Accretion-disk sizes in two quasars with interferometrically resolved broad-line regions at z =2.3 and z =4.0

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Abstract
We present the first direct comparison between accretion-disk (AD) and broad-line region (BLR) sizes in quasars at z > 2. The comparison was possible because we combined continuum reverberation mapping with interferometric BLR constraints from GRAVITY and GRAVITY+. Using medium-band photometric monitoring with the MPG/ESO 2.2 m telescope, we measured interband continuum lags in two quasars: SDSS J092034.17+065718.0 at z = 2.33 (J0920) and SMSS J052915.80–435152.0 at z = 3.96 (J0529). These are two of the most luminous quasars known ( L bol ~ 10 48 erg s −1 ) and currently the only two quasars at z > 2 with spatially resolved BLRs and dynamical black hole masses measured via interferometry, making this comparison uniquely possible. We detect significant con-tinuum lags in both quasars that increase monotonically with wavelength. The inferred UV disk sizes are R AD = 4.35 −0.91 +0.78 light-days for J0529 and R AD = 3.15 −0.48 +0.50 light-days for J0920. For J0920, which accretes at λ Edd ~ 7–20, the disk size is consistent with standard thin-disk expectations, a surprising result given that the standard thin-disk approximation is not expected to hold in this super-Eddington regime. For J0529, the disk size is consistent with thin-disk predictions under the single-epoch black hole mass but would imply disk inflation by a factor of a few if the GRAVITY+ dynamical mass – which is an order of magnitude lower – is adopted instead. This tension illustrates that UV continuum disk sizes provide an independent physical scale that any self-consistent model of the black hole mass and accretion rate must satisfy. This provides an addition way of studying objects where BLR kinematics are dominated by outflows rather than virial motion. A comparison with the interferometric BLR sizes reveals pronounced radial hierarchies, with R BLR / R AD ~ 270 for J0529 (H β ) and ~ 115 for J0920 (H α ). The successful detection of lags in both quasars at L bol ~ 10 48 erg s −1 demonstrates that continuum reverberation mapping remains feasible even at the low-amplitude variability end expected for the most luminous systems, opening a path toward extending AD size measurements to larger samples with wide-field surveys such as the Vera C. Rubin Observatory’s LSST.

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