The Extreme Rarity and Physical Properties of Low-redshift AGNs with Balmer Absorption

Balmer absorption lines are increasingly observed in the little red dots (LRDs) discovered by the James Webb Space Telescope, potentially tracing dense circumnuclear gas around rapidly accreting black holes. Motivated by this connection, we search for Balmer absorption using homogeneously analyzed spectra of a representative parent sample of 14,584 low-redshift ($z<0.35$) type 1 active galactic nuclei selected from the Sloan Digital Sky Survey. We identify seven sources with robust Balmer absorption (occurrence $\sim 0.05\%$) and model them with a partially covering absorber model, accounting for the spectral resolution. By fitting H$\alpha$, H$\beta$, and H$\gamma$ simultaneously and tying their optical-depth ratios to theoretical values, we constrain optical depth at the line center ($\tau_0$) and the covering factor ($C_f$). All sources with robust modeling require optically thick H$\alpha$ absorption and typically moderate covering factors ($C_f\approx 0.2-0.6$), while the LRD analog J1025 shows $C_f \gtrsim 0.8$ consistent with recent measurements of high-redshift LRDs. The absorbers have modest velocity offsets ($\sim 150-850\,\mathrm{km\,s^{-1}}$) and narrow intrinsic widths ($\sim 20-200\,\mathrm{km\,s^{-1}}$). Multi-epoch spectroscopy of three sources reveals Balmer-absorption variability on both year and month timescales. Three objects exhibit exceptionally weak Fe II emission, high Eddington ratio, and low gas-phase metallicity, an atypically rare combination of properties that might elevate the incidence of Balmer-absorption to $\sim$10%. We argue that low-metallicity conditions may suppress disk winds and help retain dense neutral gas along the line-of-sight in systems of high accretion rate.