Constraints on dynamically-formed massive black holes in Little Red Dots from X-ray non-detections

1. Problem Statement

The discovery of Little Red Dots (LRDs)—extremely compact and massive galaxies at high redshifts ($z \gtrsim 2$)—challenges standard models of early structure formation. These galaxies host supermassive black holes (SMBHs) with masses estimated at $10^7 - 10^8 M_\odot$ based on optical/UV spectral features (broad emission lines). However, deep X-ray observations (specifically stacking analyses by Sacchi & Bogdán 2025) have failed to detect significant X-ray emission from these sources, placing strict upper limits on their X-ray flux.

This creates a major tension:

• Optical Evidence: Suggests the presence of massive, accreting SMBHs.
• X-ray Evidence: Suggests either the black holes are much less massive than optical estimates imply, or they are heavily obscured ($N_H \gtrsim 10^{25} \text{ cm}^{-2}$) or intrinsically weak.

The paper investigates whether a collision-based black hole formation scenario (runaway stellar collisions in dense cores) can explain the existence of massive seeds in LRDs while remaining consistent with the observed X-ray non-detections, without requiring extreme obscuration.

2. Methodology

The authors constructed a dynamical evolution model for LRDs to predict the mass of collision-formed black hole seeds and their subsequent X-ray signatures.

A. Sample and Data

• Target Population: A subsample of 55 LRDs from the S+25 study (selected from Kocevski et al. 2025) that lack individual X-ray detections but were analyzed via stacking in the Chandra Deep Field South (CDF-S).
• Stellar Mass Estimation: Derived from UV absolute magnitudes ($M_{UV}$) using redshift-dependent scaling relations ($\log M_{gal} = a \cdot M_{UV} + b$).
• Radius Assumption: Since radii for the S+25 sample were unavailable, the authors assumed they follow the same mass-radius distribution as the Akins et al. (2025) sample, modeled using a Gaussian Mixture Model.

B. Dynamical Evolution Model

The evolution of the galaxy's stellar mass ($M_{gal}$) and effective radius ($R_{gal}$) is modeled as power laws:

1. Mass Evolution: $M_{gal}(t) \propto t^\alpha$, where $\alpha$ describes the star formation history (SFR).
   • $\alpha = 1$: Constant SFR.
   • $\alpha > 1$: Increasing SFR.
2. Mass-Radius Relation: $R_{gal}(t) \propto M_{gal}^\beta$, where $\beta$ is the key parameter tested.
   • Tested range: $\beta \in [0.1, 1.5]$.
   • Context: $\beta \approx 0.5$ for Nuclear Star Clusters (NSCs), $\beta \approx 0.6$ for early-type galaxies, and $\beta \approx 0.2$ for late-type spirals.

C. Black Hole Formation via Stellar Collisions

• Mechanism: In dense systems where the collisional timescale ($t_{coll}$) is shorter than the system's age ($t_H$), runaway stellar collisions occur, forming a supermassive star that collapses into an intermediate-mass black hole (IMBH).
• Efficiency: The efficiency of BH formation ($\epsilon_{BH}$) is calculated based on the ratio of galaxy mass to a critical mass ($M_{crit}$), derived from N-body simulations (Vergara et al. 2023-2025).
• Seed Mass: $M_{BH} = \epsilon_{BH} \times M_{gal}$. The model caps seed masses at $10^7 M_\odot$ based on current simulation validation limits.

D. X-ray Emission Modeling

• Spectral Model: Power law with high-energy cutoff ($f_E \propto E^{-\Gamma} e^{-E/E_{cut}}$), with $\Gamma = 1.9$ and $E_{cut} = 20$ keV.
• Luminosity: $L_X = k \cdot L_{Edd}$, where $k$ is a composite parameter representing the product of occupation fraction, duty cycle ($U_{duty}$), Eddington ratio ($\epsilon_{Edd}$), and X-ray bolometric correction ($\epsilon_X$).
• Absorption: The model includes attenuation by gas column density ($N_{ave}$) and metallicity ($Z$) using a suppression factor $\exp(-\sigma_{tot}(E)N_{ave})$.
• Comparison: Predicted X-ray fluxes (soft: 0.3–2 keV; hard: 2–7 keV) are compared against the 3$\sigma$ upper limits from S+25.

3. Key Contributions and Results

A. Constraints on Evolutionary Parameters ($\alpha$ and $\beta$)

• Mass-Radius Relation ($\beta$): The collision scenario is highly efficient only if $\beta \gtrsim 0.55$.
  • If $\beta \approx 0.6$ (similar to local early-type galaxies or NSCs), the model predicts massive seeds ($M_{BH}/M_{gal} \approx 0.1$), significantly higher than the local universe relation ($M_{BH}/M_{gal} \lesssim 0.001$).
  • If $\beta$ is too low (e.g., spiral-like $\beta \approx 0.2$), densities are insufficient for runaway collisions.
• Star Formation History ($\alpha$): Consistency with observed SFRs in LRDs requires $\alpha \gtrsim 1$ (constant or increasing SFR).
• Conclusion: The combination of $\alpha \gtrsim 1$ and $\beta \approx 0.6$ allows LRDs to form massive BH seeds efficiently while remaining consistent with X-ray non-detections.

B. X-ray Constraints and Obscuration

The study identifies specific combinations of physical parameters that reconcile massive seeds with X-ray limits:

• Low Activity/High Obscuration: Scenarios with high Eddington ratios and duty cycles (high $k$) are feasible only if accompanied by high column densities ($N_H \gtrsim 10^{21} \text{ cm}^{-2}$) and/or high metallicity.
• Moderate Sub-Eddington Accretion: A more natural solution is moderate accretion ($L/L_{Edd} \sim 0.1$) with low duty cycles. This produces massive seeds that grow slowly, naturally resulting in "X-ray weak" AGNs without requiring extreme obscuration ($N_H \sim 10^{19} - 10^{20} \text{ cm}^{-2}$).
• Metallicity Dependence: Higher metallicity increases the X-ray absorption cross-section, allowing lower column densities to suppress emission. At solar metallicity, even low column densities can hide high-activity sources.

C. Comparison with IR-Inferred Masses

• The model predicts BH masses peaking around $10^7 M_\odot$ (capped by the collision model limit).
• This is consistent with the bulk of BH masses inferred from JWST IR luminosities (assuming moderate Eddington ratios), though the IR data shows a tail extending to $>10^8 M_\odot$.
• The authors suggest that the most massive IR-inferred objects might require a combination of massive seeds (from collisions) and subsequent efficient accretion, potentially explaining the extreme $M_{BH}/M_{bulge}$ ratios ($\sim 40\%$) observed in some LRDs.

4. Significance and Implications

1. Resolution of the X-ray Tension: The paper demonstrates that LRDs do not necessarily require extreme obscuration ($N_H > 10^{25} \text{ cm}^{-2}$) to explain their X-ray weakness. Instead, the collision-based formation channel provides a natural explanation: massive seeds form early, but the subsequent accretion is either moderate/sub-Eddington or has a low duty cycle, keeping X-ray flux below detection limits.
2. Validation of Collision Models: The results support the hypothesis that dense, compact high-redshift galaxies are ideal birthplaces for massive black holes via stellar collisions, provided the mass-radius relation follows a slope $\beta \approx 0.6$.
3. Evolutionary Pathway: The study suggests that even if LRDs begin as starbursts, they are destined to evolve into AGNs. The "X-ray weakness" is a transient phase or a result of specific accretion physics rather than a lack of a central engine.
4. Future Observational Needs: The authors emphasize the need for direct measurements of gas content (column density and metallicity) in LRDs to distinguish between heavily obscured AGN scenarios and compact starburst scenarios. They also highlight the importance of radio follow-up, noting that high SFRs in LRDs may mask radio-quiet AGN signatures.

In summary, Liempi et al. provide a robust physical framework where dynamically formed massive seeds combined with regulated accretion explain the unique properties of Little Red Dots, bridging the gap between optical evidence for massive black holes and the lack of X-ray detections.