Lomb-Scargle periodograms struggle with non-sinusoidal supermassive BH binary signatures in quasar lightcurves

TL;DR

This work demonstrates that the Lomb-Scargle periodogram, a staple in quasar periodicity searches, is markedly insensitive to non-sinusoidal (sawtooth) periodicities expected from hydrodynamic SMBHB models, especially under realistic red-noise conditions described by a damped random walk. By simulating DRW quasar lightcurves with sinusoidal and sawtooth injections across idealised, PTF-like, and LSST-like data, the study shows sinusoidal recovery rates of roughly 24–45% and sawtooth recoveries of only 0.8–9%, with many true signals missed entirely. The results imply that many SMBHB candidates may be undetected by traditional LSP-based analyses and that LSST-era searches require red-noise-aware statistics and alternative detection approaches, such as matched filtering or Bayesian methods, to robustly identify non-sinusoidal periodicity in millions of quasar lightcurves. Overall, the paper highlights the need for advanced periodicity tools that incorporate realistic quasar variability to exploit upcoming time-domain surveys effectively.

Abstract

Supermassive black hole binary (SMBHB) systems are expected to form as a consequence of galaxy mergers. At sub-parsec separations, SMBHBs can be identified as quasars with periodic variability with previous periodicity searches uncovering significant candidates. However, these searches focused primarily on sinusoidal signals, while theoretical models and hydrodynamical simulations predict that binaries produce more complex non-sinusoidal pulse shapes. Here we examine the efficacy of the Lomb-Scargle periodogram (LSP; one of the most popular tools for periodicity searches in unevenly sampled lightcurves) to detect periodicities with a sawtooth shape mimicking results of hydrodynamical simulations. We simulate idealised well-sampled lightcurves, lightcurves that mimic the data in the Palomar Transient Factory (PTF) analyzed in Charisi et al., 2016, and lightcurves that resemble our expectations for single-band data in the upcoming Legacy Survey of Space and Time (LSST) of the Rubin Observatory. We approximate quasar variability with a damped random walk (DRW) model, inject sinusoidal and sawtooth pulse shapes and assess their statistical significance. We find that in the presence of red noise the LSP detects a relatively low fraction of the sinusoidal signals (~45%, ~24% and ~23%, in the PTF-like, idealised, and LSST-like lightcurves, respectively). The fraction is significantly reduced for sawtooth periodicity (with only ~9% in PTF-like and ~1% in idealised and LSST-like lightcurves). These low recovery rates imply that previous searches have missed the large majority of binaries. They also have significant implications for the detection of SMBHBs in upcoming LSST necessitating the developement of advanced tools that go beyond the simple LSP.

Figures (5)

• Figure 1: SMBH mass versus redshift for the 12,400 quasars in our sample. The marginalised distributions of the two quantities are also shown. The quasars in our sample span a wide range in SMBH mass and redshift, representative of the entire quasar population.
• Figure 2: Examples of the mock periodic lightcurves we generate to test the detectability of such signals with the LSP, with a sinusoid injected on the left panel and a sawtooth signal injected on the right panel. The noiseless periodic signals are shown with solid blue lines. On top of those we add DRW noise (the same realization in both panels), shown with the black continuous curve. Idealised lightcurves sampled daily with photometric errors are shown with gray points and the respective error bars, while the PTF-like lightcurves shown in red are obtained by downsampling the black curve to the observed times and adding PTF-like photometric errors. The simulations are sampled at the observed times of quasar SDSS J085234.09+330100.7 with an injected period of 595 days, amplitude 0.19 mag and DRW variability with parameters $\sigma=0.27$ mag and $\tau=1,246$ days.
• Figure 3: Values of the DRW parameters $\sigma$ versus $\tau$ estimated based on their SMBH mass and $i$-band magnitude MacLeod+2010 for the 12,400 quasars in our sample. The marginalised distributions of the two quantities are also shown.
• Figure 4: The Lomb-Scargle periodogram of a noiseless sinusoid (blue) and a sawtooth (red), both with a period of 200 days, and an amplitude of 0.4 shows peak power of 1 and 0.61, respectively.
• Figure 5: Recovery rates of periodic signals as a function of their properties. The left panel shows the dependence on the signal-to-noise ratio of the signal, quantified as the ratio of the amplitudes of the injected periodic signal versus the DRW noise ($A/\sigma$). The middle panel shows the dependence on the amplitude and the right panel on the period. The blue lines show the recovery rates for sinusoidal signals, while the red lines for sawtooth signals. Solid lines represent samples with PTF-like lightcurves, dashed lines are for idealised lightcurves, and dotted lines are for LSST-like simulations