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Impact of Resonance, Raman, and Thomson Scattering on Hydrogen Line Formation in Little Red Dots

Little Red Dots (LRDs) are compact sources at $z>5$ discovered through JWST spectroscopy. Their spectra exhibit broad Balmer emission lines ($\gtrsim1000\rm~km~s^{-1}$), alongside absorption features and a pronounced Balmer break -- evidence for a dense, neutral hydrogen medium with the $n=2$ state. When interpreted as arising from AGN broad-line regions, inferred black hole masses from local scaling relations exceed expectations given their stellar masses, challenging models of early black hole-galaxy co-evolution. However, radiative transfer effects in dense media may also impact the formation of hydrogen emission lines. We model three scattering processes shaping hydrogen line profiles: resonance scattering by hydrogen in the $n=2$ state, Raman scattering of UV radiation by ground-state hydrogen, and Thomson scattering by free electrons. Using 3D Monte Carlo radiative transfer simulations with multi-branching resonance transitions, we examine their imprint on line shapes and ratios. Resonance scattering produces strong deviations from Case B flux ratios, clear differences between H$α$ and H$β$, and encodes gas kinematics in line profiles but cannot broaden H$β$ due to conversion to Pa$α$. While Raman scattering can yield broad wings, scattering of UV continuum is disfavored given the absence of strong FWHM variations across transitions. Raman scattering of higher Lyman-series emission can produce H$α$/H$β$ wing width ratios of $\gtrsim1.28$, agreeing with observations. Thomson scattering can reproduce the observed $\gtrsim1000~\rm km\, s^{-1}$ wings under plausible conditions, e.g., $T_{\rm e} \sim 10^4\rm \, K$ and $N_{\rm e}\sim10^{24}\rm~cm^{-2}$ -- and lead to black hole mass overestimates by factors $\gtrsim10$. Our results provide a framework for interpreting hydrogen lines in LRDs and similar systems.