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

Abstract

We present the first direct comparison between accretion-disk (AD) and broad-line region (BLR) sizes in quasars at z > 2, combining 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 measure inter-band continuum lags in SDSS J092034.17+065718.0 at z = 2.33 (J0920) and SMSS J052915.80-435152.0 at z = 3.96 (J0529), among the most luminous quasars known (Lbol ~ 10^48 erg s^-1). These are currently the only two quasars at z > 2 with spatially resolved BLRs and dynamical black-hole masses from interferometry. We detect significant continuum lags in both quasars, increasing monotonically with wavelength. The inferred UV disk sizes are RAD = 4.35 +0.78/-0.91 light-days for J0529 and RAD = 3.15 +0.50/-0.48 light-days for J0920. For J0920, accreting at lambda_Edd ~ 7-20, the disk size is consistent with standard thin-disk expectations despite its super-Eddington regime. For J0529, the disk size agrees with thin-disk predictions using the single-epoch black-hole mass, but implies disk inflation by a factor of a few if the GRAVITY+ dynamical mass, an order of magnitude lower, is adopted. UV continuum disk sizes therefore provide an independent physical scale constraining black-hole mass and accretion-rate models, particularly where BLR kinematics are dominated by outflows. The interferometric BLR sizes reveal pronounced radial hierarchies, with RBLR/RAD ~ 270 for J0529 (Hbeta) and ~115 for J0920 (Halpha). The successful lag detections at Lbol ~ 10^48 erg s^-1 show that continuum reverberation mapping remains feasible for the most luminous systems, opening a path to larger samples with surveys such as the Vera C. Rubin Observatory's LSST.