ALMA [N \i\i ] 205 \mu m Imaging Spectroscopy of the Lensed Submillimeter galaxy ID 141 at redshift 4.24

We present the Atacama Large Millimeter/submillimeter Array (ALMA) observation of the Sub-millimeter galaxy (SMG) ID 141 at z=4.24 in the [N II] 205 $\mu$m line (hereafter [N II]) and the underlying continuum at (rest-frame) 197.6 $\mu$m. Benefiting from lensing magnification by a galaxy pair at z=0.595, ID 141 is one of the brightest z$>4$ SMGs. At the angular resolutions of $\sim 1.2\mathrm{"}$ to $1.5\mathrm{"}$ ($1\mathrm{"}\sim 6.9$ kpc), our observation clearly separates, and moderately resolves the two lensed images in both continuum and line emission at $\mathrm{S}\mathrm{/}\mathrm{N}>5$ . Our continuum-based lensing model implies an averaged amplification factor of $\sim 5.8$ and reveals that the de-lensed continuum image has the S'ersic index $\simeq 0.95$ and the S'ersic radius of $\sim 0.18\mathrm{"}(\sim 1.24$ kpc). Furthermore, the reconstructed [N II] velocity field in the source plane is dominated by a rotation component with a maximum velocity of $\sim 300$ km/s at large radii, indicating a dark matter halo mass of $\sim {10}^{12}{M}_{\odot }$. This, together with the reconstructed velocity dispersion field being smooth and modest in value ($<100$ km/s) over much of the outer parts of the galaxy, favours the interpretation of ID 141 being a disk galaxy dynamically supported by rotation. The observed [N II]/CO (7-6) and [N II]/[C II] 158 $\mu$m line luminosity ratios, which are consistent with the corresponding line ratio vs. far-infrared color correlation from local luminous infrared galaxies, imply a de-lensed star formation rate of ($1.8\pm 0.6)\times10^3M_\odot$/yr and provide an independent estimate on the size of the star-forming region $0.7_{-0.3}^{+0.3}$ kpc in radius.