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We report ALMA observations of the dust continuum and {\cii} emission of thehost galaxy of J0439+1634, a gravitationally lensed quasar at $z=6.5$.Gravitational lensing boosts the source-plane resolution to $\sim0\farcs15$$(\sim0.8\text{ kpc})$. The lensing model derived from the ALMA data isconsistent with the fiducial model in \citet{fan19} based on {\it HST} imaging.The host galaxy of J0439+1634 can be well-fitted by a S\'ersic profileconsistent with an exponential disk, both in the far-infrared (FIR) continuumand the {\cii} emission. The overall magnification is $4.53\pm0.05$ for thecontinuum and $3.44\pm0.05$ for the {\cii} line. The host galaxy of J0439+1634is a compact ultra-luminous infrared galaxy, with a total star formation rate(SFR) of $1.56\times10^{3}M_\odot/\text{year}$ after correcting for lensing andan effective radius of $0.74$ kpc. The resolved regions in J0439+1634 followthe ``{\cii} deficit," where the {\cii}-to-FIR ratio decreases with FIR surfacebrightness. The reconstructed velocity field of J0439+1634 appears to berotation-like. The maximum line-of-sight rotation velocity of 130 km/s at aradius of 2 kpc. However, our data cannot be fit by an axisymmetric thinrotating disk, and the inclination of the rotation axis, $i$, remainsunconstrained. We estimate the dynamical mass of the host galaxy to be$7.9\sin^{-2}(i)\times10^{9}M_\odot$. J0439+1634 is likely to have a highgas-mass fraction and an oversized SMBH compared to local relations. The SFR ofJ0439+1634 reaches the maximum possible values, and the SFR surface density isclose to the highest value seen in any star-forming galaxy currently known inthe universe.

astrophysical journal/the astrophysical journal

ALMA Observations of the Sub-kpc Structure of the Host Galaxy of a z=  6.5 Lensed Quasar: A Rotationally-Supported Hyper-Starburst System at the  Epoch of Reionization