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

Yi-Xian Chen, Hanpu Liu, Ruancun Li, Bingjie Wang, Yilun Ma, Yan-Fei Jiang, Jenny E. Greene, Eliot Quataert, Jeremy Goodman

First listed 2026-02-06 | Last updated 2026-02-09

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.

Short digest

The authors build dust-poor, self-gravitating AGN disk models and show that all optically thick solutions converge to an outer “disk Hayashi limit” with Teff ≈ 4000–4500 K, naturally reproducing the red optical continua of Little Red Dots without fine-tuning in Mdot, MBH, or α. Global models with radially varying accretion show that burning of embedded stellar objects powers the outer disk and hollows the inner disk, suppressing the standard variable UV/X-ray while leaving a luminous thermal optical bump plus a separate, largely non-variable UV from nuclear-to-galaxy-scale stars. They map the viable parameter space and find LRD-like appearances whenever Mdot/α ≳ 0.1 Msol/yr, largely insensitive to MBH, with a transition to classical AGN disks at lower values that should coincide with rising metallicity/dust and emerging FIR emission. Results hinge on dust-poor opacities setting the thermalization boundary that fixes the optical continuum temperature.

Key figures to inspect

• Figure 1: Use the RUBIES-40579 example to see the proposed spectral decomposition—thermal red/optical from the self-gravitating disk plus a separate stellar UV—and how the hollowed inner disk explains weak UV/X-ray variability.
• Figure 2: Inspect the dust-free Rosseland opacities and the Teff versus density curves to verify the universal transition at Teff ≈ 4–4.5 kK (gray point) and contrast it with the dusty, solar-metallicity case that would shift power to the FIR.
• Figure 3: Check how midplane temperature and Teff vary with radius for different outer accretion rates and mass-loss slopes; note where the solution transitions (vertical dotted lines) toward an inner viscous disk and how embedded-star mass loss regulates the outer profile.
• Figure 4: Compare luminosity budgets—AGN versus the optically thick self-gravitating region—and see that increasing mass-loss slope suppresses L_AGN while the thermal disk component remains nearly unchanged and can dominate even at modest Mdot; relate to the Eddington reference line.