Optimizing Optical Searches for Supermassive Black Hole Binaries in AGN Light Curves: Fourier versus Bayesian Periodicity Detection

TL;DR

The paper assesses how three periodicity-detection methods—Generalized Lomb-Scargle (GLSP), Nested Bayesian Sampler (NBS), and Weighted Wavelet Z-transform (WWZ)—perform in identifying periodic signals from SMBHBs embedded in stochastic AGN variability. By simulating CRTS, ZTF, and LSST-like light curves with damped random walk noise plus sinusoidal orbital signals, the study benchmarks detection power and false positives, highlighting that NBS offers the most robust periodicity detection and parameter recovery, while combining GLSP with NBS yields the best compromise between completeness and purity. A rapid LSST triage strategy using GLSP (with fast FAP variants) followed by joint NBS+GLSP model selection is proposed to handle millions of light curves efficiently; a database-based FAP approach further accelerates processing. The results support a scalable EM-side SMBHB search pipeline aligned with LSST and multi-messenger prospects, emphasizing tiered analysis to maximize true detections while keeping false positives low.

Abstract

Simulations predict that supermassive black hole binaries (SMBHBs) will exhibit periodic brightness variations that may exceed the stochastic variability intrinsic to active galactic nuclei (AGN). In this paper, we simulate SMBHBs with damped random walk (DRW) AGN variability and an added sinusoidal signal from the orbital motion, and test three methods -- the Generalized Lomb Scargle Periodogram (GLSP), the nested Bayesian sampler (NBS), and the Weighted Wavelet Z-Transform (WWZ) -- to determine which is best at recovering the periodicity. Our simulated light curves follow the properties of the Catalina Real-Time Transient Survey (CRTS), Legacy Survey of Space and Time (LSST), and Zwicky Transient Facility (ZTF) to best inform current and future SMBHB searches. We map a broad range of parameter space and identify which DRW-only light curves best mimic periodicity and pass each method's model selection. The NBS performs best at detecting periodicity and filtering out DRW-only light curves. Combined candidate selection with both the NBS and GLSP significantly reduces false positive rates with marginal impact to true positive rates. With this joint model selection pipeline, we find the lowest false positive rates in ZTF-like simulations and the highest detection rates in LSST-like simulations. Using a modified computation of the False Alarm Probability (FAP) with GLSP, we efficiently triage LSST AGN light curves (~10^7 light curves in ~10-30 hours) and achieve true- and false- positive rates of ~40% and ~0.5%, respectively.

Figures (13)

• Figure 1: Simulated light curves containing a DRW process (top panel) and the same DRW process plus a sinusoid (bottom panel, shown in dashed gray). Simulated observations are shown for CRTS (green X's), LSST (blue stars), and ZTF (closed yellow circles). Photometric uncertainty is for a sample 20-magnitude light curve. Note, light curves in CRTS, LSST and ZTF do not overlap as shown--x-axis shows time since first observation.
• Figure 2: Median sampling cadence ($\Delta t_{\mathrm{revisit}}$) vs. baseline for LSST light curves (top panel), showing LSST survey windows will be systematically similar. Mean (solid) and $99.73$th percentile (dashed) red noise periodogram values for "representative" LSST survey windows (bottom panel). Representative survey windows (marked by red/white stars) are drawn from groups "1" and "2" labeled in top panel.
• Figure 3: TPR-FPR (faint solid lines) and TPR($P$)-FPR curves (dashed/dotted lines) shown for each method's best classifier. Typical model selection thresholds (plus markers) produce complete samples of genuine true positives with relatively high false positive counts. Strict thresholds (open star markers) yield similar completeness with far fewer false positives. TPR($P$)s, FPRs and AUC values are shown in \ref{['tab:auc_tprp']} and \ref{['tab:auc_tprp2']}.
• Figure 4: TPR($P$) for NBS (closed purple circles), GLSP (yellow stars), and WWZ (open green circles) plotted as functions of input signal parameters $\sigma_{\mathrm{in}}$, $A_{\mathrm{in}}$, and $P_{\mathrm{in}}$. TPR($P$)s are highest for LSST data (middle panel) and lowest for CRTS data (top panel). Offsets from bin centers (marked by x-axis tick marks) are used to show errorbars. Clearly, all methods favorably detect high-amplitude, short-period, low-DRW-variability light curves.
• Figure 5: Log-scaled $\Delta\mathrm{BIC}$ vs. GLSP $\mathrm{FAP_{local}}$ (top) and $\mathrm{(S/N)_{NBS}}$ vs. WWZ $\mathrm{FAP_{local\text{-}avg}}$ (bottom) for genuine true positives (blue stars), partial true positives (black squares) and false positives (red open circles). Dashed lines mark $\Delta\mathrm{BIC} = -2$, $(1-\mathrm{FAP_{local}}) = 99.73\%$, $\mathrm{FAP_{local\text{-}avg}} = 99.73\%$, $\mathrm{(S/N)_{NBS}} = 50$. Blue stars greatly outnumber red and green stars in the blue-shaded regions (see blue star occurrence rate in bold text), indicating that joint model selection preferentially removes false positives and partial true positives while retaining high TPR($P$).