Balmer Transition Signatures from Gas-Enshrouded, Dust-Poor Active Galactic Nuclei
Little red dots (LRDs), a population of active galactic nuclei (AGNs) recently discovered by JWST, show distinctive Balmer-transition features, including prominent Balmer absorption, pronounced Balmer breaks, and large equivalent widths of broad $\mathrm{H}\alpha$ emission, all of which indicate the presence of dense gas surrounding their central black holes. A further key property of LRDs is their large Balmer decrements with broad $\mathrm{H}\alpha/\mathrm{H}\beta$ line-flux ratios far exceeding the Case B recombination value. These ratios of $\mathrm{H}\alpha/\mathrm{H}\beta>3$ have often been interpreted as evidence for heavy dust extinction ($A_V\gtrsim 3$ mag), however such dust would inevitably produce strong near-to-mid infrared re-emission that is hardly seen in JWST/MIRI observations. To investigate the physical origin of these observed Balmer features, we perform radiation transfer calculations through dust-free, dense gas. We show that the observed large Balmer decrements ($\mathrm{H}\alpha/\mathrm{H}\beta$ and $\mathrm{H}\alpha/\mathrm{H}\gamma$) naturally arise from Balmer resonance scattering without invoking dust. At sufficiently high densities ($n_\mathrm{H} \gtrsim 10^{{8}-{10}}~\mathrm{cm^{-3}}$), the elevated multiple Balmer-line ratios converge to values that closely mimic dust reddening, explaining why LRD spectra resemble obscured AGNs. Furthermore, when the Balmer break and broad Balmer lines originate in the same dense gas, their strengths are physically linked, allowing us to constrain the density structure and infer a low broad-line region gas mass of $\sim O(10~M_\odot)$. Such a small gas reservoir would be enriched by even a single supernova, implying that LRDs with observed low-metallicity signatures likely experienced minimal star formation in their nuclei.