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

TL;DR

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Abstract

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.

Figures (21)

• Figure 1: Schematic illustration of the model geometry. A central point source emits either H$\alpha$ and H$\beta$ photons (orange points for resonance and Thomson scattering) or a UV continuum (a blue point for Raman scattering), surrounded by a spherical scattering region. The sphere is divided into three wedges representing the different scattering processes: (a) Resonance scattering of Balmer lines, H$\alpha$ and H$\beta$, in a spherical H i region populated with 2s-state hydrogen atoms, characterized by a column density ${ N}_{\rm HI, 2s}$, a random motion $\sigma_{\rm R}$, and an expansion velocity $v_{\rm exp}$. (b) Raman scattering of UV photons near the Lyman series by ground-state H i atoms with a column density ${ N}_{\rm HI}$, producing broad optical and IR features (e.g., H$\alpha$, H$\beta$, Pa$\alpha$). (c) Thomson scattering of Balmer line photons by free electrons in a spherical H ii region, characterized by electron temperature $T_e$ and electron density $n_e$, producing symmetric broadening proportional to the electron’s thermal speed $v_{\rm th,e}$.
• Figure 2: Energy levels of atomic hydrogen in $n = 1-4$. Solid arrows indicate the 'resonant transitions' involved in resonance scattering (see Section \ref{['sec:resonance']}), while dashed arrows show other possible transitions for H$\alpha$, H$\beta$, and Pa$\alpha$ (omitting the higher Lyman transitions; 'case B' assumption).
• Figure 3: Schematic illustration of Raman scattering of UV radiation near Ly$\gamma$. The black solid lines represent the energy levels of atomic hydrogen. The light blue line indicates the incident UV radiation near Ly$\gamma$. The blue arrow represents Rayleigh scattering, in which the electron de-excites to the $n=1$ state, emitting Ly$\gamma$. The red and orange arrows represent Raman scattering to the $n=2$ and $n=3$ states, producing H$\beta$ and Pa$\alpha$, respectively.
• Figure 4: Conversion rate from H$\beta$ to Pa$\alpha$ through inelastic H$\beta$ scattering from $n = 2 \to 4 \to 3$, $\mathcal{C}_{\rm H\beta \to Pa\alpha}$, as a function of ${ N}_{\rm HI, 2s}$. The blue dots show the simulation results for the monochromatic case, while the red dashed line represents the analytic solution derived in Eq. \ref{['eq:Hb_to_Ha']}. The vertical dashed line represents the ${ N}_{\rm HI, 2s}$ corresponding to an optical depth of unity at the H$\beta$ line center ($\tau_{0,H\beta} = 1$). The conversion rate $\mathcal{C}_{\rm H\beta \to Pa\alpha}$ increases with ${ N}_{\rm HI, 2s}$, as higher optical depths lead to more scatterings and chances of branching via the $4p \to n = 3\ (3s/3d)$ transition.
• Figure 5: Emergent Flux ratios experiencing H$\beta$ scattering of H$\alpha$/H$\beta$ (blue), H$\beta$/Pa$\alpha$ (red), and H$\alpha$/Pa$\alpha$ (orange) as functions of ${ N}_{\rm HI, 2s}$. The ratio variations originate from H$\beta$ scattering, as shown in Fig. \ref{['fig:Hb_to_Ha']}. The vertical dashed line marks the ${ N}_{\rm HI, 2s}$ corresponding to an optical depth of unity at the H$\beta$ line center ($\tau_{0,H\beta} = 1$). The horizontal dashed lines indicate the line ratios expected under Case B recombination.