The ensemble broad-frequency power spectrum of Stripe-82 quasars from multiple surveys

Variability is a striking features of quasars, observed at all timescales wavelengths. Studying its properties and the correlations with the physical parameters (e.g. black hole mass and accretion rate) provides significant insights into accretion physics. However, the detailed picture and the exact interplay between different emitting regions are not yet clear. We combine data from Sloan Digital Sky Survey (SDSS), the Panoramic Survey Telescope and Rapid Response System 1 (Pan-STARRS1, PS1), the Zwicky Transient Facility (ZTF), and the Gaia space telescope to constrain the power spectrum of quasars in the Stripe-82 region over a broad frequency range, 10^{-1} to 10^{-3} day^{-1}(rest frame). Light curves are matched and cross-calibrated to reach \sim 20 years in the r-band for 4037 quasars. We split the sample into bins of the same black hole mass, accretion rate, and redshift, and measure the ensemble power spectral density (PSD) in each bin. The power spectra of SDSS, ZTF, and Gaia are measured independently. We do not measure it on PS1 data due to more erratic cadence, but we discuss the use of interpolation techniques, eventually allowing us to use the data together. We find significant evidence that the long-term UV/optical variability of quasars is stationary, as the ensemble PSD estimates from SDSS, Gaia and ZTF are consistent within the errors despite coming from different surveys and years. The PSD shape is consistent with a bending power law with spectral indices of -2.7 and -1 at high and low frequencies. A fit with the PSD associated with a damped random walk is significantly worse. The PSD amplitude below the break does not depend on black hole mass, but there is some evidence for anti-correlation with the accretion rate. The bending frequency, instead, scales with the black hole mass as $ν_b$ \propto M_{\mathrm{BH}}^{-0.6\pm0.1} and does not depend on the accretion rate.

💡 Research Summary

This paper presents a comprehensive study of optical variability in quasars located in the SDSS Stripe‑82 field by combining light‑curve data from four major time‑domain surveys: the Sloan Digital Sky Survey (SDSS), Pan‑STARRS1 (PS1), the Zwicky Transient Facility (ZTF), and the Gaia space telescope. Starting from the spectroscopically confirmed sample of 8,042 quasars used in Petrecca et al. (2024), the authors cross‑matched the catalogue with Gaia DR3 variable AGN entries and retained 4,037 objects for which multi‑survey coverage exists. The surveys span different epochs (SDSS 1998‑2008, PS1 2010‑2014, Gaia 2014‑2017, ZTF 2018‑2023) and employ distinct filter sets, sensitivities, and cadences. To enable a unified analysis, the authors calibrated all photometry to the SDSS r‑band system using colour terms and zero‑point adjustments (details in Appendix A), and transformed observation times to the rest‑frame of each quasar.

Using traditional Fourier periodograms, the authors estimated the power spectral density (PSD) for each individual light curve and then constructed ensemble PSDs by averaging at least 50 periodograms within bins of similar black‑hole mass (M_BH), Eddington ratio (λ_Edd), and redshift (as a proxy for rest‑frame wavelength). Crucially, the PSDs derived independently from SDSS, ZTF, and Gaia are statistically consistent, demonstrating that quasar optical variability is stationary over the ∼20‑year baseline despite the surveys’ different epochs and instrumental characteristics.

The ensemble PSD is best described by a bending power‑law: at high frequencies (≈10⁻¹ day⁻¹) the slope is –2.7 ± 0.1, while at low frequencies (≈10⁻³ day⁻¹) it flattens to –1 ± 0.1. A damped random walk (DRW) model, which predicts slopes of –2 and 0, provides a significantly poorer fit, indicating that the DRW is an oversimplified description for the full frequency range. The break (or bending) frequency ν_b scales with black‑hole mass as ν_b ∝ M_BH^{‑0.6 ± 0.1} and shows no dependence on λ_Edd. The PSD amplitude below the break is independent of M_BH but exhibits a modest anti‑correlation with λ_Edd, suggesting that higher accretion rates mildly suppress variability amplitude.

PS1 data were not used for direct PSD estimation because of an irregular cadence and a temporal gap that limits frequency coverage. Nevertheless, the authors discuss interpolation and Gaussian‑process reconstruction techniques that could incorporate PS1 points and extend the PSD to even lower frequencies in future work.

Overall, the study demonstrates that by carefully cross‑calibrating heterogeneous time‑domain data one can obtain a robust, broadband PSD spanning more than two decades in frequency. The results provide strong empirical constraints on accretion‑disk physics: variability power scales with black‑hole mass but not with accretion rate, and the characteristic timescale (the break) follows a clear mass‑dependent trend. These findings will be valuable for interpreting upcoming LSST light curves, for refining stochastic models of AGN variability, and for using variability as a probe of supermassive black‑hole growth across cosmic time.