Spectral Appearance of Self-gravitating AGN Disks Powered by Stellar Objects: Universal Effective Temperature in the Optical Continuum and Application to Little Red Dots

TL;DR

This work proposes that the optical continuum of compact, self-gravitating AGN disks heated predominantly by embedded stellar objects attains a universal outer effective temperature of $T_{ m eff}\sim 4000-4500$ K, an effect driven by dust-free H$^-$ opacity and analogous to a Hayashi-like limit for disks. By solving global disk structures with radially varying accretion rates under $Q\approx 1$, the authors show that the outer disk emission can dominate the observed optical continuum, naturally reproducing the Little Red Dots (LRD) spectral characteristics without fine-tuning. A key result is that significant UV/X-ray emission from an inner standard AGN disk can be suppressed if most mass is consumed by star formation in the outer disk, with a threshold in $\dot{M}/\alpha$ around $\gtrsim 0.1\,M_\odot\,{ m yr^{-1}}$ that is largely independent of $M_ullet$. The framework connects LRDs to AGNs, predicts a transition to dusty, FIR-bright states as metallicity rises, and motivates future multi-wavelength studies of stellar evolution in quasar disks. Overall, the paper provides a physically motivated, quantitative pathway linking LRD phenomenology to the broader AGN population with testable spectral and evolutionary implications.

Abstract

We revisit the spectral appearance of extended self-gravitating accretion disks around supermassive black holes. Using dust-poor opacity tables, we show that all optically thick disk solutions possess a universal outer effective temperature of $T_{\rm eff}\sim 4000-4500$K, closely resembling compact, high-redshift sources known as Little Red Dots (LRDs). Assuming the extended disk is primarily heated by stellar sources, this ``disk Hayashi limit" fixes the dominant optical continuum temperature of the disk spectrum independent of accretion rate $\dot{M}$, black hole mass $M_\bullet$, and disk viscosity $α$, and removes the parameter-tuning required in previous disk interpretations of LRDs. We construct global self-gravitating accretion disk models with radially varying accretion rates, suggesting that burning of embedded stellar objects can both efficiently power the emission of the outer disk and hollow out the inner disk, strongly suppressing variable UV/X-ray associated with a standard quasar. The resulting disk emission is dominated by a luminous optical continuum while a separate, non-variable UV component arises from stellar populations on the nuclear to galaxy scale. We map the optimal region of parameter space for such systems and show that LRD-like appearances are guaranteed for $\dot{M}/α\gtrsim 0.1 M_\odot /{\rm yr}$, a threshold insensitive to $M_\bullet$, below which the system may transition into classical non-self-gravitating AGN disks, potentially a later evolution stage. We expect this transition to be accompanied by the enhancement of metallicity and production of dust, giving rise to far infrared emission. This picture offers a physically motivated and quantitative framework connecting LRDs with AGNs and their associated nuclear stellar population.

Figures (9)

• Figure 1: Schematic illustration of our proposed physical interpretation of LRDs. The dominant red/optical emission arises from an optically thick, self-gravitating disk with heating primarily supplied by embedded stellar populations. The inner disk is largely hollowed out by star formation, suppressing the classical variable UV/X-ray emission from a standard AGN. A separate UV component can originate from stellar populations in a surrounding optically thin, diffuse cloud that connects the disk to the nuclear stellar population. The top row shows a schematic spectral decomposition for illustration purpose. We use the observed spectrum of a representative LRD source RUBIES-40579 WangdeGraaff2025 (black lines, top right panel) to illustrate how the total emission may be qualitatively understood as the sum of a thermalized red/optical disk component and a stellar-dominated UV component. This decomposition is not intended as a formal spectral fit, only a visual guide to the proposed physical picture.
• Figure 2: Top panel: solid lines indicate metal-free ($Z=0$) Rosseland mean opacities $\kappa_R(T)$ for different densities $\rho$. A representative $\kappa_R(T)$ profile for solar metallicity opacity with dust for $\rho =10^{-12}~$g cm$^{-3}$ is shown as green dashed line for comparison. Lower panel: effective temperature calculated by Equation \ref{['eqn:Teff_T_rho']} for different densities. The shaded region represents solutions with $T_{\rm eff} > T$ that are no longer consistent with the optically thick assumption, implying a stellar-UV rather than thermalized emission. For $Z=0$ opacities, there is a unique and universal transition at $T_{\rm eff}\approx T\approx 4000-5000$K (gray circle), regardless of density.
• Figure 3: Radial structure of fiducial disk solutions for $M_\bullet = 10^6 M_\odot$, $\alpha=0.1$ and outer boundary accretion rates of $\dot{M} = 0.1M_\odot$/year (opaque lines) and $\dot{M} = 1M_\odot$/year (semi-transparent lines), with varying mass-loss slope $\gamma$. The midplane temperature $T$ and effective temperature $T_{\rm eff}$ are shown in solid and dashed lines respectively in the top left panel. The transition towards an inner viscous $\alpha$-disk, if present, is indicated by vertical dotted lines.
• Figure 4: Summary of luminosity contributions for the accretion disk around a $10^6 M_\odot$ SMBH. The AGN component or its upper limit is shown in blue and the thermal emission from the optically thick self-gravitating region is shown in orange. The Eddington luminosity is plotted for reference (black dashed). Across all models, increasing $\gamma$ systematically suppresses $L_{\rm AGN}$, while $L_{\rm disk}$ remains largely unchanged and often dominates even at $\gamma$ for lower accretion rates.
• Figure 5: Radial structure of fiducial disk solutions for $M_\bullet = 10^7 M_\odot$, $\alpha=0.1$ and outer boundary accretion rates of $\dot{M} = 0.1M_\odot$/year (opaque lines) and $\dot{M} = 1M_\odot$/year (semi-transparent lines), similar to Figure \ref{['fig:m6a01']}.