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Among more than 200 quasars known at $z\gtrsim6$, only one object, J0100+2802(z=6.327), was found hosting a $>10^{10}M_\odot$ super-massive black hole(SMBH). In order to investigate the host galaxy properties of J0100+2802, weperformed multi-band ALMA observations, aiming at mapping the dust continuum,[CII] and CO(6-5) emission lines with sub-kiloparsec scale resolution, as wellas detecting high-J CO lines in CO(11-10), CO(10-9), and CO(7-6). The galaxysize is measured to be $R_{\rm major}=3.6\pm0.2$ kpc from the high resolutioncontinuum observations. No ordered motion on kilo-parsec scales was found inboth [CII] and CO(6-5) emissions. The velocity dispersion is measured to be161$\pm$7 km s$^{-1}$, $\sim$3 times smaller than that estimated from the localM-$\sigma$ relation. In addition, we found that the CO emission is moreconcentrate (a factor of 1.8$\pm$0.4) than the [CII] emission. Together withCO(2-1) detected by VLA, we measured the CO Spectral Line Energy Distribution(SLED), which is best fit by a two-components model, including a cool componentat $\sim24$ K with a density of $n_{\rm (H_2)}$=10$^{4.5}$ cm$^{-3}$, and awarm component at $\sim224$ K with a density of $n_{\rm (H_2)}$=10$^{3.6}$cm$^{-3}$. We also fitted the dust continuum with a graybody model, whichindicates that it has either a high dust emissivity $\beta\gtrsim2$ or a hotdust temperature $T_{\rm dust}\gtrsim60$ K, or a combination of both factors.The highly excited CO emission and hot dust temperature suggest that thepowerful AGN in J0100+2802 could contribute to the gas and dust heatingalthough future observations are needed to confirm this.

Spatially Resolved Interstellar Medium and Highly-Excited Dense Molecular Gas in the Most Luminous Quasar at z=6.327