ALMA High- J CO Spectroscopy of High-redshift Galaxies. II. 0 . ″ 03 Resolution CO Kinematics Reveal Super-Eddington Accretion in a Dust-obscured Galaxy at z = 3.111

We present ultrahigh-resolution ( 0 . ″ 03 ≈ 230 pc) Atacama Large Millimeter/submillimeter Array (ALMA) observations of the hyperluminous dust-obscured galaxy W2305−0039 at z = 3.111, targeting the CO J = 7–6 and J = 11–10 lines. The CO (11–10) emission is extremely compact and exhibits anomalously high excitation relative to CO (7–6) within the central ≲500 pc. X-ray-dominated region models successfully reproduce this excitation, providing strong evidence for intense X-ray irradiation by a deeply obscured active galactic nucleus (AGN), while photodissociation region models fail to match the observed ratio. Forward modeling of the nuclear CO(11–10) position–velocity diagram yields a dynamical black hole mass of log ( M BH / M ⊙ ) = 8 . 3 − 0.6 + 0.7 and an intrinsic gas velocity dispersion of σ gas = 27 7 − 14 + 16 km s −1 . Combined with the AGN luminosity from infrared spectral energy distribution decomposition, these measurements imply a highly super-Eddington accretion state with λ Edd ≳ 4. Our results provide dynamical evidence that the most rapid phases of black hole growth can occur within a compact, heavily obscured nuclear region. Extending ALMA beyond its current 16 km maximum baselines will be essential for pushing such dynamical measurements to tens-of-parsec scales and resolving the black hole sphere of influence in massive galaxies at z ≳ 6.