Direct Collapse Black Holes

• Direct collapse black holes are massive seed black holes (10^4–10^6 M☉) formed in atomic-cooling halos with suppressed H₂ cooling.
• Their formation involves nearly isothermal collapse at ~8000–10^4 K with high inflow rates, regulated by chemical and radiative interactions.
• Magnetic fields and controlled fragmentation reduce multiplicity, supporting the buildup of a dominant ~10^5 M☉ clump critical for subsequent growth.

to=arxiv_search.search 乐亚json {"query":"Direct collapse black holes radio signals from early direct collapse black holes (Yue et al., 2021)", "max_results": 5} to=arxiv_search.search ＿天天json {"query":"Role of magnetic fields in the formation of direct collapse black holes (Latif et al., 2022)", "max_results": 5} to=arxiv_search.search 手机天天彩票json {"query":"3-cm Fine Structure Masers unique signature of supermassive black hole formation via direct collapse early universe (Dijkstra et al., 2016)", "max_results": 5} to=arxiv_search.search 彩神争霸苹果json {"query":"The Formation of Direct Collapse Black Holes at Cosmic Dawn and 21 cm Global Spectrum (Zhang et al., 28 Mar 2025)", "max_results": 5} to=arxiv_search.search 天天中彩票是不是json {"query":"Little Red Dots as Direct-collapse Black Hole Nurseries (Cenci et al., 20 Aug 2025)", "max_results": 5} Direct-collapse black holes (DCBHs) are massive black-hole seeds, typically with initial masses of about $10^4$–$10^6\,M_\odot$, that are hypothesized to form at high redshift in atomic-cooling halos where $\mathrm{H}_2$ cooling is suppressed, the gas remains near $T \approx 8000$–$10^4\,\mathrm{K}$, and collapse proceeds through a supermassive-star or closely related intermediate stage rather than through ordinary star formation. In this framework, DCBHs are attractive progenitors of the first supermassive black holes because they start much heavier than stellar remnants, but their viability depends on a tightly coupled set of chemical, radiative, dynamical, and environmental conditions, and their post-birth growth is not guaranteed (Latif et al., 2022, Agarwal et al., 2012, Chon et al., 2020).

1. Formation pathway and defining conditions

In the direct-collapse pathway, the host is an atomic-cooling halo with virial temperature above the atomic threshold, conventionally $T_{\rm vir} \gtrsim 10^4\,\mathrm{K}$. A widely used scaling is

$$T_{\rm vir} \approx 1.98\times10^4\,{\rm K}\,\Big(\frac{\mu}{0.6}\Big)\Big(\frac{M}{10^8\,h^{-1}\,M_\odot}\Big)^{2/3}\Big(\frac{\Omega_m \Delta_c}{18\pi^2}\Big)^{1/3}\Big(\frac{1+z}{10}\Big),$$

which places the relevant halos at characteristic masses of $\gtrsim 10^7\,M_\odot$ at high redshift. The gas must remain pristine or nearly so, because metal-line cooling and dust-assisted fragmentation otherwise redirect collapse toward conventional star formation. In the idealized limit of suppressed molecular cooling, the collapse is nearly isothermal at $T \approx 8000\,\mathrm{K}$, and the inflow rate is set by the sound speed,

$$\dot M \approx \frac{c_s^3}{G} \approx 0.1\,M_\odot\,{\rm yr}^{-1},$$

which is sufficient to assemble a supermassive star of $10^6\,M_\odot$0 in $10^6\,M_\odot$1–$10^6\,M_\odot$2 before collapse to a massive seed black hole (Latif et al., 2022, Agarwal et al., 2012).

The chemical bottleneck is the formation of $10^6\,M_\odot$3, primarily through the $10^6\,M_\odot$4 channel,

$10^6\,M_\odot$5

and DCBH formation requires that this pathway be suppressed long enough for the halo to enter the atomic-cooling regime. This may be achieved by Lyman–Werner dissociation of $10^6\,M_\odot$6, by photodetachment of $10^6\,M_\odot$7, or by combinations of radiative and dynamical effects that keep the $10^6\,M_\odot$8 cooling time above the relevant collapse timescale. A recent single-zone formulation makes this explicit by requiring the $10^6\,M_\odot$9 cooling time to exceed the Hubble time until the gas reaches $\mathrm{H}_2$0, thereby defining an atomic-cooling-halo condition rather than an already fully monolithic collapse state (Aggarwal et al., 29 Sep 2025).

Seed masses in this literature span roughly $\mathrm{H}_2$1–$\mathrm{H}_2$2, with $\mathrm{H}_2$3 often serving as the fiducial direct-collapse product. That range recurs across radiative-transfer, MHD, near-infrared, radio, and gravitational-wave studies, and is central to why DCBHs are considered heavy seeds rather than merely efficient stellar remnants (Yue et al., 2021, Dijkstra et al., 2016, Pacucci et al., 2015).

2. Radiative regulation and the non-universality of the critical field

A persistent theme in DCBH theory is that there is no single universal critical radiation threshold. Earlier work often parameterized the condition for direct collapse by a scalar $\mathrm{H}_2$4 in units of $\mathrm{H}_2$5, but detailed SED-dependent calculations show that the relevant control parameters are the $\mathrm{H}_2$6 photodissociation rate and the $\mathrm{H}_2$7 photodetachment rate, and that the same $\mathrm{H}_2$8 can correspond to very different chemistry depending on the source spectrum. For realistic stellar populations, the allowed threshold spans

$\mathrm{H}_2$9

rather than a fixed number, and the direct-collapse boundary is better represented as a critical curve in the $T \approx 8000$0 plane than as a universal flux level (Agarwal et al., 2015, Zhang et al., 28 Mar 2025).

This SED sensitivity is reinforced by environmental models. In cosmological clustering calculations, the local LW field from nearby Pop II sources can exceed the mean background by up to $T \approx 8000$1, and the onset of Pop II star formation at $T \approx 8000$2 coincides with the onset of DCBH formation because Pop II spectra are more efficient than Pop III spectra at pushing pristine atomic-cooling halos above the relevant threshold. In that framework, Pop III sources alone do not reach the required conditions, whereas local Pop II irradiation can do so, especially in clustered environments where source–target separations are only a few kpc (Agarwal et al., 2012).

A more restrictive but physically explicit version is the synchronized-halo scenario. High-resolution radiation-hydrodynamics simulations show that a low-level background field of

$T \approx 8000$3

can delay prior star formation, while a nearby star-bursting primary halo at separation $T \approx 8000$4, turning on within $T \approx 8000$5 of secondary collapse, can drive the secondary onto the nearly isothermal atomic-cooling track without photoevaporating it or polluting it with metals, provided the primary remains luminous for $T \approx 8000$6 (Regan et al., 2017).

Obscured DCBHs themselves can also act as radiative triggers for further DCBH formation. One-zone calculations using Compton-thick DCBH SEDs filtered through columns of $T \approx 8000$7–$T \approx 8000$8 find remarkably low thresholds,

$T \approx 8000$9

which rise only to

$10^4\,\mathrm{K}$0

even when the DCBH-sourced X-ray background is pushed to the maximum allowed by the present-day unresolved X-ray background. The reason is spectral: obscuration converts much of the ionizing output into sub-$10^4\,\mathrm{K}$1 continuum that efficiently photodetaches $10^4\,\mathrm{K}$2 without generating as much X-ray catalysis of $10^4\,\mathrm{K}$3 formation as normal galaxies do (Yue et al., 2016).

Internal radiation generated by the collapsing cloud further complicates the threshold picture. Trapped Ly$10^4\,\mathrm{K}$4 cooling photons can photodetach $10^4\,\mathrm{K}$5 and lower the external field required for direct collapse by up to a factor of a few, with the largest effect for hard background spectra characteristic of hot young stellar populations. In one-zone models this shifts $10^4\,\mathrm{K}$6 from $10^4\,\mathrm{K}$7 to $10^4\,\mathrm{K}$8 or even $10^4\,\mathrm{K}$9 for $T_{\rm vir} \gtrsim 10^4\,\mathrm{K}$0, depending on the assumed central concentration of the Ly$T_{\rm vir} \gtrsim 10^4\,\mathrm{K}$1 source (Johnson et al., 2016).

3. Collapse dynamics, magnetic support, and fragmentation

The adjective “direct” does not imply a featureless or strictly fragmentation-free collapse. The most detailed cosmological MHD calculations evolved for a full $T_{\rm vir} \gtrsim 10^4\,\mathrm{K}$2 show that magnetic fields are rapidly amplified by strong accretion shocks at disk edges and by turbulence, far beyond simple flux freezing. In these runs the magnetic field grows by $T_{\rm vir} \gtrsim 10^4\,\mathrm{K}$3 orders of magnitude for a fiducial seed field and by up to $T_{\rm vir} \gtrsim 10^4\,\mathrm{K}$4 orders for a weaker seed, with a growth time of about $T_{\rm vir} \gtrsim 10^4\,\mathrm{K}$5, and saturates near equipartition with turbulent energy over the inner tens of parsecs. By the end of the simulations, the field reaches $T_{\rm vir} \gtrsim 10^4\,\mathrm{K}$6 within the central $T_{\rm vir} \gtrsim 10^4\,\mathrm{K}$7 and $T_{\rm vir} \gtrsim 10^4\,\mathrm{K}$8 at $T_{\rm vir} \gtrsim 10^4\,\mathrm{K}$9–$$T_{\rm vir} \approx 1.98\times10^4\,{\rm K}\,\Big(\frac{\mu}{0.6}\Big)\Big(\frac{M}{10^8\,h^{-1}\,M_\odot}\Big)^{2/3}\Big(\frac{\Omega_m \Delta_c}{18\pi^2}\Big)^{1/3}\Big(\frac{1+z}{10}\Big),$$0 (Latif et al., 2022).

In that regime, magnetic support is dynamically important. Using

$$T_{\rm vir} \approx 1.98\times10^4\,{\rm K}\,\Big(\frac{\mu}{0.6}\Big)\Big(\frac{M}{10^8\,h^{-1}\,M_\odot}\Big)^{2/3}\Big(\frac{\Omega_m \Delta_c}{18\pi^2}\Big)^{1/3}\Big(\frac{1+z}{10}\Big),$$1

the inner disk satisfies $$T_{\rm vir} \approx 1.98\times10^4\,{\rm K}\,\Big(\frac{\mu}{0.6}\Big)\Big(\frac{M}{10^8\,h^{-1}\,M_\odot}\Big)^{2/3}\Big(\frac{\Omega_m \Delta_c}{18\pi^2}\Big)^{1/3}\Big(\frac{1+z}{10}\Big),$$2 and $$T_{\rm vir} \approx 1.98\times10^4\,{\rm K}\,\Big(\frac{\mu}{0.6}\Big)\Big(\frac{M}{10^8\,h^{-1}\,M_\odot}\Big)^{2/3}\Big(\frac{\Omega_m \Delta_c}{18\pi^2}\Big)^{1/3}\Big(\frac{1+z}{10}\Big),$$3–$$T_{\rm vir} \approx 1.98\times10^4\,{\rm K}\,\Big(\frac{\mu}{0.6}\Big)\Big(\frac{M}{10^8\,h^{-1}\,M_\odot}\Big)^{2/3}\Big(\frac{\Omega_m \Delta_c}{18\pi^2}\Big)^{1/3}\Big(\frac{1+z}{10}\Big),$$4, so magnetic pressure is comparable to thermal pressure. A convenient description is to define an effective sound speed

$$T_{\rm vir} \approx 1.98\times10^4\,{\rm K}\,\Big(\frac{\mu}{0.6}\Big)\Big(\frac{M}{10^8\,h^{-1}\,M_\odot}\Big)^{2/3}\Big(\frac{\Omega_m \Delta_c}{18\pi^2}\Big)^{1/3}\Big(\frac{1+z}{10}\Big),$$5

which raises both the effective Toomre stability parameter and the magnetically supported Jeans mass,

$$T_{\rm vir} \approx 1.98\times10^4\,{\rm K}\,\Big(\frac{\mu}{0.6}\Big)\Big(\frac{M}{10^8\,h^{-1}\,M_\odot}\Big)^{2/3}\Big(\frac{\Omega_m \Delta_c}{18\pi^2}\Big)^{1/3}\Big(\frac{1+z}{10}\Big),$$6

The numerical consequence is not the elimination of substructure but a systematic reduction in multiplicity: MHD disks are larger and smoother, fragmentation is significantly reduced, and the surviving central clump typically still reaches $$T_{\rm vir} \approx 1.98\times10^4\,{\rm K}\,\Big(\frac{\mu}{0.6}\Big)\Big(\frac{M}{10^8\,h^{-1}\,M_\odot}\Big)^{2/3}\Big(\frac{\Omega_m \Delta_c}{18\pi^2}\Big)^{1/3}\Big(\frac{1+z}{10}\Big),$$7 by $$T_{\rm vir} \approx 1.98\times10^4\,{\rm K}\,\Big(\frac{\mu}{0.6}\Big)\Big(\frac{M}{10^8\,h^{-1}\,M_\odot}\Big)^{2/3}\Big(\frac{\Omega_m \Delta_c}{18\pi^2}\Big)^{1/3}\Big(\frac{1+z}{10}\Big),$$8 with mean inflow rates of $$T_{\rm vir} \approx 1.98\times10^4\,{\rm K}\,\Big(\frac{\mu}{0.6}\Big)\Big(\frac{M}{10^8\,h^{-1}\,M_\odot}\Big)^{2/3}\Big(\frac{\Omega_m \Delta_c}{18\pi^2}\Big)^{1/3}\Big(\frac{1+z}{10}\Big),$$9, broadly similar to non-MHD runs because rapid coalescence in purely hydrodynamic disks compensates for their larger number of fragments (Latif et al., 2022).

This matters because it corrects a common oversimplification. DCBH formation is not equivalent to the absolute absence of fragmentation. Rather, the pathway tolerates fragmentation so long as the global thermal state, inflow rate, and merger/coalescence history preserve the build-up of a dominant $\gtrsim 10^7\,M_\odot$0 clump or supermassive star. Magnetic fields therefore appear to stabilize the pathway mainly by reducing multiplicity and supporting coherent inflow, not by shutting off all small-scale structure (Latif et al., 2022).

4. Seed birth, early growth, and post-formation dynamics

Direct collapse solves the initial-mass problem, but not automatically the growth problem. In the most optimistic environments, a newly born $\gtrsim 10^7\,M_\odot$1 seed can sit at the nexus of cold accretion flows and remain near the Eddington limit for long enough to reach quasar scale. A radiation-hydrodynamics calculation that “switches on” a $\gtrsim 10^7\,M_\odot$2 DCBH at $\gtrsim 10^7\,M_\odot$3 inside a $\gtrsim 10^7\,M_\odot$4 atomically cooling halo finds a birth luminosity of

$\gtrsim 10^7\,M_\odot$5

corresponding to $\gtrsim 10^7\,M_\odot$6, and follows the host’s growth to $\gtrsim 10^7\,M_\odot$7 by $\gtrsim 10^7\,M_\odot$8 under sustained cold-flow feeding (Whalen et al., 2020).

Other cosmological simulations reach the opposite conclusion. When the Bondi scale is resolved during long-term post-formation evolution, accretion can remain far below Eddington because the seed forms in a metal-free environment typically $\gtrsim 10^7\,M_\odot$9 from the first galaxy, falls into the potential well, and acquires a relative velocity of order

$T \approx 8000\,\mathrm{K}$0

with respect to the gas. In that regime the effective Bondi rate

$T \approx 8000\,\mathrm{K}$1

is strongly suppressed. An analytic estimate then implies that DCBH formation must occur within

$T \approx 8000\,\mathrm{K}$2

of the galactic center for dynamical friction to decelerate the black hole before $T \approx 8000\,\mathrm{K}$3, but such locations are expected to have metallicities of

$T \approx 8000\,\mathrm{K}$4

which is in tension with the pristine requirement of classical direct collapse (Chon et al., 2020).

The earliest post-birth phase may itself be violent. In one model, the newborn DCBH is surrounded by a self-gravitating nuclear disk that fragments at

$T \approx 8000\,\mathrm{K}$5

into clumps of initial mass

$T \approx 8000\,\mathrm{K}$6

which evolve into massive Pop III stars and assemble a compact nuclear star cluster. Stellar relaxation can scatter some of these stars into the black hole’s loss cone on timescales $T \approx 8000\,\mathrm{K}$7, producing tidal disruption events with jet luminosities

$T \approx 8000\,\mathrm{K}$8

and observed prompt X-ray durations

$T \approx 8000\,\mathrm{K}$9

followed by radio afterglows potentially detectable even from $$\dot M \approx \frac{c_s^3}{G} \approx 0.1\,M_\odot\,{\rm yr}^{-1},$$0 (Kashiyama et al., 2016).

Taken together, these results imply that DCBHs are heavy seeds, not guaranteed quasars. Their later fate depends on where they form, how rapidly they couple to the densest gas, and whether cold inflows, mergers, or central metal-enriched pathways can keep them fueled (Whalen et al., 2020, Chon et al., 2020).

5. Observational signatures from Ly$$\dot M \approx \frac{c_s^3}{G} \approx 0.1\,M_\odot\,{\rm yr}^{-1},$$1 to radio continua

The simplest intrinsic line signature is Ly$$\dot M \approx \frac{c_s^3}{G} \approx 0.1\,M_\odot\,{\rm yr}^{-1},$$2. During collapse powered only by gravitational heating, the Ly$$\dot M \approx \frac{c_s^3}{G} \approx 0.1\,M_\odot\,{\rm yr}^{-1},$$3 cooling luminosity is limited to

$$\dot M \approx \frac{c_s^3}{G} \approx 0.1\,M_\odot\,{\rm yr}^{-1},$$4

because collisional de-excitation eventually suppresses escape. Photoionization by a central accreting source is far more luminous and can produce

$$\dot M \approx \frac{c_s^3}{G} \approx 0.1\,M_\odot\,{\rm yr}^{-1},$$5

during favorable evolutionary stages. The emergent Ly$$\dot M \approx \frac{c_s^3}{G} \approx 0.1\,M_\odot\,{\rm yr}^{-1},$$6 profile is highly sensitive to $$\dot M \approx \frac{c_s^3}{G} \approx 0.1\,M_\odot\,{\rm yr}^{-1},$$7 column density, geometry, and velocity field: predicted widths and offsets range from a few tens to a few thousands of $$\dot M \approx \frac{c_s^3}{G} \approx 0.1\,M_\odot\,{\rm yr}^{-1},$$8. Applied to CR7, these models imply that if the source is black-hole powered, the Ly$$\dot M \approx \frac{c_s^3}{G} \approx 0.1\,M_\odot\,{\rm yr}^{-1},$$9 luminosity alone requires

$10^6\,M_\odot$00

while the observed line width favors

$10^6\,M_\odot$01

and an outflowing medium, indicating that the original high-column formation conditions have already been erased (Dijkstra et al., 2016).

A more specialized but exceptionally distinctive signature is the fine-structure maser at rest wavelength $10^6\,M_\odot$02, arising when trapped Ly$10^6\,M_\odot$03 photons overpopulate the $10^6\,M_\odot$04 level of atomic hydrogen. The inversion condition is

$10^6\,M_\odot$05

which produces negative opacity in the $10^6\,M_\odot$06–$10^6\,M_\odot$07 transition. In simplified DCBH collapse models, this can amplify the CMB by up to $10^6\,M_\odot$08 before saturation, generating a broad asymmetric line with hyperfine structure, a flux of about $10^6\,M_\odot$09–$10^6\,M_\odot$10, an angular scale of $10^6\,M_\odot$11–$10^6\,M_\odot$12, and an observed frequency in the range $10^6\,M_\odot$13–$10^6\,M_\odot$14 for $10^6\,M_\odot$15–$10^6\,M_\odot$16. The required combination of dust-free gas, very high $10^6\,M_\odot$17, and extremely low $10^6\,M_\odot$18 makes this a particularly specific DCBH marker (Dijkstra et al., 2016).

Near-infrared searches target the birth phase and the first tens of megayears thereafter. Radiation-hydrodynamics plus Cloudy post-processing predicts that newborn DCBHs in cold accretion flows are brightest in the reddest JWST/NIRCam bands, with apparent magnitudes

$10^6\,M_\odot$19

across $10^6\,M_\odot$20–$10^6\,M_\odot$21 in the $10^6\,M_\odot$22 and $10^6\,M_\odot$23 filters. In $10^6\,M_\odot$24 exposures they are detectable in all four long-wavelength NIRCam filters out to $10^6\,M_\odot$25, and redward of $10^6\,M_\odot$26 detectability extends to $10^6\,M_\odot$27. Because Euclid and Roman are shallower but wider, strong lensing becomes decisive there: for reasonable host-halo abundances, Roman, Euclid, and JWST could potentially find hundreds of strongly lensed DCBHs at $10^6\,M_\odot$28–$10^6\,M_\odot$29, with Roman performing best at $10^6\,M_\odot$30 and JWST at higher redshift (Whalen et al., 2020, Vikaeus et al., 2022).

Radio predictions bifurcate according to the emission model. If accreting DCBHs launch blazar-like jets with power

$10^6\,M_\odot$31

then at $10^6\,M_\odot$32 SKA-mid and ngVLA can detect sources with

$10^6\,M_\odot$33

and an optimistic normalization of

$10^6\,M_\odot$34

yields about

$10^6\,M_\odot$35

above the SKA1-mid threshold in $10^6\,M_\odot$36, provided all DCBHs are active and jetted. The low-frequency spectrum is often strongly suppressed by synchrotron self-absorption and, if the emitting region remains inside the dense envelope, by free–free absorption, so joint SKA-low and SKA-mid observations become a discriminant against star-forming galaxies (Yue et al., 2021). A more conservative approach, using several fundamental planes of black-hole accretion and assuming no jets, still finds that SKA-FIN could detect a $10^6\,M_\odot$37 DCBH at $10^6\,M_\odot$38 out to $10^6\,M_\odot$39, while SKA and ngVLA could probe $10^6\,M_\odot$40–$10^6\,M_\odot$41 black holes to $10^6\,M_\odot$42; by contrast, $10^6\,M_\odot$43 DCBHs at $10^6\,M_\odot$44 remain beyond current limits in that framework (Whalen et al., 2021).

6. Population histories, cosmological probes, and related high-redshift populations

Semi-analytic and simulation-based population models span a wide dynamic range. In one cosmological treatment that explicitly follows merger trees, stellar populations, and local LW fields, the direct-collapse formation rate rises from

$10^6\,M_\odot$45

at $10^6\,M_\odot$46 to

$10^6\,M_\odot$47

at $10^6\,M_\odot$48, with the first DCBHs appearing by $10^6\,M_\odot$49 and with local LW intensities that can exceed the spatially averaged background by up to $10^6\,M_\odot$50. In that picture, DCBH hosts are more clustered than similar-mass non-DCBH halos, especially at $10^6\,M_\odot$51 (Agarwal et al., 2012).

A different but influential formulation is the brief “DCBH era.” In that model, once a few Compton-thick DCBHs form, their reprocessed LW/NIR emission triggers a runaway rise in further DCBH formation. The universe enters a DCBH-dominated phase at

$10^6\,M_\odot$52

the comoving mass density rises from

$10^6\,M_\odot$53

at $10^6\,M_\odot$54 to

$10^6\,M_\odot$55

at $10^6\,M_\odot$56 in the fiducial case, and new DCBH formation is then almost completely shut off by photoevaporation after

$10^6\,M_\odot$57

The entire era lasts only $10^6\,M_\odot$58 (Yue et al., 2014).

Several indirect cosmological probes have now been attached to DCBH phenomenology. One is the global 21-cm absorption trough. In a model that combines a JWST-consistent UV luminosity function with X-ray-dependent critical curves for direct collapse, the trough depth correlates with seed abundance: if

$10^6\,M_\odot$59

DCBHs are expected to be rare; if

$10^6\,M_\odot$60

then

$10^6\,M_\odot$61

while deeper troughs allow substantially larger abundances (Zhang et al., 28 Mar 2025).

Another connection is to the JWST population of Little Red Dots. Preliminary MELIORA cosmological hydrodynamics runs that implement explicit DCBH criteria find that newly formed DCBHs are associated with a gas-compaction event, spend roughly $10^6\,M_\odot$62–$10^6\,M_\odot$63 in a bright near-Eddington phase, and inhabit dense compact reservoirs with

$10^6\,M_\odot$64

The abundance of these newborn seeds declines steeply at $10^6\,M_\odot$65, paralleling the observed decline of LRDs, and the combination of a compact neutral reservoir, strong obscuration, and the onset of Pop III star formation has been proposed as a possible explanation for the weak X-ray and hot-dust emission of at least a fraction of LRDs (Cenci et al., 20 Aug 2025).

More speculative variants extend the radiative trigger beyond galaxies and DCBHs themselves. One such model proposes that axion-like dark matter decays in the IGM inject $10^6\,M_\odot$66–$10^6\,M_\odot$67 photons that populate finite slices of the LW band. In that single-zone analysis, atomic-cooling-halo formation at $10^6\,M_\odot$68 is achieved for

$10^6\,M_\odot$69

and

$10^6\,M_\odot$70

with the line-resolved treatment of the LW band identified as essential (Aggarwal et al., 29 Sep 2025).

Gravitational waves provide yet another window. An early analytic estimate of the stochastic signal from DCBH formation bursts found a very low duty cycle,

$10^6\,M_\odot$71

a peak background amplitude

$10^6\,M_\odot$72

at

$10^6\,M_\odot$73

and a peak signal-to-noise ratio of about $10^6\,M_\odot$74 at $10^6\,M_\odot$75 for Ultimate-DECIGO, albeit below the Galactic confusion foreground (Pacucci et al., 2015). More recent numerical-relativity pipeline work aims to derive physically anchored collapse waveforms for LISA from cosmological DCBH initial conditions, but explicitly emphasizes that population properties such as masses, mass ratios, spins, and eccentricities remain poorly constrained (Kelly et al., 9 Dec 2025).

7. Open issues, tensions, and common misconceptions

One common misconception is that DCBH formation is controlled by a single $10^6\,M_\odot$76. The accumulated evidence points the other way: the relevant threshold depends on the source SED, on whether one works with $10^6\,M_\odot$77 or with the two-rate plane $10^6\,M_\odot$78, on X-ray backgrounds, on trapped Ly$10^6\,M_\odot$79 feedback, on obscuration, and on the geometry and timing of nearby sources (Agarwal et al., 2015, Zhang et al., 28 Mar 2025, Johnson et al., 2016).

A second misconception is that “direct collapse” means perfectly monolithic collapse with no fragmentation. Long-duration MHD simulations show that magnetic fields reduce multiplicity and stabilize disks, but do not erase all clump formation; similarly, the immediate post-birth disk around a DCBH may fragment into massive stars whose later dynamics feed back on the seed through tidal disruptions and photoevaporation. The operative criterion is therefore not zero fragmentation, but whether the thermal and inflow conditions still deliver a dominant central object of order $10^6\,M_\odot$80 (Latif et al., 2022, Kashiyama et al., 2016).

A third misconception is that producing a heavy seed is enough to explain the first quasars. In fact, direct-collapse sites can be hostile to growth. Radiative feedback, large BH–gas relative velocities, and off-center birth locations can hold accretion far below Eddington for $10^6\,M_\odot$81, whereas only special environments such as sustained cold accretion flows or perhaps central, mildly metal-enriched pathways appear able to maintain the required fueling (Chon et al., 2020, Whalen et al., 2020).

Finally, observational forecasts are model-contingent. Radio source counts depend on the unknown jetted fraction, jet duty cycle, spin, envelope absorption, and whether a fundamental-plane extrapolation is appropriate at all for newborn DCBHs; lensing yields depend on high-magnification tails and source sizes; 21-cm mappings retain at least dex-level uncertainty; and the abundance of viable pristine halos remains highly sensitive to clustering, metal transport, and radiative backgrounds (Yue et al., 2021, Whalen et al., 2021, Zhang et al., 28 Mar 2025, Agarwal et al., 2012).

These tensions do not invalidate the DCBH hypothesis; they delimit it. A plausible implication is that “DCBH” is best treated not as a single sharply defined channel, but as a family of heavy-seed pathways centered on atomic-cooling collapse under suppressed molecular cooling, with outcomes controlled by the interplay of radiation fields, magnetic support, inflow history, obscuration, and subsequent environmental coupling.