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

Vincenzo Petrecca, Iossif E. Papadakis, Maurizio Paolillo, Demetra De Cicco, Franz E. Bauer, Maria Isabel Carnerero, Claudia Maria Raiteri, Marta Fatovic

TL;DR

This work constrains the ensemble UV/optical power spectra of Stripe-82 quasars by combining SDSS, PS1, Gaia, and ZTF light curves to cover rest-frame frequencies from approximately $10^{-1}$ to $10^{-3}$ day$^{-1}$. The authors find a bending power-law PSD with a high-frequency slope of $-2.7$ and a low-frequency slope of $-1$, with a bend frequency scaling as $ν_b \propto M_{BH}^{-0.6\pm0.1}$ and little dependence on accretion rate, while a damped random walk model provides a poorer fit. Moreover, the PSD appears stationary over ~20 years across surveys, and its amplitude does not strongly depend on black hole mass, offering constraints on disc variability and potential X-ray reprocessing scenarios. The study advances quasar variability analysis by delivering a broad-band, cross-survey PSD and establishes a legacy dataset to inform LSST-era time-domain AGN research.

Abstract

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.

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

TL;DR

This work constrains the ensemble UV/optical power spectra of Stripe-82 quasars by combining SDSS, PS1, Gaia, and ZTF light curves to cover rest-frame frequencies from approximately to day. The authors find a bending power-law PSD with a high-frequency slope of and a low-frequency slope of , with a bend frequency scaling as and little dependence on accretion rate, while a damped random walk model provides a poorer fit. Moreover, the PSD appears stationary over ~20 years across surveys, and its amplitude does not strongly depend on black hole mass, offering constraints on disc variability and potential X-ray reprocessing scenarios. The study advances quasar variability analysis by delivering a broad-band, cross-survey PSD and establishes a legacy dataset to inform LSST-era time-domain AGN research.

Abstract

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 \propto M_{\mathrm{BH}}^{-0.6\pm0.1} and does not depend on the accretion rate.

Paper Structure

This paper contains 14 sections, 11 equations, 13 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Data
  3. Estimating the power spectrum.
  4. High-frequency PSD from ZTF
  5. Low-frequency PSD from SDSS, ZTF, and Gaia
  6. The broad-band power spectrum of quasars
  7. The dependence of the quasar PSD on BH mass and accretion rate
  8. Discussion and conclusions
  9. Comparison with X-rays and additional physical constraints
  10. Comparison with P24 and other past results
  11. Very-low-frequency PSD from combined light curves: Attempts at interpolation
  12. Cross-calibration of light curves
  13. PSD of simulated light curves
  14. RBF interpolation

Figures (13)

  • Figure 1: Distributions of bolometric luminosity (left panel) and BH mass (right panel) for the 8042 SDSS+PS1+ZTF quasars (red) and the subset of 4037 sources in common with Gaia DR3 (blue).
  • Figure 2: Example of r-band light curve for a Stripe-82 quasar combining SDSS (blue), PS1 (green), Gaia (orange), and ZTF (red) data. Colour corrections and calibrations are given in Appendix \ref{['subsec:agn_lc_calib']}.
  • Figure 3: Example light curve for a ZTF quasar in the r band. Grey points are the original flux measurements, while yellow stars indicate the binned-interpolated values turning each season into an evenly sampled time series to compute the high-frequency PSD in Sect. \ref{['sec:ztf_psd']}. The second half of the first season shows data points rejected from the analysis due to the quality cuts applied. Blue squares are yearly-binned points used for the low-frequency PSD in Sect. \ref{['sec:combined1']}.
  • Figure 4: Ensemble power spectrum for the master sample of the quasars. Different colours and symbols show PSD estimates calculated using various light curves, as labelled (see Sect. \ref{['sec:psd-shape']} for details).
  • Figure 5: Top panel: Best-fit PL, DRW, and BPL models to the ensemble PSD of the master sample. Horizontal lines mark the noise floor level for each model. Bottom panels: Respective best-fit residuals plots; i.e. observed PSD--model+error.
  • ...and 8 more figures