Understanding the process of quenching is one of the major open questions in galaxy evolution, and crucial insights may be obtained by studying quenched galaxies at high redshifts, at epochs when the Universe and the galaxies were younger and simpler to model. However, establishing the degree of quiescence in high redshift galaxies is a challenging task. One notable example is Hyde, a recently discovered galaxy at z=3.709. As compact (r~0.5 kpc) and massive (M*~1e11 Msun) as its quenched neighbor Jekyll, it is also extremely obscured yet only moderately luminous in the sub-millimeter. Panchromatic modeling suggested it could be the first galaxy found in transition to quenching at z>3, however the data were also consistent with a broad range of star-formation activity, including moderate SFR in the lower scatter of the galaxy main-sequence (MS). Here, we describe ALMA observations of the [CII] 157um and [NII] 205um far-infrared emission lines. The [CII] emission within the half-light radius is dominated by ionized gas, while the outskirts are dominated by PDRs or neutral gas. This suggests that the ionization in the center is not primarily powered by on-going star formation, and could come instead from remnant stellar populations formed in an older burst, or from a moderate AGN. Accounting for this information in the multi-wavelength modeling provides a tighter constraint on the star formation rate of SFR=$50^{+24}_{-18}$ Msun/yr. This rules out fully quenched solutions, and favors SFRs more than factor of two lower than expected for a galaxy on the MS, confirming the nature of Hyde as a transition galaxy. Theses results suggest that quenching happens from inside-out, and starts before the galaxy expels or consumes all its gas reservoirs. Similar observations of a larger sample would determine whether this is an isolated case or the norm for quenching at high-redshift. [abriged]
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