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

TL;DR

The study develops an ensemble structure-function analysis of continuum variability using over 2 million SDSS spectroscopic pairings for ~90k AGNs, revealing that the variability timescale $\tau$ scales with luminosity and wavelength as $\tau \propto L^{0.62}\lambda^{1.74}$ (dropping to $\lambda^{1.12}$ when long-wavelength contamination is removed). By fixing either luminosity or Eddington ratio, the authors show luminosity is the primary driver of variability, with Eddington ratio playing a secondary role; BH mass has little impact. The results broadly agree with the standard accretion-disk framework in predicting a luminosity-wavelength dependence of variability but imply a steeper disk temperature profile than the classic model, or contamination explained by models like CHAR. The work highlights the value of time-domain spectroscopy in reliably measuring continuum variability free from strong emission-line contamination and Balmer continuum effects, offering important insights into AGN accretion physics and disk structure.

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.

Figures (8)

• Figure 1: Density distributions of luminosities at 1350 $\AA$ and 3000 $\AA$ for our sample. Red solid and dashed lines denote the best regression and its $1\sigma$ scatter, respectively. The best-fit result displayed in the panel was used to convert between the two luminosities.
• Figure 2: Distributions of BH mass and bolometric luminosity for our sample. The solid, dashed, and dotted lines correspond to Eddington ratios of 1, 0.1, and 0.01, respectively.
• Figure 3: Ensemble SF at $\Delta t < 2$ days (SF$_{\rm 2days}$) plotted against continuum brightness across different wavelengths. The solid line represents the fitting results with a smooth double power-law model.
• Figure 4: Distribution of observed spectroscopic pairwise combinations at each $\Delta t$ for our sample. Colors denote continuum wavelengths.
• Figure 5: Ensemble SFs for subgroups categorized according to bolometric luminosity ($a$), BH mass ($b$), and Eddington ratio ($c$). The size of the symbols denotes the continuum wavelength.