Central concentration of warm and dense molecular gas in a strongly lensed submillimeter galaxy at z=6

We report the detection of the CO(12-11) line emission toward G09-83808 (or H-ATLAS J090045.4+004125), a strongly-lensed submillimeter galaxy at $z = 6.02$, with Atacama Large Millimeter/submillimeter Array observations. Combining previously detected [O III]$\,88\:\mathrm{\mu m}$, [N II]$\,205\:\mathrm{\mu m}$, and dust continuum at 0.6$\:$mm and 1.5$\:$mm, we investigate the physical properties of the multi-phase interstellar medium in G09-83808. A source-plane reconstruction reveals that the region of the CO(12-11) emission is compact ($R_\mathrm{{e, CO}}=0.49^{+0.29}_{-0.19}\,\mathrm{kpc}$) and roughly coincides with that of the dust continuum. Non-local thermodynamic equilibrium radiative transfer modeling of CO spectral-line energy distribution reveals that most of the CO(12-11) emission comes from a warm (kinetic temperature of $T_{\mathrm{kin}}=320\pm170\:$K) and dense ($\log(n_{\mathrm{H2}}/\mathrm{cm^{-3}})=5.4\pm0.6$) gas, indicating that the warm and dense molecular gas is concentrated in the central 0.5-kpc region. The luminosity ratio in G09-83808 is estimated to be $L_\mathrm{{CO(12-11)}} / L_\mathrm{{CO(6-5)}}=1.1\pm0.2$. The high ratio is consistent with those in local active galactic nuclei (AGNs) and $6<z