2021ApJ...917...99Y

We report Atacama Large Millimeter/Submillimeter Array (ALMA) observations of the dust continuum and [C II] emission of the host galaxy of J0439+1634, a gravitationally lensed quasar at z = 6.5. Gravitational lensing boosts the source-plane resolution to ∼0.''15 (∼0.8 kpc). The lensing model derived from the ALMA data is consistent with the fiducial model in Fan et al. based on HST imaging. The host galaxy of J0439+1634 can be well-fitted by a Sersic profile consistent with an exponential disk, both in the far-infrared (FIR) continuum and the [C II] emission. The overall magnification is 4.53 ± 0.05 for the continuum and 3.44 ± 0.05 for the [C II] line. The host galaxy of J0439+1634 is a compact ultraluminous infrared galaxy, with a total star formation rate (SFR) of 1.56 x 10³M_☉ yr^–1 after correcting for lensing and an effective radius of 0.74 kpc. The resolved regions in J0439+1634 follow the "[C II] deficit," where the [C II]-to-FIR ratio decreases with FIR surface brightness. The reconstructed velocity field of J0439+1634 appears to be rotation-like. The maximum line-of-sight rotation velocity is 130 km s^–1 at a radius of 2 kpc. However, our data cannot be fit by an axisymmetric thin rotating disk, and the inclination of the rotation axis, i, remains unconstrained. We estimate the dynamical mass of the host galaxy to be 7.9sin^–2(i)×10⁹M_☉. J0439+1634 is likely to have a high gas-mass fraction and an oversized SMBH compared to local relations. The SFR of J0439+1634 reaches the maximum possible values, and the SFR surface density is close to the highest value seen in any star-forming galaxy currently known in the universe.