Identifying Compact Chirping SMBHBs in LSST Using Bayesian Analysis

Abstract The Legacy Survey of Space and Time (LSST) is expected to observe up to ∼100 million quasars in the next decade. In this work, we show that it is possible to use such data to measure the characteristic frequency evolution of a “chirp” induced by gravitational waves, which can serve as robust evidence for the presence of a compact supermassive black hole binary. Following the LSST specifications, we generate mock lightcurves consisting of (i) a post-Newtonian chirp produced by orbital motion through, e.g., relativistic Doppler boosting, (ii) a damped random walk representing intrinsic quasar variability, and (iii) Gaussian photometric errors, while assuming nonuniform observations with extended gaps over a period of 10 yr. Through a fully Bayesian analysis, we show that we can simultaneously measure the chirp and noise parameters with little degeneracy between the two. For chirp signals with an amplitude of A = 0.5 mag and a range of times to merger ( t m = 15–10 4 yr), we can typically measure a nonzero amplitude and positive frequency derivative with over 5 σ credibility. For binaries with t m = 50 yr, we achieve 3 σ (5 σ ) confidence that the signal is chirping for A ≳ 0.1 ( A > 0.2). The median runtime of our analysis is 5.6 minutes, with a minimum as low as 35 s, making it scalable to a large number of lightcurves. This implies that LSST could, on its own, establish the presence of a compact supermassive black hole binary, and thus discover gravitational wave sources detectable by LISA and by Pulsar Timing Arrays.