Silencing the Giant: Evidence of AGN Feedback and Quenching in a Little Red Dot at z = 4.13

The James Webb Space Telescope (JWST) has uncovered a ubiquitous population of dust-obscured compact sources at $z\gtrsim 4$. Many of these objects exhibit signs of active galactic nucleus (AGN) activity, making their study crucial for understanding the formation of supermassive black holes (SMBHs) and their growth with host galaxies. In this work, we examine low and medium resolution JWST/NIRSpec spectra from the JADES GTO public data release in the GOODS-N field of a red, luminous ($M_{\rm B}\sim-22.2$ mag) and compact ($<500$ pc) source at $z=4.13$. The rest-optical ($\lambda_{\rm rest}>4000$ A) continuum of this source is strongly dominated by a massive (log$_{10}$[$M_*/M_\odot] \sim 10.6$), quenched (log$_{10}$[sSFR/yr$^{-1}$] $<-11$) galaxy, as indicated by the clear presence of a Balmer break and stellar absorption lines. Star-formation history modeling reveals a starburst episode followed by rapid quenching about 200 Myr ago. The spectrum shows extremely broad (FWHM $\sim 2500$ km/s) H$\alpha$ emission and elevated optical line ratios, indicating an actively accreting SMBH. Moreover, our work has potentially revealed clear AGN signatures in the rest-UV in LRDs for the first time, via a detection of a strong Ly$\alpha$ emission and a broad MgII, doublet. The derived black hole mass of log$_{10}$($M_{\rm BH}/M_\odot) \sim 7.3$ results in $M_{\rm BH}/M_*\sim 0.04$ %, consistent with the local relations, unlike the elevated ratios in other high-$z$ reddened AGN. Finally, we use JWST data from AGN at $z=4-10$ to explore an evolutionary link between high-$z$ reddened AGN, early quiescent galaxies, and local ellipticals.