Identifying massive black hole binaries via light curve variability in optical time-domain surveys

Accreting massive black hole binaries (MBHBs) often display periodic variations in their emitted radiation, thus providing a distinctive signature for their identification. For this work we explored the identification of MBHBs via optical variability studies by simulating the observations of the Vera C. Rubin Observatory's Legacy Survey of Space and Time (LSST). To this end, we generated a population of MBHBs using the L-Galaxies semi-analytical model, focusing on systems with observed orbital periods <= 5 years. This ensures that at least two complete cycles of emission could be observed within the ten-year mission of LSST. To construct mock optical light curves, we first calculated the MBHB average magnitudes in each LSST filter by constructing a self-consistent spectral energy distribution that accounts for the binary accretion history and the emission from a circumbinary disc and mini-discs. We then added variability modulations by using six 3D hydrodynamic simulations of accreting MBHBs with different eccentricities and mass ratios as templates. To make the light curves more realistic, we mimicked the LSST observation patterns and cadence, and we included stochastic variability and LSST photometric errors. Our results show from 10(-2) to 10(-1) MBHBs per square degree, with light curves that are potentially detectable by LSST. These systems are mainly low-redshift (z less than or similar to 1.5), massive (M greater than or similar to 10(7) M-circle dot), of equal mass (q approximate to 0.9), and relatively eccentric (e approximate to 0.6), and have modulation periods of around 3.5 years. Using periodogram analysis, we find that LSST variability studies have a higher success rate (greater than or similar to 50%) for systems with high eccentricities (e greater than or similar to 0.6). Additionally, at fixed eccentricity, detections tend to favour systems with more unequal mass ratios. The false alarm probability (FAP) shows similar trends. Circular binaries systematically feature high FAP values (greater than or similar to 10(-1)). Eccentric systems have low-FAP tails, down to approximate to 10(-8).