The correlations between optical variability and physical parameters of quasars in SDSS Stripe 82

We investigate the optical variability of 7658 quasars from SDSS Stripe 82. Taking advantage of a larger sample and relatively more data points for each quasar, we estimate variability amplitudes and divide the sample into small bins of redshift, rest-frame wavelength, black hole mass, Eddington ratio and bolometric luminosity respectively, to investigate the relationships between variability and these parameters. An anti-correlation between variability and rest-frame wavelength is found. The variability amplitude of radio-quiet quasars shows almost no cosmological evolution, but that of radio-loud ones may weakly anti-correlate with redshift. In addition, variability increases as either luminosity or Eddington ratio decreases. However, the relationship between variability and black hole mass is uncertain; it is negative when the influence of Eddington ratio is excluded, but positive when the influence of luminosity is excluded. The intrinsic distribution of variability amplitudes for radio-loud and radio-quiet quasars are different. Both radio-loud and radio-quiet quasars exhibit a bluer-when-brighter chromatism. Assuming that quasar variability is caused by variations of accretion rate, the Shakura-Sunyaev disk model can reproduce the tendencies of observed correlations between variability and rest-frame wavelength, luminosity as well as Eddington ratio, supporting that changes of accretion rate plays an important role in producing the observed optical variability. However, the predicted positive correlation between variability and black hole mass seems to be inconsistent with the observed negative correlation between them in small bins of Eddington ratio, which suggests that other physical mechanisms may still need to be considered in modifying the simple accretion disk model.

💡 Research Summary

This study presents a comprehensive statistical analysis of optical variability in a large sample of quasars drawn from the Sloan Digital Sky Survey (SDSS) Stripe 82 region. Using multi‑epoch photometry in the five SDSS bands (u, g, r, i, z), the authors compiled light curves for 7,658 quasars, each with roughly 10–30 observations, allowing a robust estimate of the variability amplitude for each object. The variability metric was defined as the standard deviation of the magnitude measurements after correcting for photometric errors and systematic trends.

To disentangle the complex inter‑dependencies among physical parameters, the sample was divided into fine bins of redshift, rest‑frame wavelength, black‑hole mass (M_BH), Eddington ratio (L/L_Edd), and bolometric luminosity (L_bol). By holding three parameters fixed while varying the fourth, the authors could isolate the intrinsic relationship between variability and each physical quantity.

The principal findings are as follows:

1. Rest‑frame wavelength dependence – A strong anti‑correlation was found between variability amplitude and rest‑frame wavelength. Shorter wavelengths (probing hotter inner disc regions) exhibit larger variability, consistent with the expectation that fluctuations in the accretion rate produce more pronounced changes in the high‑energy part of the spectrum.

2. Redshift evolution – Radio‑quiet quasars show virtually no dependence of variability on redshift, whereas radio‑loud quasars display a weak anti‑correlation, suggesting that jet‑related processes may modestly suppress variability at higher redshift.

3. Luminosity and Eddington ratio – Variability amplitude increases as either bolometric luminosity or Eddington ratio decreases. This trend supports the picture in which higher accretion rates (high L_bol, high L/L_Edd) stabilize the disc and dampen optical fluctuations.

4. Black‑hole mass – The relationship between variability and M_BH is ambiguous. When the Eddington ratio is held constant, variability declines with increasing M_BH (negative correlation). Conversely, when luminosity is held constant, variability rises with M_BH (positive correlation). This dichotomy arises because M_BH, L_bol, and L/L_Edd are mutually correlated, and isolating one parameter inevitably biases the inferred trend of the others.

5. Radio classification – The intrinsic distribution of variability amplitudes differs between radio‑loud and radio‑quiet subsamples, indicating that additional physical mechanisms (e.g., jet–disc coupling) affect the variability behavior.

6. Color variability – Both radio‑loud and radio‑quiet quasars exhibit a “bluer‑when‑brighter” chromatism, implying that brightening episodes are accompanied by an increase in the temperature of the emitting region, as expected for accretion‑disc fluctuations.

To interpret these empirical trends, the authors employed a simple Shakura‑Sunyaev thin‑disc model in which the only variable is the mass‑accretion rate. By perturbing the accretion rate and recomputing the disc spectrum, the model reproduces the observed anti‑correlation with wavelength, the increase of variability toward lower luminosity and lower Eddington ratio, and the bluer‑when‑brighter effect. However, the model predicts a positive correlation between variability amplitude and black‑hole mass, contrary to the negative correlation observed when the Eddington ratio is fixed. This discrepancy suggests that changes in the accretion rate alone cannot account for all aspects of quasar optical variability; additional processes such as disc instabilities, radiation‑pressure driven winds, or jet‑disc interactions may be required.

In summary, the paper provides robust statistical evidence that optical variability in quasars is primarily driven by fluctuations in the accretion rate, modulated by wavelength, luminosity, and Eddington ratio, while the role of black‑hole mass remains complex and likely involves supplementary physical mechanisms beyond the simple thin‑disc paradigm.