an observer, and finally $i$ is the inclination angle between $\textbf{L}$ and the line of sight. $M_1$ and $M_2$ are the masses of the two MBHs, while $a$ is the binary separation. The binary separation and the BLR characteristic radius are not drawn to scale.
• Figure 4: Geometry of the system seen as face-on. The rotation of the angles relative to the Cartesian co-ordinate system is clockwise.
• Figure 5: Results for the fit of the relation between the boosted ionising flux, $\rm{F_{ion}^{boost}}$, and the Doppler coefficient for an MBH of $10^6 \rm{M_{\odot}}$ at Eddington ratios equal to $f_{\rm{Edd}}=[0.25,0.50,0.75]$.