A Black-Hole Envelope Interpretation for Cosmological Demographics of Little Red Dots

TL;DR

The paper addresses the puzzling nature of Little Red Dots (LRDs) by applying the Black Hole Envelope (BHE) model, which posits an accreting black hole enshrouded by an optically thick envelope. Using ~400 LRDs from the COSMOS-Web survey, the authors fit SEDs with a photospheric blackbody at $T_{ m ph} oughly 4000$–$6000$ K, finding bolometric luminosities lower by ~1–2 dex than dusty-AGN templates, thereby bringing the inferred luminosity function, black hole accretion density (BHAD), and black hole mass function (BHMF) into agreement with the broader AGN population at $z<5$. The LRD-derived BHMF and BHAD suggest a dominant, short-lived super-Eddington growth phase contributing to early black hole assembly and a parallel evolution of stellar and black hole mass densities up to $z\,sim10$, with only moderate excess in $M_{ m BH}/M_\star$ relative to the local relation. The results constrain the duty cycle of the LRD phase to about 20% and provide a coherent framework linking high-redshift black hole growth to conventional AGN demographics, while outlining observational tests for future JWST programs to confirm the envelope scenario.

Abstract

Little red dots (LRDs) newly discovered with JWST are active galactic nuclei (AGN) that may represent black hole (BH) growth at the earliest cosmic epochs. These sources show puzzling features unlike typical AGNs, including red optical continua, weak hot-dust emission, and a lack of detectable X-rays. Previously, LRDs have often been interpreted as dust-reddened AGNs, leading to severe inconsistencies with the luminosity and BH mass densities inferred for previously known AGNs over $0<z<5$. The BH-envelope (BHE) model has been proposed to explain these characteristics, in which an accreting BH is enshrouded by a dense, optically thick gaseous envelope. In this Letter, we reanalyze the SEDs of $\sim 400$ photometric LRDs in the COSMOS-Web survey using the BHE model and reassess their implications for cosmological BH evolution. We find that the optical-NIR spectra of LRDs are well reproduced by blackbody emission with an effective temperatures of $4000-6000~\K$. Within the BHE framework, the inferred bolometric luminosities decrease by $\gtrsim1-2$ orders of magnitude compared to dust-reddened AGN assumptions. As a result, the revised luminosity function, BH accretion density, and BH mass function become consistent with those of AGNs at $z<5$. The stellar masses of LRD hosts are estimated by attributing the UV excesses to star formation. Although the resulting $M_{\rm BH}/M_\star$ ratio remains higher than the local empirical value, the excess is modest. Overall, the BHE model not only resolves the spectral features of LRDs but also brings their statistical properties into agreement with the broader cosmological BH population.

Figures (5)

• Figure 1: Left: Example posterior distribution from the SED fitting. The top panels in each column represent the 1D marginalized PDF for the corresponding parameters, while the remaining panels display the 2D marginalized PDFs for each parameter pair. Right: Posterior PDF of the BHE-based SED fitting for one LRD from Akins25 (COS-145575). Black data points with error bars show the observed photometric fluxes. The red solid lines indicate SED realization drawn from the posterior PDF, and the red points show the corresponding model photometric fluxes and uncertainties. The median and 68-th percentile parameter constraints are as follows: $z={6.00}^{+0.64}_{-0.77}$, $A_1/{\rm nJy}={124}_{-58}^{+101}$, $T_{\rm ph}/{\rm K}={5670}_{-690}^{+820}$, $A_2/{\rm nJy}={56.3}_{-16.5}^{+22.6}$, $\beta_{\rm UV}={-2.14}_{-0.44}^{+0.43}$, and $A_{V}/{\rm mag}={0.55}_{-0.40}^{+0.72}$. The shaded curves at the bottom of the panel represent the transmission curves of the filters used in the fitting.
• Figure 2: Left: Comparison of the bolometric luminosities between the BHE model ($L_{\rm bol,~BHE}$) and dust-reddened AGN model ($L_{\rm bol,~QSO}$). The sold, dashed, and dotted lined represent $L_{\rm bol,~BHE}/L_{\rm bol,~QSO}=1.0$, $0.1$, and $0.01$, respectively. Right: Hertzsprung-Russell diagram for the fiducial LRD sample (red circles) and full sample (open circles), showing effective temperatures and luminosities under the assumption of blackbody spectra. Dotted lines indicate the loci of constant photospheric radius of $R_{\rm ph}=10^{-3}$ and $10^{-2}~{\rm pc}$. The narrow temperature range over $T_{\rm eff}\simeq 4500-6000~{\rm K}$ is consistent with the tip of the Hayashi track extrapolated from from the locus of red supergiant stars in the Milk Way (shaded region).
• Figure 3: Left: The bolometric luminosity function of the AGNs at $z\sim6$. Number density of the LRDs are shown in the red circles. We adopt bolometric luminosity of LRD based on BHE model. We also present the bolometric luminosity function of QSO based on the Subaru surveys by Niida20, shown in the black color. The dashed line represent the luminosity function inferred from the X-ray observations from Ueda14. The red crosses represent the luminosity function from Akins25 derived assuming QSO model. We also show the bolometric luminosity function from Greene25 in the non-filled yellow stars. Right: The bolometric luminosity function of the AGNs at $z\sim8$. Number density of the LRDs are shown in the red color. We adopt bolometric luminosity of LRD based on BHE model. We also present the bolometric luminosity function of QSO based on the Subaru surveys by Matsuoka23, shown in the black color. Other legends represents the same thing as they do in the left panel.
• Figure 4: Left: Black hole mass functions of LRDs at $z\sim 6$ (blue) and $z\sim 8$ (red). Black hole masses are estimated from the bolometric luminosity in the BHE model, assuming $\lambda_{\rm Edd}=0.5$ (filled circles). For each redshift, the shaded region denotes the BHMF range obtained with $\lambda_{\rm Edd}=0.1-1$. Cross symbols show the BHMF inferred under the dust-reddened AGN hypothesis Akins25 with $\lambda_{\rm Edd}=0.5$. For the comparison, BHMF constraints for AGNs at $z=3-5$ derived from single-epoch virial mass estimates are overlaid with open symbols (circle: 2025ApJ...986..165T, square: Matthee24, diamond: 2024ApJ...962..152H). Right: Relation between host stellar mass and black hole mass for LRDs in the BHE framework (red circles) including uncertainties from the assumed $\lambda_{\rm Edd}$ values. Measurements of the $M_{\rm BH}-M_\star$ relation at $z=0$ (grey square and black diagonal line: KormendyHo13) and $z\sim6$ (blue circle: Izumi21) are shown for comparison. The LRD population tends to be overmassive ($M_{\rm BH}/M_\star\simeq 0.005$) relative to the local relation, although the offset is moderate. Black hole masses inferred from the H$\alpha$-based single-epoch method Kocevski25 are also plotted (orange diamonds). Dashed lines indicate $M_{\rm BH}/M_\star = 10^{-3}$, $10^{-2}$, and $10^{-1}$.
• Figure 5: Left: Black hole accretion density (BHAD) of LRDs as a function of by redshift (red circles). BHAD are estimated from the bolometric luminosity function based on BHE model, assuming $\epsilon_{\rm rad}=0.1$. Measurements based on Akins25$z\sim6-8$ LRD sample (filled) and $z\sim10$ LRD (open) from Tanaka25 are shown together with original BHAD measurements from Akins25 with QSO model (grey circles) For the comparison we present BHAD constraints from observations in mid-IR (orange: Delvecchio14) and X-ray (grey region: Aird15, black region: Pouliasis24, black dashed line: Ananna19). We also plot the redshift evolution of star formation rate density $\rho_{\rm SFR}$ in blue symbols (dotted line: Harikane22, circles:Harikane25a). We scale $\rho_{\rm SFR}$ by a factor of 1/3000 to match the BHAD at $z<3$. Right: The black hole mass density (BHD) by redshifts. The red circles represent the $\rho_{\rm BH}$ derived from integrating BHMF of LRDs at $z=6$ and 8. The open circle represent the $\rho_{\rm BH}$ estimated using a $z>10$ LRD candidate reported by Tanaka25. The error bars include the systematic offset arising from adopting $\lambda_{\rm Edd}=0.1$ versus $\lambda_{\rm Edd}=1$. The pink shades represents the $1\sigma$ upper and lower limit ranges $\Delta\rho_{\rm BH}$ calculated from integrating BHAD of LRD by time ($\Delta t$) corresponding to the redshift binning width. The grey circles represent the $\Delta\rho_{\rm BH}$ estimated based on BHAD assuming QSO model Akins25. The orange region represent the $\rho_{\rm BH}$ at $z=0$ measured by Shankar09. The black solid line represent the $\Delta\rho_{\rm BH}$ estimated from the BHAD of $0<z<5$ ordinary AGNs with $\epsilon_{\rm rad}=0.1$Ueda14. For the comparison, we plot recent stellar mass density measurements from Shuntov25 in blue line.