Light Seed Black Holes (LSBHs)

• Light Seed Black Holes (LSBHs) are low-mass remnants (10–10^3 M☉) from Population III stars and stellar collisions in dense, metal-free environments.
• They form through two main channels—direct collapse remnants of massive stars and runaway collisions in clusters—with growth limited by radiative feedback and environmental factors.
• Observational signatures include distinct AGN luminosity functions, high dwarf galaxy occupation fractions, and gravitational-wave events that differentiate LSBH evolution from heavy-seed scenarios.

Light Seed Black Holes (LSBHs) are the remnants of Population III (Pop III) stellar evolution and the products of stellar dynamical processes in dense primordial environments, representing the lowest end of the black hole seed mass spectrum that ultimately grows into the observed supermassive black hole (SMBH) population. The archetypal LSBH has an initial mass in the range $M_{\rm LSBH} \sim 10^{1-3}\,M_\odot$, with their initial cosmological abundance exceeding that of heavy seed black holes by factors of $10^3$–$10^5$ at high redshift. Their formation pathways, accretion physics, environment-driven evolution, and observational signatures have been captured in a variety of recent simulation and analytic frameworks, which also elucidate the critical physical restrictions on their efficiency as progenitors of SMBHs.

1. Formation Pathways and Initial Mass Spectrum

The two principal astrophysical routes to LSBH formation entail:

• Population III Stellar Remnants: Metal-free gas within minihalos ($$M_{\rm halo} \sim 10^5\text{–}10^6\,M_\odot,\ T_{\rm vir} \lesssim 10^4$$ K) undergoes H$_2$-dominated cooling, allowing the assembly of very massive ($\sim10$–$10^3\,M_\odot$) primordial stars. The end states include direct collapse or core-collapse SNe, producing black holes with $M_{\rm seed} \sim 10$–$1000\,M_\odot$ depending on the progenitor mass and the pair-instability window ($140$–$260\,M_\odot$ stars do not form BHs) (Regan et al., 2024, Sicilia et al., 2021, Sassano et al., 2021).
• Runaway Collisions in Dense Stellar Clusters: In more massive atomic-cooling halos ($M_{\rm halo} \sim 10^7$–$10^8\,M_\odot$) and with $Z \lesssim 10^{-4}\,Z_\odot$, core-collapse and subsequent stellar mergers in clusters can yield seeds in the IMBH regime ($M_{\rm seed} \sim 10^2$–$10^3\,M_\odot$) (Regan et al., 2024, Colpi, 2018).

The resulting initial mass function is generally log-normal or a shallow power law, with $M_c\sim30$–$100\,M_\odot$, $\sigma\sim0.5$–$1$ dex, and a normalization set by the Pop III star formation rate at $z\sim10$–$20$ (Regan et al., 2024, Sicilia et al., 2021, Colpi, 2018, Ricarte et al., 2018). The co-moving number density at this epoch is $n_{\rm LSBH} \sim 0.1$–$10\,{\rm cMpc}^{-3}$ and the number ratio to heavy seeds is estimated as $n_{\rm LSBH}/n_{\rm HSBH} \sim 10^3$–$10^5$ (Regan et al., 2024).

2. Growth Mechanisms, Accretion Physics, and Environmental Effects

Once formed, LSBHs face a sequence of bottlenecks and physical regimes that control their mass growth:

• Gas Accretion: Classic spherical Bondi–Hoyle–Lyttleton accretion is initially suppressed by radiative feedback, reducing the average accretion rate to $\langle\dot M\rangle \sim 0.01\dot M_{\rm Bondi}$ for seeds in low-mass, bulge-free systems (Park et al., 2015). Only when embedded in bulges exceeding $M_{\rm bulge,crit} \sim 10^6\,M_\odot$ does the accretion regime transition to “force-fed,” enabling more efficient ($\sim$Eddington) fuelling (Park et al., 2015). In the earliest galaxies, super-Eddington and hyper-Eddington accretion are possible in rare, dense, low-vorticity clumps, but typically affect only $\sim1\%$ of the seed population and have short duty cycles ($\lesssim10^6$ yr) (Mehta et al., 2024, Mehta et al., 20 Jan 2026, Mehta et al., 2024). Systematic high-resolution simulations demonstrate that achieving $n \gtrsim 10^7$–$10^8$ cm$^{-3}$ and $T\lesssim6\times10^3$ K enables Eddington or higher rates, but supernova and AGN feedback efficiently curtail sustained accretion episodes (Kiyuna, 18 Jun 2025).
• Gravitational-Wave Driven Mergers: Dynamical interactions and mergers among LSBHs, especially in merging mini-halos or proto-galactic nuclei, can rapidly build up more massive black holes, but this contribution rarely dominates over gas accretion except in specialized scenarios (Ellis et al., 2023, Colpi, 2018).

Environmental impediments—most notably, off-center seed formation, efficient feedback, and limited bulge assembly—can delay the migration of LSBHs to the nucleus or suppress their further growth, leading to up to 10-fold reductions in the abundance of $10^5\,M_\odot$ BHs and high-luminosity quasars at $z>4$ (Izquierdo-Villalba et al., 15 Sep 2025).

3. Analytical Limitations on Super-Eddington Growth

Recent analytic constraints strongly limit the maximum achievable mass gain of LSBHs through repeated super- or hyper-Eddington “clump-capture” or envelope phases. In the optimal regime ($n_{\rm H}=10^{7-8}\,\rm cm^{-3},\ T\simeq2$–$6\times10^3$ K), a $10^3\,M_\odot$ seed can at most quadruple its mass before being expelled by radiation-driven shell acceleration or exhausting the available gas, leading to a maximum $M_{\rm fin} \lesssim 4 \times 10^3\,M_\odot$ (empirically, $$M_{\rm fin}/M_{\rm seed}\propto M_{\rm seed}^{-0.4}$$) (Kiyuna, 18 Jun 2025, Mehta et al., 20 Jan 2026). This sets a hard ceiling: beyond $M_{\rm BH} \gtrsim 10^4\,M_\odot$ the mechanism becomes inefficient. Thus, if Eddington-limited accretion is the subsequent channel, LSBHs alone cannot generate the $\sim10^5$–$10^6\,M_\odot$ “heavy” seeds needed to explain $z>6$ SMBHs via continuous super-Eddington growth alone (Kiyuna, 18 Jun 2025).

4. Evolutionary Signatures and Mass Functions

The cosmic abundance and relic mass function of LSBHs are predicted in both ab initio stellar population synthesis and semi-analytic models:

• The relic BH mass function is flat in $\mathrm{d}N/\mathrm{d}\log m$ up to $\sim50\,M_\odot$, then rolls off log-normally for higher masses, consistent from $z=10$ to $z=0$ (Sicilia et al., 2021). Mergers and binary evolution slightly broaden but do not significantly shift the distribution; most present-day stellar BH mass density ($$\rho_{\bullet}\sim5\times10^7\,M_\odot\,\mathrm{Mpc}^{-3}$$) is contained in $20$–$50\,M_\odot$ objects that originated as “light seeds.”
• In cosmological simulations, the successful fraction of rapid-growing LSBHs is $\sim$1–2%, with the remaining majority failing to reach masses above a few $10^3\,M_\odot$ before gas supply is terminated by feedback (Mehta et al., 20 Jan 2026, Mehta et al., 2024). The characteristic number densities established at $z\gtrsim10$ by Pop III remnant birth rates ($\sim1$–$10\, \rm cMpc^{-3}$) set a strong upper bound for subsequent SMBH assembly (Regan et al., 2024, Sassano et al., 2021).
• The role of LSBHs in the high-$z$ quasar population is sub-dominant if only Eddington-limited growth and usual radiative feedback are operative (Sassano et al., 2021). In “biased” regions forming $z > 6$ SMBHs, most seeds remain below the mass required for luminous AGN activity, but a small number can reach the $M > 10^5$\,$M_\odot$ regime via rare, sustained gas-rich environments (Mehta et al., 2024, Mehta et al., 20 Jan 2026).

5. Observational Signatures and Discriminants

Multi-wavelength and gravitational-wave observables are the key discriminants between light- and heavy-seed scenarios:

• Occupation Fractions and Dwarf Galaxy Nuclei: One primary signature of LSBH seeding is a high ($\sim$unity) central black hole occupation fraction in low-mass galaxies ($M_* \sim 10^8$–$10^9\,M_\odot$) at $z=0$ (Ricarte et al., 2018). Heavy-seed models typically predict lower ($\sim0.2$) occupation fractions in the same regime.
• High-Redshift AGN and Quasar Luminosity Functions: LSBHs, being abundant, predict a larger population of low-luminosity ($L < 10^{10}\,L_\odot$) AGN at $z > 7$, with the bright end evolving more rapidly due to the slow mass growth of small seeds. Deep JWST and Lynx fields are expected to differentiate models via AGN counts at these epochs (Ricarte et al., 2018, Valiante et al., 2018).
• Spectral Diagnostics: Rapidly accreting or starburst-coincident light seeds exhibit V-shaped UV–optical SEDs, strong Balmer-breaks (from $\sim$5000 K envelopes), and suppressed X-ray/IR/radio emission due to dense, radiation-trapped envelopes—matching the “Little Red Dot” JWST population (Inayoshi et al., 23 Sep 2025, Valiante et al., 2018).
• Gravitational-Wave Detections: Mergers of LSBHs yield characteristic gravitational-wave signatures in the $10^2$–$10^4\,M_\odot$ range with predicted event rates of $\mathcal{O}(100)$ yr$^{-1}$ for LISA and AEDGE under the low-mass-seed scenario (Ellis et al., 2023, Colpi, 2018, Ricarte et al., 2018). Key discriminants include the redshift and chirp-mass distribution of detected events: the continuous tail of $M_c\lesssim10^3\,M_\odot$ is unique to light-seeds, while a sharp cutoff at $M_c\sim10^4\,M_\odot$ points to a heavy-seed dominated pathway.

The combination of occupation fractions, faint AGN counts, SED features, and LISA event statistics provides a robust, multi-messenger test of the light-seed formation paradigm (Ricarte et al., 2018, Ellis et al., 2023).

6. Theoretical Extensions: Black Hole Formation from Photons

Beyond astrophysical seeds, the formation of LSBHs via the collapse of pure electromagnetic radiation has been explored in both classical general relativity and quantum field theory:

• Classical Hoop Conjecture Realizations: Collision of oppositely propagating, highly collimated electromagnetic pulses with sufficient energy density within the Schwarzschild radius can, in principle, generate black holes purely from light (“kugelblitz”) (Page, 22 May 2025). The minimum black hole mass is set by the pulse energy, length, and transverse profile, with the process analytically tractable for idealized configurations.
• Quantum Electrodynamic Constraints: Quantum processes (Schwinger pair production, vacuum polarization) set a lower bound on the permissible horizon radius due to catastrophic energy dissipation via $e^{\pm}$ pairs if the field exceeds a critical strength. Thus, naturally occurring or laboratory-formed “light black holes from light” are forbidden for $10^{-29}$ m $< R < 10^{8}$ m (Halilsoy et al., 2024, Page, 22 May 2025). At cosmological scales ($R\gtrsim10^8$ m), hypothetical formation via colliding gamma-ray fronts in the early universe remains a mathematical possibility, but no observational evidence currently exists (Halilsoy et al., 2024).

LSBHs generated via electromagnetic channel would possess extremal Reissner–Nordström metrics, with a near-horizon geometry matching the Bell–Szekeres interaction region of colliding light beams (Halilsoy et al., 2024). Associated impulsive gravitational wave bursts would be a telltale, though as yet undetected, signature.

7. Summary and Open Problems

LSBHs are the cosmologically ubiquitous, low-mass endpoints of metal-free star formation and primordial stellar dynamical interactions, with typical initial masses $10\text{–}10^3\,M_\odot$ and formation epochs $z\sim15$–$30$. Their subsequent contribution to the SMBH population is regulated by accretion physics (Eddington-limited, super-Eddington, or suppressed by feedback), bulge assembly, and environmental migration. While LSBHs dominate the initial seed number density by several orders of magnitude, only a small fraction ($\lesssim1\%$ by $z\sim10$) successfully grow into $>10^5\,M_\odot$ SMBH progenitors through rare, sustained episodes of gas-rich accretion or dynamical sinking to galactic centers (Mehta et al., 20 Jan 2026, Mehta et al., 2024, Izquierdo-Villalba et al., 15 Sep 2025). Smoking-gun multi-messenger signatures are predicted in AGN statistics, dwarf galaxy occupation fractions, and LISA-band black hole mergers. However, robust constraints linking the high-redshift LSBH distribution to observed SMBHs, and separating their role from heavy seeds or other exotic channels, remain an outstanding challenge for current and next-generation observational campaigns (Ricarte et al., 2018, Ellis et al., 2023, Regan et al., 2024).