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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, Comment: 13 pages, 11 figures, accepted for publication in PASJ

We present observations of [NII] 205 $\mu$m, [OIII] 88 $\mu$m and dust emission in a strongly-lensed, submillimeter galaxy (SMG) at $z=6.0$, G09.83808, with the Atacama Large Millimeter/submillimeter Array (ALMA). Both [NII] and [OIII] line emissions are detected at $>12\sigma$ in the 0.8$"$-resolution maps. Lens modeling indicates that the spatial distribution of the dust continuum emission is well characterized by a compact disk with an effective radius of 0.64$\pm$0.02 kpc and a high infrared surface brightness of $\Sigma_\mathrm{IR}=(1.8\pm0.3)\times10^{12}~L_\odot$ kpc$^{-2}$. This result supports that G09.83808 is the progenitors of compact quiescent galaxies at $z\sim4$, where the majority of its stars are expected to be formed through a strong and short burst of star formation. G09.83808 and other lensed SMGs show a decreasing trend of the [NII] line to infrared luminosity ratio with increasing continuum flux density ratio between 63 $\mu$m and 158 $\mu$m, as seen in local luminous infrared galaxies (LIRGs). The decreasing trend can be reproduced by photoionization models with increasing ionization parameters. Furthermore, by combining the [NII]/[OIII] luminosity ratio with far-infrared continuum flux density ratio in G09.83808, we infer that the gas phase metallicity is already $Z\approx 0.5-0.7~Z_\odot$. G09.83808 is likely one of the earliest galaxies that has been chemically enriched at the end of reionization., Comment: 8 pages, 5 figures, accepted for publication in PASJ

Observations of low order CO transitions represent the most direct way to study galaxies' cold molecular gas, the fuel of star formation. Here we present the first detection of CO(2-1) in a galaxy lying on the main-sequence of star-forming galaxies at z>6. Our target, G09-83808 at z=6.03, has a short depletion time-scale of T_dep~50Myr and a relatively low gas fraction of M_gas/M_star=0.30 that contrasts with those measured for lower redshift main-sequence galaxies. We conclude that this galaxy is undergoing a starburst episode with a high star formation efficiency that might be the result of gas compression within its compact rotating disk. Its starburst-like nature is further supported by its high star formation rate surface density, thus favoring the use of the Kennicutt-Schmidt relation as a more precise diagnostic diagram for starbursts. Without further significant gas accretion, this galaxy would become a compact, massive quiescent galaxy at z~5.5. In addition, we find that the calibration for estimating ISM masses from dust continuum emission satisfactorily reproduces the gas mass derived from the CO(2-1) transition (within a factor of ~2). This is in line with previous studies claiming a small redshift evolution in the gas-to-dust ratio of massive, metal-rich galaxies. In the absence of gravitational amplification, this detection would have required of order ~1000h of observing time. The detection of cold molecular gas in unlensed star-forming galaxies at high redshifts is thus prohibitive with current facilities and requires a ten-fold improvement in sensitivity, such as that envisaged for the ngVLA., Accepted for publication in The Astrophysical Journal