Characterising the X-ray variability of QSOs to the highest Eddington ratios and black hole masses with eROSITA light curves

TL;DR

This work addresses how X-ray variability from QSOs traces the inner accretion flow across the most massive black holes and highest Eddington ratios. It introduces eBExVar, a hierarchical Bayesian framework that models Poisson X-ray counts to infer the population-level ensemble NEV from multi-epoch eROSITA light curves of SDSS DR16 QSOs. The authors find a clear anti-correlation between NEV and $M_{BH}$ on rest-frame timescales of months and a surprising U-shaped dependence on $\\lambda_{Edd}$, with NEV increasing toward the Eddington limit in several mass bins, challenging simple PSD expectations. They argue that an additional variability component (e.g., winds/shielding or corona geometry changes) is required near the Eddington limit and highlight the need for future hard X-ray timing to disentangle absorption from intrinsic variability, with implications for understanding the innermost accretion physics of QSOs.

Abstract

An important diagnostic of the inner structure of accretion flows onto supermassive black holes are the stochastic flux variations at X-ray wavelengths. Despite its significance, a systematic characterisation of the statistical properties of the X-ray variability to the highest Eddington ratios and most massive black holes is still lacking. In this paper we address this issue using SRG/eROSITA 5-epoch light curves to characterise the mean X-ray variability of optically selected SDSS QSOs extending to black holes masses of $10^{10}$ solar and accretion rates close to the Eddington limit. The adopted variability statistic is the ensemble normalised excess variance, which is measured using a novel hierarchical Bayesian model (eBExVar) tailored to the Poisson nature of the X-ray light curves. We find a clear anti-correlation of the ensemble variability with black hole mass, extending previous results to time scales of months. This can be interpreted as evidence for an X-ray corona size and/or physical conditions that scale with black holes mass. We also find an unexpected increase of the ensemble normalised excess variance close to the Eddington limit, which is contrary to the predictions of empirical variability models. This result suggests an additional variability component for fast growing black holes that may be related to systematic variations of the hot corona size with Eddington ratio or shielding of the hot corona by an inner puffed-up disk and/or outflows.

Figures (18)

• Figure 1: Distribution of the baseline sample of SDSS DRQ16 QSOs (see Section \ref{['sec:observations']}) on the Eddington ratio vs black hole mass plane. The contour levels are chosen to enclose 34, 68, 95 and 99 per cent of the QSO population. The 1-dimensional projections of this distribution along the black hole mass and Eddington ratio axes are also shown by the histograms on the top and to the right of the main panel respectively.
• Figure 2: Distribution of the baseline sample of SDSS DRQ16 QSOs (see Section \ref{['sec:observations']}) on the bolometric luminosity vs redshift plane. The contour levels are chosen to enclose 34, 68, 95 and 99 per cent of the QSO population. The 1-dimensional projections of this distribution along the bolometric luminosity and redshift axes are also shown by the histograms on the right and at the top of the main panel respectively.
• Figure 3: Histogram of the rest-frame light-curve duration probed by the baseline sample of SDSS DRQ16 QSOs (see Section \ref{['sec:observations']}).
• Figure 4: Example light curve of the SDSS DRQ16 QSO 022040.01-084545.3. The top panel plots the observed eROSITA photon counts (blue filled circles) as a function of the observation epoch in years. The errorbars associated with each point are Poisson uncertainties. The bottom panel plots the estimated photon count rate of the same source as function of time in years. The single epoch rates are inferred from eBExVar (see Section \ref{['sec:method']}, parameter $f_{i}$ in Equation \ref{['eq:like-single']} or $f_{i,k}$ in Equation \ref{['eq:like-ensemble']}). The uncertainties correspond to the 68% confidence interval around the median of the posterior distributions of the single epoch photon count rates. The dashed black line shows the mean count rate of the light curve also inferred from the Bayesian approach of Section \ref{['sec:method']} (i.e. parameter $\mu$ in Equation \ref{['eq:like-single']} or $\mu_k$ in Equation \ref{['eq:like-ensemble']}). The shaded region is the $1\,\sigma$ uncertainty of the mean count rate.
• Figure 5: Inferred log-normal distribution of the normalised excess variance for the sample of SDSS DRQ16 QSOs with black hole masses in the range $\log\,M_{BH} = \rm [8.0,8.5]$ and Eddington ratios in the interval $\log\,\lambda_{Edd} = \rm [-0.5,0.0]$. The shaded region shows the 68th confidence interval of the reconstructed log-normal distribution of the population using the posteriors of the model parameters $\varSigma$, $B$ of Equation \ref{['eq:like-ensemble']}. The histogram is constructed from the inferred $\sigma_{NEV, k}$ (see Equation \ref{['eq:like-ensemble']}) of individual light curves.