A Scaling Relation of LRDs between Broad H$α$ and Bolometric Luminosities: Enhanced Broad H$α$ Emission Relative to Low-$z$ Type 1 AGN

Hiroto Yanagisawa, Masami Ouchi, Tomokazu Kiyota, Yuta Kageura, Makoto Ando, Yuichi Harikane, Minami Nakane, Yoshiaki Ono, Yui Takeda

First listed 2026-06-09 | Last updated 2026-06-08

Abstract

We investigate the demography of little red dots (LRDs) using 37 objects at $z\sim3$-$7$ with JWST/NIRSpec PRISM and grating spectra compiled from various JWST programs. We focus on spectroscopic quantities of the broad H$α$ luminosity $L_\mathrm{Hα,broad}$ (and the broad H$β$ luminosity $L_\mathrm{Hβ,broad}$ where available) and the bolometric luminosity $L_\mathrm{bol}$ represented by modified blackbody emission, avoiding quantities contaminated by host-galaxy emission (e.g., total H$α$ luminosity). We identifiy a tight scaling relation between $L_\mathrm{Hα,broad}$ and $L_\mathrm{bol}$, supporting the interpretation that these emissions are primarily powered by the central engine. Interestingly, the $L_\mathrm{Hα,broad}$-$L_\mathrm{bol}$ scaling relation of LRDs is enhanced by a factor of $\sim40$ in $L_\mathrm{Hα,broad}$ relative to that of low-$z$ Type 1 AGN. A similar trend is found in the $L_\mathrm{Hβ,broad}$-$L_\mathrm{bol}$ relation, although the enhancement in $L_\mathrm{Hβ,broad}$ is smaller, only by a factor of $\sim10$. We explore the physical origin of these enhancements and find that \textsc{Cloudy} photoionization modeling within the classic locally optimally-emitting cloud (LOC) framework can explain them through an increase in the covering factor from $\sim20$\% (Type 1 AGN) to $\sim100$\% (LRDs), together with an increase in the hydrogen column density from $N_\mathrm{H}\sim10^{23}\,\mathrm{cm}^{-2}$ to $\gtrsim10^{24}\,\mathrm{cm}^{-2}$, with a preferred gas density of $\sim10^{10}\,\mathrm{cm}^{-3}$, successfully reproducing the modified blackbody emission. Such a nearly unity covering factor without requiring a gas density increase may result from a significant increase in the BLR filling factor or size, corresponding to a ``stuffed BLR" or ``giant BLR," respectively.

Short digest

Using 37 little red dots at z≈3–7 with JWST/NIRSpec PRISM plus grating spectroscopy, this paper isolates broad Balmer-line emission and a modified-blackbody-based bolometric luminosity to minimize host-galaxy contamination. The main empirical result is a tight broad Hα–Lbol scaling relation, with a similar trend for broad Hβ, supporting a central-engine origin for both the line and continuum emission. At fixed bolometric luminosity, LRDs sit far above low-z Type 1 AGN, with broad Hα enhanced by about 40× and broad Hβ by about 10×. Cloudy LOC modeling ties this offset to an almost unity covering factor and very large column densities, with a preferred density around 10^10 cm^-3, pointing to a “stuffed” or “giant” BLR that can also reproduce the red optical continuum.

Key figures to inspect

• Figure 1. Use this figure to introduce the actual spectroscopic sample behind the scaling-relation analysis. It shows the rest-frame 5100 Å luminosity and redshift coverage of the LRD and non-LRD objects, making clear the z≈3–7 parameter space over which the later broad-line versus bolometric-luminosity trends are established.
• Figure 3. This is the paper’s key empirical figure. It shows the broad Hα and Hβ luminosities against continuum and bolometric luminosities and makes the central claim visually obvious: the LRD sequence is offset above the low-z Type 1 AGN relations, demonstrating unusually strong broad Balmer emission at fixed luminosity.
• Figure 6. This is the main data-model comparison figure and should be featured prominently. By overlaying the observed broad Balmer-line luminosities and bolometric luminosities with Cloudy photoionization predictions for different covering factors and column densities, it directly motivates the inference that LRDs require much larger covering factors and higher NH than standard Type 1 AGN.
• Figure 7. This figure is the clearest physical diagnostic for what drives the offset in the scaling relations. It shows how the broad Balmer-line to bolometric-luminosity ratios respond to density, column density, and ionization parameter, and it is where the preferred high-NH, near-unity-covering-factor solution and the favored density around 10^10 cm^-3 become easiest to understand.
• Figure 8. Include this figure because it connects the line-based interpretation to the continuum phenomenology of LRDs. The mock PRISM spectrum from the favored Cloudy model is compared directly to GN-9771 and shows that the same BLR conditions invoked to explain the Balmer-line enhancement can also reproduce the modified-blackbody-like red optical continuum.