Identification of periodicities with arbitrary shapes in AGN light curves

TL;DR

This paper develops a GP-based Bayesian framework to detect periodicities of arbitrary shape in AGN light curves dominated by red noise, addressing limitations of quasi-sinusoidal Lomb-Scargle methods. By combining a DRW-like exponential kernel with a flexible generic periodic kernel, and performing model comparison via nested sampling to obtain Bayes factors, it can identify non-sinusoidal periodicities such as sawtooth shapes. The authors validate the approach on extensive mock light curves across ideal, PTF-like, and LSST-like cadences, deriving ROC-based Bayes-factor thresholds and showing substantial improvements over cosine-kernel GP fits and LSP analyses, especially for non-sinusoidal signals and longer baselines. They find that detection efficiency scales with the number of observed cycles and that multi-band GP implementations and GPU acceleration will be important for applying the method to large quasar samples in upcoming surveys. The work thus enhances the prospects for discovering MBHBs through time-domain photometry and provides a framework adaptable to other periodic phenomena in astrophysical time series, including lensing and Doppler-boosting scenarios.

Abstract

Massive black hole binaries are expected to be observable as periodic AGN in time-domain photometric surveys. Periodicities may originate from different physical processes, including the intermittent gas feeding of the black holes caused by the time-varying non-axisymmetric binary potential, the Doppler boosting of the flux emitted by individual accretion discs bound to the orbiting BHs, and the gravitational lensing of the accretion disc of one black hole due to the presence of the other. Only the Doppler boost scenario applied to circular binaries with non-modulated accretion predicts a sinusoidal light curve, while in the general case, binary signals are expected to show more complex periodic patterns. Current searches for massive black hole binaries rely on techniques tailored to quasi-sinusoidal light curves, but fail to identify the more complex periodicities predicted. We present an alternative method that leverages Gaussian processes, making use of a generic periodic kernel flexible enough for the identification of arbitrary periodicities in unevenly sampled light curves with realistic quasar noise. We demonstrate that it outperforms previously proposed strategies in identifying general periodicities by analysing mock light curves with different baselines. Specifically, we find that our analysis can detect non-sinusoidal periodicities (e.g., sawtooth-shaped) and retrieves a higher fraction of true periodicities when compared to periodogram analysis or Gaussian processes analysis with less flexible periodic kernels. Furthermore, by comparing the retrieved fraction of periodicities between mock PTF light curves and mock LSST light curves, we find that our analysis is most sensitive to the number of observed cycles. The application of this analysis has the potential to greatly increase the scientific return of current and upcoming large time-domain photometric surveys.

Figures (14)

• Figure 1: Posterior predictive distributions from GP inference on a sinusoidal light curve (upper panel) and a sawtooth light curve (lower panel). Results from the cosine kernel (Equation \ref{['eq:cos_kernel']}) are shown in red, and from the periodic kernel (Equation \ref{['eq:periodic_kernel']}) in blue. Shaded regions indicate the $1\sigma$ (dark) and $2\sigma$ (light) credible intervals. The solid lines and shaded regions in the upper panel clearly show that both the periodic and cosine kernels can reproduce the sinusoidal signal as they overlap. The bottom panel, instead, highlights both the inadequacy of the cosine kernel in modelling non-sinusoidal light curves and the flexibility of the periodic kernel that allows it to describe periodicities with arbitrary shapes.
• Figure 2: Examples of the same sampled sinusoidal light curve for the three baselines. The LSST light curve is shown in the main panel, while the PTF (blue points) and ideal (orange points) light curves are displayed in the inset (lower right). The dashed red rectangle in the main panel highlights the typical duration of the PTF and ideal sampling, emphasising the longer observational coverage of the LSST baseline.
• Figure 3: Distribution of the Bayes factors for the $10^4$ noise-only light curves for the PTF using the periodic kernel and cosine kernel (blue and dark blue distributions) and ideal using the periodic kernel and cosine kernel (orange and red distributions) baselines, and the $10^3$ noise-only light curves for the LSST (green distribution) baseline found by analysing the light curves with the generic periodic kernel. The vertical lines refer to the Bayes factor threshold identified for a fair comparison with the LSP analysis discussed in more detail in Section \ref{['sec:LSP_comparison']}.
• Figure 4: Fraction of realisation with a Bayes factor greater than a threshold as a function of the assumed threshold. Solid lines refer to the sinusoidal light curves, while dotted lines refer to sawtooth light curves. Blue, red and green colours refer to the ideal, PTF and LSST baselines, respectively. The vertical lines refer to the Bayes factor threshold of $\log_{10} B_{\rm{trs}}=5$ for the ideal, and PTF baselines (solid line) and $\log_{10} B_{\rm{trs}}=3$ for the LSST baseline (dashed line) used to compare the results with the LSP-analysis, see Section \ref{['sec:LSP_comparison']}.
• Figure 5: ROC curves of the different combinations of baselines and periodicity shape. Solid lines refer to sinusoidal light curves, while dashed lines refer to sawtooth light curves. Blue lines refer to the PTF-like baseline, orange lines refer to the idealised baseline, while green lines refer to the LSST baseline. Circles and squares identify the points at the identified Bayes threshold for the sinusoidal and sawtooth cases, respectively. Blue markers refer to PTF-like light curves, orange markers refer to ideal light curves and finally, green markers refer to LSST-like light curves.