A thin disk and a nearly universal accretion rate in luminous quasars

TL;DR

This work proposes that luminous SDSS quasars are powered by a standard optically thick, geometrically thin accretion disk operating at a nearly fixed Eddington ratio, $\lambda_{\rm EDD} \approx 0.1$, which naturally explains the observed uniformity of their optical–UV continua. By analyzing SDSS DR16 masses and luminosities, the authors show the intrinsic dispersion in $\lambda_{\rm EDD}$ is very small, implying luminosity primarily traces $M_{\rm BH}$ and that a single parameter governs quasar emission. They test the scenario against the observed SEDs and the Baldwin effect, finding that the predicted spectral peak positions, the He II $1640$ line proxy, and line–continuum slopes ($\alpha \approx 0.65$–$0.75$ with low dispersion) align with the constant-$\lambda_{\rm EDD}$ model. The results yield tighter black hole mass estimates and argue against a significant population of super-Eddington SDSS quasars, though applicability to obscured or non-blue quasars remains to be established. Overall, the study reduces the quasar emission physics to a single dominant parameter, $M_{\rm BH}$, modulated by a nearly universal accretion rate, with important implications for mass estimation and the interpretation of quasar spectra in blue, optically selected samples.

Abstract

Quasars accretion models predict a broad range of optical and ultraviolet properties that depend primarily on black hole mass and accretion rate. Yet, most optically selected luminous quasars display strikingly similar continuum spectra. We show that this uniformity can be explained by a nearly constant luminosity to mass (Eddington) ratio, L_EDD and by thermal emission from a standard, optically thick, geometrically thin accretion disc. A standard disk with an Eddington ratio L_EDD=0.1 reproduces both the black hole mass/luminosity distribution of Sloan Digital Sky Survey (SDSS) quasars and their principal continuum properties. In this framework, the spectral energy distribution peaks beyond the observable ultraviolet range for nearly all sources. We show that the few quasars, expected to be cold enough to shift the peak into the observable region, indeed show this behaviour. This scenario is further supported by an analysis of the relation between the luminosity of the main broad emission lines and the continuum luminosity (i.e. the Baldwin effect). We find that 1) the observed slopes of the line to continuum relations match the expectations from the standard disk model, if we assume that the line emission is a good proxy of the ionizing luminosity; 2) the dispersions of the line-continuum luminosity relations are very small (as small as 0.13 dex), suggesting that the physics of the disk-broad line region system is dominated by only one parameter (the black hole mass) with a nearly constant Eddington ratio. Finally, we notice that our hypothesis of constant L_EDD=0.1 provides a black hole mass estimate (based on the observed luminosity) with a smaller error than the virial estimate.

Figures (8)

• Figure 1: Eddington ratio versus bolometric luminosity for a sample of SDSS quasars. The luminosities are obtained from the monochromatic values of wu2022 assuming a standard disk model, while the black hole masses are estimated with the virial method vestergaard2006. The diamonds show the mean $\lambda_{{\rm EDD}}$ values in small luminosity bins, with error bars showing their dispersions. The total distributions are shown as magenta histograms in the side panels. The green histogram shows the “intrinsic” distribution of $\lambda_{{\rm EDD}}$ needed to reproduce the small increase of $\lambda_{{\rm EDD}}$ with luminosity. The width of this distribution is $\sigma$=0.05 dex. Contours enclose 68, 95 and 99% of the underlying population.
• Figure 2: Central panel: expected peak wavelength of the quasar spectrum based on virial masses (x-axis) and on our assumption of constant Eddington ratio (y-axis). The pink and green lines show the maximum value $\lambda\sim1,600$ Å (corresponding to a maximum disk temperature $T_{MAX}=90,000~K$) required to see a clear spectral change with respect to the disk power law in the observed UV spectrum, i.e. at wavelengths shorter than the Lyman limit. While the virial masses predict a significant fraction of “cold” objects that should show the emission peak in the observed spectral range (and it is not seen), we predict that only very few quasars are cold enough to show the peak. Right panel: stacked spectra of SDSS quasars with expected peak temperatures $T_{MAX}> 90,000~K$. The values of $T_{MAX}$ are obtained from a standard disk model with a black hole mass $M_{BH}$ estimated with the virial method. The dashed line shows the expected continuum spectrum based on these assumptions, superimposed (not fitted) on the data and rescaled to the average continuum intensity at 2,500 Å, as estimated in the SDSS DR16 quasar catalogue. The solid line shows the expected average spectrum assuming a constant Eddington ratio $\lambda_{{\rm EDD}}$=0.1. Left panel: the same, with $T_{MAX}$ estimated from a standard disk model with $\lambda_{{\rm EDD}}$=0.1. The mismatch between the observed spectra and the predictions based on the virial masses is obvious. Conversely, the average spectra with $\lambda_{{\rm EDD}}$=0.1 are in good agreement with the observed data.
• Figure 3: Test of disk models based on three observables in quasar spectra: the continuum luminosity at 3,000 Å, the FWHM of the Mg II $\lambda$ 2800 Å line and the equivalent width of the high ionization He II $\lambda$ 1640 Å line. Assuming that the equivalent width of the He II is proportional to the ionizing luminosity it is possible to predict its dependence on the black hole mass and Eddington ratio in several physical scenarios: a standard disk assuming virial black hole masses and a constant (e.g. R06; green arrow) or luminosity-dependent bolometric correction (blue arrow); the accretion disk model of hopkins2025 (orange arrow); a standard disk with constant $\lambda_{{\rm EDD}}$ (red arrow). The latter scenario is the only one in agreement with the observational results obtained via the PCA and the linear regression.
• Figure 4: Examples of line-continuum relations for three broad emission lines (Mg II $\lambda 2800$ Å in the upper panel, C III] $\lambda~1909$ Å in the middle panel, C IV $\lambda$ 1549 Å in the lower panel) in three small redshift intervals ($\Delta[(\log(z)]\sim0.03$. The values in the labels refer to the best-fit slope, $\alpha$, and the intrinsic dispersion $\delta$ with respect to the linear log-log relation.
• Figure 5: Best fit slopes as a function of redshift for all the analyzed emission lines. The black lines and the grey region show the average slope and its uncertainty for each line. The red dashed lines show the expectation based on a standard disk model (see text for details). The lower part shows the intrinsic dispersion in each redshift bin.