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The properties of primordially-seeded black holes and their hosts in the first billion years: implications for JWST

Pratika Dayal, Roberto maiolino

TL;DR

PHANES introduces an analytic framework to study primordially seeded black holes accelerating early structure formation in the first Gyr, exploring PBH mass spectra with slopes $\alpha \in \{2,3\}$ and spins $s \in \{0,\,-1,\,+1\}$, coupled to gas accretion, star formation, feedback, and metal enrichment. Across redshifts $z \sim 5-15$, the framework yields BH mass functions, stellar mass functions, MBH–M* relations, Eddington fractions, and metallicities, which are then confronted with JWST constraints from high-redshift BHs like GHZ9 and UHZ1 and with little-obscured LRDs. The results show that PBH seeds can naturally produce overmassive BHs relative to their hosts (e.g., $M_{ m BH}/M_* \gtrsim 0.25$ for $s=0$ or $s=-1$) and extremely metal-poor hosts ($Z \lesssim 10^{-2} Z_\odot$) while maintaining a PBH DM fraction $f_{\rm PBH} \lesssim 10^{-9}$, though the stellar mass function remains far below observed galaxy counts, indicating PBH seeds do not dominate early star-forming demographics. The analysis highlights the $s=0$ case as particularly compatible with several JWST trends and emphasizes that metallicity measurements and dynamical mass estimates will be critical to testing PBH seeding as a viable pathway to the early supermassive black holes reported by JWST.

Abstract

James Webb Space Telescope (JWST) observations have opened a tantalising new window onto possible black holes as early as redshifts of $z \sim 10.4$. These show a number of puzzling properties including unexpectedly massive black holes in place by $z \sim 10$ and inexplicably high black hole-to-stellar mass ratios of $M_{\rm BH}/M_*\geq 0.1$. These pose a serious challenge for "astrophysical" seeding and growth models that we aim to explain with ``cosmological" primordial black holes (PBHs) in this work. We present PHANES, an analytic framework that follows the evolution of dark matter halos, and their baryons in the first billion years, seeded by a population of PBHs with seed masses between $10^{0.5}-10^6 M_\odot$. PBH seeded models yield a black hole mass function that extends between $10^{1.25-11.25} ~(10^{0.75-7.25})M_\odot$ at $z \sim 5 (15)$ for the different models considered in this work. Interestingly, PBH-seeded models (with spin $s=0$ or $-1$) naturally result in extremely high values of $M_{\rm BH}/M_*\geq 0.25$ at $z \sim 5-15$. For a typical stellar mass of $M_* =10^9 M_\odot$, we find an average value of $M_{\rm BH}/M_* \sim 0.4~ (1.6)$ for $s=0~(-1)$ at $z=5$, providing a smoking gun for PBH-seeded models. Another particularity of PBH-seeded models is their ability of producing systems with high black hole-to-stellar mass ratios that are extremely metal poor ($Z \leq 10^{-2}~Z_\odot$). Yielding a PBH-to-dark matter fraction $\leq 10^{-9}$ and a stellar mass function that lies four orders of magnitude below observations, our model is in accord with all current cosmological and astrophysical bounds.

The properties of primordially-seeded black holes and their hosts in the first billion years: implications for JWST

TL;DR

PHANES introduces an analytic framework to study primordially seeded black holes accelerating early structure formation in the first Gyr, exploring PBH mass spectra with slopes and spins , coupled to gas accretion, star formation, feedback, and metal enrichment. Across redshifts , the framework yields BH mass functions, stellar mass functions, MBH–M* relations, Eddington fractions, and metallicities, which are then confronted with JWST constraints from high-redshift BHs like GHZ9 and UHZ1 and with little-obscured LRDs. The results show that PBH seeds can naturally produce overmassive BHs relative to their hosts (e.g., for or ) and extremely metal-poor hosts () while maintaining a PBH DM fraction , though the stellar mass function remains far below observed galaxy counts, indicating PBH seeds do not dominate early star-forming demographics. The analysis highlights the case as particularly compatible with several JWST trends and emphasizes that metallicity measurements and dynamical mass estimates will be critical to testing PBH seeding as a viable pathway to the early supermassive black holes reported by JWST.

Abstract

James Webb Space Telescope (JWST) observations have opened a tantalising new window onto possible black holes as early as redshifts of . These show a number of puzzling properties including unexpectedly massive black holes in place by and inexplicably high black hole-to-stellar mass ratios of . These pose a serious challenge for "astrophysical" seeding and growth models that we aim to explain with ``cosmological" primordial black holes (PBHs) in this work. We present PHANES, an analytic framework that follows the evolution of dark matter halos, and their baryons in the first billion years, seeded by a population of PBHs with seed masses between . PBH seeded models yield a black hole mass function that extends between at for the different models considered in this work. Interestingly, PBH-seeded models (with spin or ) naturally result in extremely high values of at . For a typical stellar mass of , we find an average value of for at , providing a smoking gun for PBH-seeded models. Another particularity of PBH-seeded models is their ability of producing systems with high black hole-to-stellar mass ratios that are extremely metal poor (). Yielding a PBH-to-dark matter fraction and a stellar mass function that lies four orders of magnitude below observations, our model is in accord with all current cosmological and astrophysical bounds.

Paper Structure

This paper contains 12 sections, 13 equations, 6 figures, 2 tables.

Table of Contents

  1. Introduction
  2. A theoretical framework for primordial black holes as seeds of early galaxy assembly
  3. The primordial black hole mass spectrum
  4. The dark matter and gas assembly of PBH-seeded systems
  5. Star formation, black hole growth and feedback
  6. The metal enrichment of early systems
  7. The emerging properties of early black holes and their hosts
  8. Black hole and stellar mass functions at $z \sim 5-15$
  9. The black hole mass-stellar mass relation
  10. Eddington accretion fraction as a function of black hole and stellar mass
  11. Gas phase metal enrichment as a function of black hole and stellar mass
  12. Conclusions and discussion

Figures (6)

  • Figure 1: A schematic of the key epochs modelled in phanes. As shown, this includes PBH seeds (stage a) linearly accreting a dark matter halo between the epoch of recombination ($z \sim 3400$) and $z \sim 34$; halo growth becomes non-linear below this redshift (stage b). Halos can sustain a gas mass once they exceed a baryonic over-density of 200 (stage c). At stage d, gas is allowed to be accreted onto the central black hole, and form stars. We also account for the associated feedback from both black hole accretion and star formation, and include metal enrichment from Supernovae.
  • Figure 2: The black hole mass as a function of the initial PBH seed mass, at $z \sim 5$ (left panel) and $z \sim 15$ (right panel). As marked, in both panels, the yellow, red and green points show results for non-spinning ($s=0$), retrograde ($s=-1$) and prograde ($s=+1$) black holes for the parameter values noted in Table \ref{['table1']}.
  • Figure 3: The redshift evolution of the black hole mass function (top panel) and the stellar mass function (bottom panel) at $z \sim 5-15$, as marked. Lines show PBH-seeded mass functions for different spectral slopes and spins, as marked. In panel (a), we show the observed BHMF at $z\sim 5$ from a number of groups: Wil+10 willott2010, Mat+24 matthee2024, Kok+24 kokorev2024 and Tay+25 taylor2025a. In the bottom panels (e-g), points show the observed stellar mass functions inferred by Nav+24 navarro-carrera2024, Wei+24 weibel2024, Bha+19 bhatawdekar2019, Har+25 harvey2025 and Ste+21 stefanon2021, as marked.
  • Figure 4: The black hole mass-stellar mass relation at $z \sim 5-15$, as marked. In each panel, points show PBH-seeded relations for different spins (0, $+1$ and $-1$), as marked. At $z\sim 5-10$, we show observational results from a number of groups: Har+23 harikane2023bh, Mai+24 maiolino2024_jades, Koc+23,24 kocevski2023kocevski2025, Fur+23 furtak2024, Tri+24 tripodi2024, Juo+24 juodzbalis2024, Aki+25 akins2025, Mai25 maiolino2025, Kok+23 kokorev2023, Lar+23 larson2023, Bog+24 bogdan2024, Kov+24 kovacs2024, Nap+24 Napolitano2025_Xray and Tay+25 taylor2025. In all panels, long- and dot-dashed lines show observationally-inferred local relations from reines2015 and suh2020, respectively. Finally, the dotted and short-dashed lines show a relation where the black hole mass is 25% and 100% of the stellar mass, respectively.
  • Figure 5: The (log of the) Eddington accretion fraction as a function of the black hole mass. Columns (left to right) show results for PBH-seeded systems with spin=0, -1 and +1 as marked; rows (from top to bottom) show results at $z \sim 5,7, 10$ and 15. In each panel, colours show the associated stellar mass for each source from phanes, as marked in panel l. Finally, large points show observational results at $z\sim 5$ and $7$ from harikane2023bh, matthee2024 and greene2024. At $z \sim 5$ and $7$, solid squares show the results from maiolino2024_jades and juodzbalis2024, respectively. All of the data points are color-coded by the stellar mass scheme used for the theoretical model - black points are used in cases where no observational stellar mass estimates are available.
  • ...and 1 more figures