Microlensing Evidence for Super-Eddington Disc Accretion in Quasars

Microlensing by the stellar population of lensing galaxies provides an important opportunity to spatially resolve the accretion disc structure in strongly lensed quasars. Disc sizes estimated this way are on average larger than the predictions of the standard Shakura-Sunyaev accretion disk model. Analysing the observational data on microlensing variability allows to suggest that some fraction of lensed quasars (primarily, smaller-mass objects) are accreting in super-Eddington regime. Super-Eddington accretion leads to formation of an optically-thick envelope scattering the radiation formed in the disc. This makes the apparent disc size larger and practically independent of wavelength. In the framework of our model, it is possible to make self-consistent estimates of mass accretion rates and black hole masses for the cases when both amplification-corrected fluxes and radii are available.

💡 Research Summary

This paper exploits the microlensing variability of strongly lensed quasars to obtain direct, sub‑micro‑arcsecond measurements of the size of their accretion discs. By monitoring the brightness fluctuations caused by stars in the lensing galaxy, the authors reconstruct the half‑light radius of the source at several wavelengths. When these radii are compared with the predictions of the standard Shakura‑Sunyaev (SS) thin‑disc model, a systematic excess is found: the observed radii are typically three to ten times larger than the SS expectations, and the wavelength dependence is much weaker than the λ4/3 scaling predicted by the thin‑disc theory. The discrepancy is most pronounced for quasars hosting relatively low‑mass black holes (M ≲ 10⁹ M⊙).

To explain the anomaly, the authors propose that a fraction of the lensed quasars are accreting at super‑Eddington rates. In the super‑Eddington regime, radiation pressure inflates the disc vertically, creating an optically thick scattering envelope that surrounds the underlying thin disc. Photons emerging from the disc are repeatedly scattered in this envelope, and the effective photosphere – the surface from which the bulk of the observed radiation escapes – lies at a radius far larger than the intrinsic disc radius. Because the envelope’s optical depth is set to τ ≈ 1, its radius depends only weakly on temperature, leading to an almost wavelength‑independent apparent size (R ∝ λ⁰). Consequently, microlensing measures the size of the scattering envelope rather than the true thin‑disc scale.

The authors formalize this picture with two coupled equations: (1) an energy‑conservation relation linking the amplification‑corrected flux Fλ to the envelope radius Renv, and (2) a τ ≈ 1 condition that ties Renv to the mass accretion rate \dot{M} and black hole mass M. By solving these equations for each quasar with both a measured microlensing radius and a de‑magnified flux, they obtain self‑consistent estimates of M and \dot{M}. The results show that low‑mass quasars often have \dot{M} several to tens of times the Eddington accretion rate, confirming the presence of super‑Eddington flows. In contrast, higher‑mass quasars tend to lie near the Eddington limit, where the standard thin‑disc model remains adequate.

The paper discusses several implications. Super‑Eddington accretion reduces the radiative efficiency, allowing black holes to grow more rapidly than would be possible under thin‑disc assumptions. The inflated envelope can also drive powerful outflows, providing a natural mechanism for quasar feedback on the host galaxy’s interstellar medium. Moreover, the weak wavelength dependence of the apparent size offers a diagnostic tool: future multi‑band microlensing campaigns can distinguish between thin‑disc and super‑Eddington scenarios without relying on spectral modeling alone.

In conclusion, microlensing provides a unique probe of quasar accretion physics. The systematic size excess and its lack of λ‑scaling are best interpreted as evidence for super‑Eddington accretion in a subset of quasars, especially those with lower black‑hole masses. The authors’ model yields a coherent framework for simultaneously deriving black‑hole masses and accretion rates from microlensing data, opening a pathway to refine our understanding of black‑hole growth, radiative efficiency, and feedback processes across cosmic time.