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WISE J224607.6-052634.9 (W2246-0526) is a hot dust-obscured galaxy at $z$ =4.601, and the most luminous obscured quasar known to date. W2246-0526 harborsa heavily obscured supermassive black hole that is most likely accreting abovethe Eddington limit. We present observations with the Atacama LargeMillimeter/submillimeter Array (ALMA) in seven bands, including band 10, of thebrightest far-infrared (FIR) fine-structure emission lines of this galaxy:[OI]$_{63\mu m}$, [OIII]$_{88\mu m}$, [NII]$_{122\mu m}$, [OI]$_{145\mu m}$,[CII]$_{158\mu m}$, [NII]$_{205\mu m}$, [CI]$_{370\mu m}$, and [CI]$_{609\mum}$. A comparison of the data to a large grid of Cloudy radiative transfermodels reveals that a high hydrogen density ($n_{H}\sim3\times10^3$ cm$^{-3}$)and extinction ($A_{V}\sim300$ mag), together with extreme ionization($log(U)=-0.5$) and a high X-ray to UV ratio ($\alpha_{ox}\geq-0.8$) arerequired to reproduce the observed nuclear line ratios. The values of$\alpha_{ox}$ and $U$ are among the largest found in the literature and implythe existence of an X-ray-dominated region (XDR). In fact, this componentexplains the a priori very surprising non-detection of the [OIII]$_{88\mu m}$emission line, which is actually suppressed, instead of boosted, in XDRenvironments. Interestingly, the best-fitted model implies higher X-rayemission and lower CO content than what is detected observationally, suggestingthe presence of a molecular gas component that should be further obscuring theX-ray emission over larger spatial scales than the central region that is beingmodeled. These results highlight the need for multiline infrared observationsto characterize the multiphase gas in high redshift quasars and, in particular,W2246-0526 serves as an extreme benchmark for comparisons of interstellarmedium conditions with other quasar populations at cosmic noon and beyond.

A benchmark for extreme conditions of the multiphase interstellar medium in the most luminous hot dust-obscured galaxy at z = 4.6