Continuum variability in multi-epoch quasar spectra from the Sloan Digital Sky Survey

¹ Department of Astronomy, Yonsei University, 50 Yonsei-ro, Seoul 03722, Korea
² Kavli Institute for Astronomy and Astrophysics, Peking University, Beijing 100871, China
³ Department of Astronomy and Atmospheric Sciences, Kyungpook National University, Daegu 41566, Korea
⁴ Department of Astronomy, School of Physics, Peking University, Beijing 100871, China

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 16 October 2025
Accepted: 12 November 2025

Abstract

We examine the continuum variability of active galactic nuclei (AGNs) by analyzing the multi-epoch spectroscopic data from the Sloan Digital Sky Survey. To achieve this, we utilized approximately 2 million spectroscopic pairwise combinations observed across different epochs for ∼90 000 AGNs. We estimated the ensemble variability structure function (SF) for subsamples categorized by various AGN properties, such as black hole mass, AGN luminosity (L), and Eddington ratio, to investigate how AGN variability depends on these parameters. We found that the SFs are strongly correlated with L, the Eddington ratio, and the rest-frame wavelength (λ). The analysis, with each parameter held fixed, reveals that SFs primarily depend on L and λ, but not on the Eddington ratio. Consequently, under the assumption that AGNs follow a universal SF, we found that the variability timescale (τ) is proportional to both L and λ, expressed as τ ∝ L^{0.62 ± 0.07}λ^{1.74 ± 0.23}. This result is broadly consistent with predictions from the standard accretion disk model (τ ∝ L^0.5λ²). However, when only considering shorter wavelengths (λ ≤ 3050 Å) to minimize contamination from the host galaxy and the Balmer continuum, the power-law index for λ drops significantly to 1.12 ± 0.24. This value is lower than predicted by approximately 3–4 σ, which suggests that the radial temperature profile may be systematically steeper than that predicted by the standard disk model, although other mechanisms may also contribute to this discrepancy. These findings highlight the power of temporal spectroscopic data in probing AGN variability, as they enable a robust estimation of continuum fluxes without interference from strong emission lines.