Emission line formation in scattering dominated media: implications for LRDs
Recent JWST observations of ``Little Red Dots'' (LRDs) reveal broad and prominent Balmer emission lines. We present a theoretical framework for intrinsic emission line formation and broadening within static, optically thick, scattering-dominated gas envelopes with thermal populations. Using random-walk and diffusion approximations, we derive analytical line profiles for lines forming intrinsically within the scattering medium. We demonstrate that a geometrically thin planar photosphere produces a shallow line profile characterized by a logarithmic plateau and a $v^{-1}$ wing. A radially extended photosphere yields a broken power-law spectrum transitioning from $v^{-\alpha}$ to $v^{-(\alpha+1)}$, with $0 < \alpha < 1$. This is in contrast to a scattering medium external to the line-forming region, which produces an exponential line profile. We show that this broken power-law model can fit the $\mathrm{H}\alpha$ line profiles observed in LRDs. Higher quality spectra may be able to distinguish between intrinsic and extrinsic models for the line broadening in LRDs. In our LTE models, the high contrast between the $\mathrm{H}\alpha$ and continuum flux cannot be explained. Quantitative comparison to LRD spectra requires expanding our models to non-LTE situations.