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

¹ INAF – Osser vatorio Astronomico di Capodimonte Salita Moiariello 16 80131 Napoli, Italy
² Dipartimento di Fisica “Ettore Pancini”, Università di Napoli Federico II Via Cinthia 9 80126 Napoli, Italy
³ Department of Physics and Institute of Theoretical and Computational Physics, University of Crete 71003 Heraklion, Greece
⁴ Institute of Astrophysics, FORTH GR-71110 Heraklion, Greece
⁵ INFN – Sezione di Napoli Via Cinthia 9 80126 Napoli, Italy
⁶ Millennium Institute of Astrophysics, Nuncio Monseñor Sótero Sanz 100, Of 104 Providencia Santiago, Chile
⁷ Instituto de Alta Investigación, Universidad de Tarapacá Casilla 7D Arica, Chile
⁸ INAF – Osservatorio Astrofisico di Torino Via Osservatorio 20 I-10025 Pino Torinese, Italy
⁹ Ruđer Bošković Institute Bijenička Cesta 54 10000 Zagreb, Croatia

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Received: 29 August 2025
Accepted: 17 November 2025

Abstract

Context. Variability is one of the most striking features of quasars, observed at all timescales and throughout the electromagnetic spectrum. The study of variability properties and their 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.

Aims. 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, from 10⁻¹ to 10⁻³ day⁻¹ in the rest frame.

Methods. The light curves of multiple surveys were matched and cross-calibrated to reach ∼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 (as a proxy of rest-frame wavelength) and measured the ensemble power spectral density (PSD) in each bin. The power spectra of SDSS, ZTF, and Gaia were measured independently. We did not measure the PSD on PS1 data due to a more erratic cadence, as well as the similarity in terms of baseline compared to the other surveys. However, we discuss the use of interpolation techniques that eventually enable us to use the data together and probe frequencies lower than 10⁻³ day⁻¹ in the rest frame.

Results. We find significant evidence that the long-term ultraviolet/optical variability of quasars is stationary, as the ensemble PSD estimates from SDSS, Gaia, and ZTF are consistent within the errors despite their originating from different surveys and different 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 model PSD associated with a damped random walk model (spectral indices –2 and 0) is significantly worse. The power spectrum amplitude below the break does not depend on black hole mass, but there is some evidence to support an anti-correlation with the accretion rate. The bending frequency, instead, scales with the black hole mass as ν_b ∝ M_BH^−0.6±0.1 and it does not depend on the accretion rate.