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

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 spectroscopy pairwise combinations observed across different epochs for $\sim90,000$ AGNs. We estimate 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 $L$, Eddington ratio, and rest-frame wavelength ($λ$). The analysis, with each parameter held fixed, reveals that SFs depend primarily 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 $τ\propto L^{0.62\pm0.07} λ^{1.74\pm0.23}$. This result is broadly consistent with predictions from the standard accretion disk model ($τ\propto L^{0.5} λ^{2}$). However, when considering only shorter wavelengths ($λ\leq 3050$ Å) to minimize contamination from the host galaxy and the Balmer continuum, the power-law index for $λ$ drops significantly to $1.12 \pm 0.24$. This value is lower than predicted by approximately $3-$4\ σ$, suggesting 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 allow robust estimation of continuum fluxes without interference from strong emission lines.