Identifying the electromagnetic counterparts of LISA massive black hole binaries in archival LSST data

Abstract

ABSTRACT LSST will catalogue the light curves of up to 100 million quasars. Among these there can be $\sim$100 ultra-compact massive black hole (MBH) binaries, whose gravitational waves (GWs) can be detected 5–15 yr later by LISA. Here, we assume such a LISA detection occurred, and assess whether or not its electromagnetic (EM) counterpart can be identified as a periodic quasar in archival LSST data. We use the binary’s properties derived from the LISA waveform, including the evolution of its orbital frequency, its total mass, distance, and sky localization, to predict the redshift, magnitude, and historical periodicity of the quasar expected in the LSST data. We then use Monte Carlo simulations to compute the false alarm probability (FAP), i.e. the number of quasars in the LSST catalogue matching these properties by chance, based on the (extrapolated) quasar luminosity function, the cadence of LSST, and intrinsic ‘damped random walk’ quasar variability. We analyse four fiducial LISA binaries, with masses and redshifts of $(M_{\rm bin}/{\rm M_{\odot }},z) = (3\times 10^5,0.3)$, $(3\times 10^6,0.3)$, $(10^7,0.3)$, and $(10^7,1)$. While noise and aliasing due to LSST’s cadence produces false periodicities by chance, we find that the frequency chirp of the LISA source during the LSST observations washes out these noise peaks and allows the genuine source to stand out in appropriately scaled Lomb–Scargle periodograms. We find that all four fiducial binaries can be uniquely identified, with ${\rm FAP}\lt 10^{-5}$, a week or more before merger. This should enable follow-up EM observations targeting individual EM counterparts during their inspiral stage.