Spatially Resolved Interstellar Medium and Highly-Excited Dense
  Molecular Gas in the Most Luminous Quasar at z=6.327
  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, we
performed multi-band ALMA observations, aiming at mapping the dust continuum,
[CII] and CO(6-5) emission lines with sub-kiloparsec scale resolution, as well
as detecting high-J CO lines in CO(11-10), CO(10-9), and CO(7-6). The galaxy
size is measured to be $R_{\rm major}=3.6\pm0.2$ kpc from the high resolution
continuum observations. No ordered motion on kilo-parsec scales was found in
both [CII] and CO(6-5) emissions. The velocity dispersion is measured to be
161$\pm$7 km s$^{-1}$, $\sim$3 times smaller than that estimated from the local
M-$\sigma$ relation. In addition, we found that the CO emission is more
concentrate (a factor of 1.8$\pm$0.4) than the [CII] emission. Together with
CO(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 component
at $\sim24$ K with a density of $n_{\rm (H_2)}$=10$^{4.5}$ cm$^{-3}$, and a
warm 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, which
indicates that it has either a high dust emissivity $\beta\gtrsim2$ or a hot
dust temperature $T_{\rm dust}\gtrsim60$ K, or a combination of both factors.
The highly excited CO emission and hot dust temperature suggest that the
powerful AGN in J0100+2802 could contribute to the gas and dust heating
although future observations are needed to confirm this.
