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We present new Atacama Large Millimeter/submillimeter Array (ALMA)observations of the dust continuum and [C II] 158 $\mu$m fine structure lineemission towards a far-infrared-luminous quasar, ULAS J131911.29$+$095051.4 at$z=6.13$, and combine the new Cycle 1 data with ALMA Cycle 0 data. The combineddata have an angular resolution $\sim$ $0.3$, and resolve both the dustcontinuum and the [C II] line emission on few kpc scales. The [C II] lineemission is more irregular than the dust continuum emission which suggestsdifferent distributions between the dust and [C II]-emitting gas. The combineddata confirm the [C II] velocity gradient that we previously detected in lowerresolution ALMA image from Cycle 0 data alone. We apply a tilted ring model tothe [C II] velocity map to obtain a rotation curve, and constrain the circularvelocity to be 427 $\pm$ 55 km s$^{-1}$ at a radius of 3.2 kpc with aninclination angle of 34$^\circ$. We measure the dynamical mass within the 3.2kpc region to be 13.4$_{-5.3}^{+7.8}$ $\times 10^{10}\,M_{\odot}$. This yieldsa black hole and host galaxy mass ratio of 0.020$_{-0.007}^{+0.013}$, which isabout 4$_{-2}^{+3}$ times higher than the present-day $M_{\rm BH}$/$M_{\rmbulge}$ ratio. This suggests that the supermassive black hole grows the bulk ofits mass before the formation of the most of stellar mass in this quasar hostgalaxy in the early universe.

Gas dynamics of a luminous $z$ = 6.13 quasar ULAS J1319$+$0950 revealed by ALMA high resolution observations