The Balmer Absorber Strength Problem of Little Red Dots

Little Red Dots (LRDs) commonly show Balmer absorption features. Some observed LRD spectra have weaker absorption in H$α$ than in H$β$, in apparent contradiction to atomic physics according to standard attenuation models. This tension is naturally resolved when one considers emission from the absorbing medium itself, which is ignored in the standard model: when the Balmer absorption is optically thick, a non-negligible source function could fill in the H$α$ absorption trough and reduce its observed absorption equivalent width (EW). With proof-of-concept photoionization models we show that the source function of H$α$ could be systematically stronger than that of H$β$. This is due to radiative trapping preferentially populating the $n=3$ level of neutral hydrogen, which operates efficiently when the medium is optically thick to H$α$ but not very optically thick to Paschen-$α$. Such line-dependent source functions could lead to significant corrections to the expected EW and selectively weaken H$α$ absorption, consistent with observations. Quantitatively, this depends on the distance of the absorbing medium and its internal structure, providing a new diagnostic of the environment around LRDs. Future modeling of the absorbers may also potentially open a new avenue for estimating the mass of the central engine.