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

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.