The Deepest GLIMPSE of a Dense Gas Cocoon Enshrouding a Little Red Dot

Abstract: The detection of strong Balmer breaks and absorption features in Little Red Dots (LRDs) suggests they host AGN embedded within dense gas envelopes, potentially powered by super-Eddington accretion. We present GLIMPSE-17775, a luminous ($L_{\rm bol}\sim10^{45}$ erg s$^{-1}$) LRD at $z=3.501$ behind Abell S1063 ($μ\sim2$), observed with deep JWST/NIRCam and a $\sim$20 hr (80 hr de-lensed) NIRSpec/G395M spectrum. The data reveal 40+ emission and absorption features, including a rich forest of low-ionization FeII lines and numerous broad hydrogen recombination transitions. We use this depth to test the dense-gas interpretation through five independent diagnostics. Nearly all permitted lines show exponential wings with consistent FWHM, the signature of Thomson scattering requiring $n_e\gtrsim10^8$ cm$^{-3}$. Adopting this width yields $M_{\rm BH}\sim10^{6.7}M_\odot$, a factor of ten lower than Gaussian fits, and $λ{\rm Edd}\sim1.8$. Additional diagnostics support the same picture: a pronounced Balmer break ($f{ν,4050}/f_{ν,3670}=2.0\pm0.1$), enhanced HeI $\lambda7065$ and $\lambda10830$ with P-Cygni absorption, Bowen-fluorescent OI $\lambda8446$-$\lambda11290$ emission requiring Ly$β$ pumping, and 16 FeII lines matching fluorescence models. These features indicate a dense ($n\sim10^8$ cm$^{-3}$), partially ionized cocoon where scattering and fluorescence dominate line formation, providing strong evidence that at least some LRDs are powered by super-Eddington black-hole growth in the early Universe.