Direct-Collapse Black Holes (DCBHs)

• Direct-collapse black holes (DCBHs) are massive black hole seeds of 10^4–10^6 Mₒ formed through rapid, isothermal collapse of pristine or metal-poor gas in early universe dark matter halos.
• Their formation requires high virial temperatures, suppressed H₂ cooling through critical Lyman-Werner flux, and low metallicities, enabling monolithic collapse without fragmentation.
• DCBHs are identified via unique multiwavelength signatures including steep red infrared SEDs and potential gravitational-wave emissions, offering insight into early supermassive black hole assembly.

Direct-collapse black holes (DCBHs) are massive black hole seeds with characteristic masses of $\sim 10^{4}$–$10^{6}\ M_\odot$ that form from the rapid, isothermal monolithic collapse of primordial or extremely metal-poor gas in atomic-cooling dark matter halos in the early universe. They are a leading candidate for the progenitors of $\gtrsim 10^9\ M_\odot$ supermassive black holes (SMBHs) observed as luminous quasars at $z \gtrsim 7$, when the universe was less than 800 Myr old. The DCBH scenario is motivated by the need for efficient early SMBH seeding and accretion in cosmological conditions that suppress the otherwise ubiquitous fragmentation of gas into Population III stars. Observational and theoretical efforts increasingly focus on distinguishing DCBHs from alternative channels, constraining their formation rates, and identifying their multiwavelength signatures—including future gravitational-wave detections.

1. Physical Formation Criteria for DCBHs

The DCBH formation mechanism requires several stringent environmental and thermochemical criteria, rooted in the physics of gas cooling and fragmentation in high-$z$ halos:

• Halo Mass and Virial Temperature: The host dark matter halo must achieve $T_{\mathrm{vir}} \gtrsim 10^4\, \text{K}$, corresponding to $M_{\mathrm{halo}} \gtrsim 10^{7}\ M_\odot$ at $z \gtrsim 10$–20, so that atomic hydrogen cooling (through Ly$\alpha$ and two-photon emission) can bring the gas to $T\sim8000\,\text{K}$ and induce an isothermal collapse without fragmentation (Agarwal et al., 2012, Regan et al., 2017, Jeon et al., 19 Aug 2025).
• Suppression of H$_2$ Cooling: Molecular hydrogen must be efficiently destroyed to prevent fragmentation into stars. This is operationalized as a critical local Lyman-Werner background:

$J_{\rm LW,\, crit} \sim 30\text{--}300$

(Pop II spectrum, in units of $$10^{-21}\,\text{erg\,s}^{-1}\,\text{cm}^{-2}\,\text{Hz}^{-1}\,\text{sr}^{-1}$$), or up to $10^3$ for harder Pop III-like sources (Yue et al., 2014, Agarwal et al., 2015, Jeon et al., 19 Aug 2025). The precise value depends sensitively on the spectral energy distribution (SED) of irradiating sources, their age/metallicity, and three-body H$_2$ formation rates (Agarwal et al., 2015).

• Metallicity Constraint: Metallicity must remain below a critical threshold to avoid metal-line and dust-induced fragmentation, typically $Z < 2 \times 10^{-4}\ Z_\odot$ (Jeon et al., 19 Aug 2025).
• Radiative Backgrounds and Feedback: The required LW field is most efficiently provided by nearby Pop II star-forming galaxies or, in some scenarios, existing DCBHs (which themselves generate hard spectra highly efficient at H$_2$ suppression). The cumulative X-ray and ionizing backgrounds can in turn promote or suppress DCBH formation by modifying the electron fraction and thus H$_2$ formation rates (Yue et al., 2016, Zhang et al., 28 Mar 2025).
• Monolithic Isothermal Collapse: With H$_2$ and metallicity suppressed, gas collapses nearly isothermally, with the Jeans mass remaining $M_J \sim 10^{5}$–$10^{6}\ M_\odot$, favoring formation of a single massive object rather than a stellar cluster (Jeon et al., 19 Aug 2025).

These criteria are realized in cosmological settings through a combination of synchronized halo assembly, proximity to ongoing star-formation, and avoidance of metal enrichment (Regan et al., 2017, Agarwal et al., 2012).

2. Theoretical Evolution, Seed Mass Scale, and Early Growth

DCBHs are seeded following the collapse of supermassive stars (SMSs) or quasi-stars, yielding initial black hole masses of $M_{\rm seed} \sim 10^{4}$–$10^{6}\ M_\odot$ (Nabizadeh et al., 2023, Latif et al., 2020, Jeon et al., 19 Aug 2025). The subsequent accretion history is controlled by the gas reservoir, feedback mechanisms, and the kinematics of the black hole within the host halo:

• Initial Growth: Simulations show that the earliest accretion rates can approach or exceed the Eddington limit (modestly super-Eddington accretion, $L/L_{\rm Edd} \sim 1$–3) during the "Compton-thick" phase, with duty cycles $f_{\rm duty} \sim 0.5$–0.8 over timescales up to $\Delta t_{\rm DC} \sim 10$–$100\ \rm Myr$ (Nabizadeh et al., 2023, Jeon et al., 19 Aug 2025).
• SED and Photometric Signature: During this phase, emergent SEDs are extremely steep and red across the $1$–$5\ \mu$m range, $F_\nu \propto \nu^{\alpha}$, $\alpha \sim -3$ to $-4$ in models such as Pacucci et al. These objects are Compton-thick ($N_{\rm H} \gtrsim 10^{24}\ \rm cm^{-2}$), efficiently reprocessing ionizing photons into the infrared (Nabizadeh et al., 2023, Yue et al., 2016).
• Metallicity and Gas Reservoir: While formation favors pristine environments, efficient long-term accretion is often stifled by radiative/SN feedback, turbulent kinematics, and the need to sink to galactic centers for sustained growth (Chon et al., 2020). Formation in slightly metal-enriched gas (dust-regulated collapse) at $Z \sim 10^{-5}$–$10^{-3}\ Z_\odot$ may enable central positioning required for efficient accretion (Chon et al., 2020).
• Multiplicity: Disk fragmentation in the immediate post-collapse phase may yield binary/multiple SMSs and hence DCBH binaries, with subsequent implications for GW signals (Latif et al., 2020).

3. Clustering, Abundance, and Population Synthesis

The DCBH formation rate and spatial distribution result from the interplay of rarity and local clustering of requisite conditions:

• Abundance Estimates: Models predict a formation rate of $dn_{\rm DCBH}/dz \sim 10^{-3}$–$10^{-2}\ \rm Mpc^{-3}\ z^{-1}$ at $z=6$–14 (Agarwal et al., 2012, Zhang et al., 28 Mar 2025). Observational upper limits in wide area deep JWST surveys currently constrain the comoving number density of steep-slope DCBHs to $$n_{\rm hosts} \lesssim 5 \times 10^{-4}\ \rm cMpc^{-3}$$ at $z \sim 6$–14 (Nabizadeh et al., 2023), already ruling out the highest predicted theoretical yields.
• Triggered Runaway Formation ("DCBH factories"): Once a first generation of DCBHs forms, their hard SEDs lower the required $J_{\rm LW}^{\rm crit}$ in neighboring halos, potentially triggering a runaway cascade of DCBH formation in overdense regions (Yue et al., 2014, Yue et al., 2016). Simulation-based studies find that spatial clustering of such events can lead to a "brief era" of rapid DCBH assembly at $z\sim14$–20 before photoevaporative feedback suppresses further formation (Yue et al., 2014).
• Stochasticity and SED dependence of $J_{\rm crit}$: There is no unique "critical" LW threshold; realistic stellar populations and SEDs broaden the effective $J_{\rm crit}$ from $\sim 0.1$ to $\sim 10^3$ depending on distance, age, star formation rate, and metallicity. This results in orders-of-magnitude variation in DCBH formation rates with small changes in environment (Agarwal et al., 2015).
• Host Properties and Demographics: The host halos of DCBHs are more massive and clustered than the typical dark matter halos at similar epochs, and early DCBH hosts are compact, overmassive (high $M_{\rm BH}/M_\star$), and metal-poor (Jeon et al., 19 Aug 2025).

4. Multiwavelength and Gravitational-Wave Observational Signatures

DCBHs are multi-messenger targets, with predicted electromagnetic and gravitational-wave signatures across the cosmic dawn and reionization epochs:

• Infrared and Photometric Identification: The initial Compton-thick growth phase yields very red, featureless SEDs across JWST/NIRCam bands, often with "V-shaped" continua and strong Balmer breaks. These can mimic obscured AGN or extremely dusty galaxies at intermediate redshift, requiring follow-up spectroscopy to distinguish true DCBHs (Nabizadeh et al., 2023, Jeon et al., 19 Aug 2025).
• High-Resolution Spectroscopy: Confirmatory spectroscopic signatures include high Balmer decrements ($\rm H\alpha/H\beta \gg 3$), strong He II $\lambda 1640$, and the absence of metal-line forests. The lack of [O III], [Ne III], and Fe II lines is a critical discriminant from AGN and starburst interlopers (Nabizadeh et al., 2023, Jeon et al., 19 Aug 2025).
• Radio Emission: While most DCBHs form in radiatively efficient, thin-disk accretion modes, a subset may launch powerful relativistic jets, yielding detectable GHz–mm continuum signals in future SKA and ngVLA surveys. Predicted radio flux densities for $M_{\rm BH} \gtrsim 10^{5}\ M_\odot$ seeds are $\gtrsim$ tens of nJy at $z \sim 10$, with spectral turnover due to synchrotron self-absorption and free-free absorption in the dense envelope (Whalen et al., 2021, Yue et al., 2021, Latif et al., 2022).
• Ly$\alpha$ and UV Lines: DCBHs can power Ly$\alpha$ emitters, but strong collisional de-excitation limits observable Ly$\alpha$ to specific evolutionary windows. Case B recombination yields $$L_{\rm Ly\alpha, rec, max} \sim 2\times 10^{43}(M_{\rm BH}/10^{6}\ M_\odot)\ {\rm erg\,s}^{-1}$$; observed Ly$\alpha$ emission requires significant growth ($M_{\rm BH} > 10^7\ M_\odot$) and low $N_{\rm HI}$ columns (Dijkstra et al., 2016).
• Tidal Disruption Events and X-ray/Radiative Flares: Early nuclear disks fragment into Pop III stars, leading to multiple tidal disruption events (TDEs) during the first Myr after DCBH formation, with jet luminosities $L_{\rm j} \gtrsim 10^{50}\ \rm erg\,s^{-1}$ and peak X-ray transients detectable to $z\sim20$ with future wide-field X-ray facilities (Kashiyama et al., 2016, Latif et al., 2020).
• 21 cm Cosmology: The global 21 cm absorption depth during cosmic dawn ($\delta T_b^{\rm trough}$) encodes the abundance of DCBHs, via their impact on the X-ray heating budget. For $$-150\ \rm mK \lesssim \delta T_b^{\rm trough} \lesssim -100\ \rm mK$$, models predict $n_{\rm DCBH} \sim 10^{-2}$–$10^{-3}\ \rm cMpc^{-3}$, matching the observed SMBH abundance at $z\gtrsim6$ (Zhang et al., 28 Mar 2025).
• Gravitational Wave Emission: Binary DCBH systems formed in high-redshift nuclear disks or via early halo mergers are expected LISA sources. Inspiral and merger events of $M_{\rm tot} \sim 10^{5}$–$10^{6}\ M_\odot$ binaries yield GW frequencies peaking at $f_{\rm peak} \sim 0.5$–$1$ mHz, within LISA’s sensitivity window, with SNR $\sim 10$–$50$ at $z\sim10$ (Kelly et al., 9 Dec 2025, Pacucci et al., 2015, Latif et al., 2020). Collapse of single SMSs to DCBHs also produce short-duration (2–30 s) GW bursts at $0.8$–$300$ mHz with "popcorn" statistics and a peak energy-density $\Omega_{\rm gw} \sim 10^{-54}$, detectable in the Ultimate-DECIGO band (Pacucci et al., 2015).

5. Magnetohydrodynamics, Jets, and Impact of Microphysics

The full formation and growth pathway of DCBHs is sensitive to magnetic fields, radiation hydrodynamics, and chemical microphysics:

• Magnetic Field Amplification and Fragmentation Suppression: 3D cosmological MHD simulations find that even weak primordial seed fields are quickly amplified to equipartition with turbulence by small-scale dynamos driven by accretion shocks. Magnetic pressure enhances the effective Jeans mass, stabilizing disks, and reducing SMS multiplicity (favoring single or binary formation in MHD runs versus multiples in pure HD) (Latif et al., 2022).
• Jet Launching and Feedback: In the presence of strong ordered fields and rapid rotation (magnetically-arrested disks, MADs), DCBHs can launch relativistic jets, producing significant kinetic feedback and clearing outflows that may regulate subsequent accretion and be detected as synchrotron transients (Yue et al., 2021, Latif et al., 2022).
• Feedback-Regulated Accretion: Photoionization, X-ray, and mechanical (jet/wind) feedback limit the gas supply and can rapidly reduce accretion from Eddington to sub-Eddington rates, constraining the lifetime during which DCBHs are observable as luminous infrared or X-ray sources (Kashiyama et al., 2016, Chon et al., 2020).
• Alternative Seed Channels: Models comparing DCBH seeding to Pop III remnant BHs consistently find that heavy seeds (DCBHs) naturally match the properties (e.g., high $M_{\rm BH}/M_\star$, extreme red SEDs) of compact AGN-dominated systems (such as JWST-detected "Little Red Dots"), while light seeds cannot account for the observed demographics without invoking fine-tuned super-Eddington accretion or extreme gas/dust environments (Jeon et al., 19 Aug 2025).

6. Current Constraints, Uncertainties, and Future Directions

Despite significant theoretical and observational progress, several outstanding uncertainties remain in the demographics and identification of DCBHs:

• Degeneracy of Photometric Signatures: Even with multi-band JWST/NIRCam data, DCBH candidates remain photometrically degenerate with dusty starburst galaxies and obscured AGN between $z\sim2$–$10$; robust classification will require high S/N spectroscopy to isolate unique emission line features and measure gas-phase metallicity (Nabizadeh et al., 2023).
• Timing and Duration of the "DCBH Era": The rapid build-up and subsequent termination of DCBH formation due to photoevaporation and metal enrichment imply only brief cosmic windows for their efficient assembly ($\approx$150 Myr, ending by $z \sim 13$) (Yue et al., 2014).
• Abundance Uncertainty and SED-Dependence: The $\sim$2–3 orders-of-magnitude range in number density predictions due to SED-dependent $J_{\rm crit}$ underscores the importance of modeling cosmic environments and stellar populations in detail (Agarwal et al., 2015).
• Relevance for Local SMBH Populations: If DCBH seeds with $M_{\rm seed} \sim 10^5\ M_\odot$ were common at $n\sim10^{-4}\ \rm cMpc^{-3}$, they can account for the observed abundance of $z\sim6$–7 SMBHs (quasars) given plausible efficiency for subsequent mergers and accretion. A lower density would necessitate more extreme super-Eddington growth or alternative SMBH seeding channels (Nabizadeh et al., 2023).
• Key Observational Prospects:
  • JWST, Euclid, and Roman can identify candidates at $z\lesssim 19$ in deep IR fields through their distinct SEDs (Whalen et al., 2020, Nabizadeh et al., 2023).
  • SKA/ngVLA will probe jet-producing DCBHs through their GHz radio signals (Whalen et al., 2021, Yue et al., 2021).
  • All-sky X-ray (eROSITA, Athena) and future GW missions (LISA, Ultimate-DECIGO) will individually constrain event rates, merger properties, and mass functions (Pacucci et al., 2015, Latif et al., 2020, Kelly et al., 9 Dec 2025).
  • Global 21cm experiments (EDGES, SARAS, REACH) will constrain DCBH abundance through X-ray heating signatures (Zhang et al., 28 Mar 2025).
• Crucial Discriminants: Measurement of gas-phase metallicity and $M_{\rm BH}/M_\star$ ratios, together with resolved rest-optical line diagnostics, will be pivotal in distinguishing heavy seed (DCBH) channels from alternatives at both high and intermediate redshift (Jeon et al., 19 Aug 2025, Nabizadeh et al., 2023).

DCBHs remain a central focus in efforts to explain rapid SMBH assembly and probe the extremes of early structure formation and black hole astrophysics in the high-redshift universe.