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We report the detection of an ionized gas outflow from an $X$-ray activegalactic nucleus (AGN) hosted in a massive quiescent galaxy in a protoclusterat $z=3.09$ (J221737.29+001823.4). It is a type-2 QSO with broad ($W_{80}>1000$km s$^{-1}$) and strong ($\log (L_{\rm [OIII]}$ / erg s$^{-1})\approx43.4$) [O{\footnotesize III}]$\lambda\lambda$4959,5007 emission lines detected by slitspectroscopy in three-position angles using Multi-Object Infra-Red Camera andSpectrograph (MOIRCS) on the Subaru telescope and the Multi-Object SpectrometerFor Infra-Red Exploration (MOSFIRE) on the Keck-I telescope. In the all slitdirections, [O {\footnotesize III}] emission is extended to $\sim15$ physicalkpc and indicates a powerful outflow spreading over the host galaxy. Theinferred ionized gas mass outflow rate is $\rm 22\pm3~M_{\odot}~yr^{-1}$.Although it is a radio source, according to the line diagnostics usingH$\beta$, [O {\footnotesize II}], and [O {\footnotesize III}], photoionizationby the central QSO is likely the dominant ionization mechanism rather thanshocks caused by radio jets. On the other hand, the spectral energydistribution of the host galaxy is well characterized as a quiescent galaxythat has shut down star formation by several hundred Myr ago. Our resultssuggest a scenario that QSOs are powered after the shut-down of the starformation and help to complete the quenching of massive quiescent galaxies athigh redshift.

An AGN with an ionized gas outflow in a massive quiescent galaxy in a protocluster at $\bf z=3.09$