Emission line formation in scattering dominated media: implications for LRDs

Elisha Modelevsky, Omri Nitzan, Re'em Sari, Eliot Quataert

First listed 2026-08-07 | Last updated 2026-08-05

Abstract

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 $v^{-α}$ to $v^{-(α+1)}$, with $0 < α< 1$. 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 $\mathrm{H}α$ 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 $\mathrm{H}α$ and continuum flux cannot be explained. Quantitative comparison to LRD spectra requires expanding our models to non-LTE situations.

Short digest

Modelevsky et al. develop an analytic radiative-transfer framework for Balmer lines produced intrinsically inside static, optically thick, scattering-dominated envelopes, a geometry directly relevant if LRD central engines are hidden by dense gas. Unlike externally broadened, backlit or reflected lines, which generically acquire exponential wings, an extended intrinsic photosphere produces a broken power-law profile, transitioning from v^{-α} to v^{-(α+1)} with 0<α<1; this form fits the Hα profiles of JADES-GN-73488 and JADES-GN-68797. The result offers a line-shape diagnostic for distinguishing intrinsic from extrinsic Thomson broadening in LRDs, although the LTE calculation cannot reproduce the observed high Hα-to-continuum contrast and ultimately requires non-LTE modeling.

Key figures to inspect

• Figure 1. This schematic cleanly defines the paper’s central physical distinction: backlit and reflected geometries broaden a line formed elsewhere, whereas the intrinsic case creates and broadens Balmer photons within the same opaque envelope.
• Figure 2. This density-temperature map establishes the assumed opacity hierarchy, showing where Hα line opacity dominates while Thomson scattering exceeds continuum absorption, the parameter regime required for the proposed intrinsic line-formation mechanism.
• Figure 3. The Monte Carlo comparison validates the planar analytic solution and isolates its core, logarithmic plateau, and v^{-1} wing, providing the radiative-transfer origin of the non-exponential intrinsic profile.
• Figure 4. This is the observational payoff: broken-power-law fits are compared directly with the two-sided Hα profiles of JADES-GN-73488 and JADES-GN-68797, alongside exponential alternatives expected for extrinsic scattering.
• Figure 5. The rate comparison exposes the main physical limitation of the LTE treatment: photoionization need not sustain thermal level populations in the relevant scattering-dominated conditions, motivating non-LTE models to address the strong observed line-to-continuum contrast.