Researchers are now investigating the origins of supermassive black holes, following recent James Webb Space Telescope observations revealing their existence at unexpectedly early cosmic times. Nirmali Das, Sanjeev Kalita, and Ankita Kakati, all from the Department of Physics at Gauhati University, explore how these behemoths could have formed by modelling the growth of ‘seed’ black holes within different cosmological frameworks, including standard CDM and alternative braneworld models. Their work demonstrates that massive seeds, formed at high redshifts, can indeed grow into the SMBHs observed today via both Eddington-limited and super-Eddington accretion in all tested cosmologies. Significantly, this research calculates the potential contribution of primordial black holes to dark matter and examines their role in seeding the formation of early galaxies, offering crucial insights into the conditions necessary for the emergence of these cosmic giants.
This study generates seeds for these SMBHs within various cosmological frameworks, investigating the cosmic timescales required for black hole growth.
Researchers considered three general relativistic cosmological models, ΛCDM, ωCDM, and Dynamical Dark Energy (DDE) , alongside braneworld cosmology, to model black hole evolution through both Eddington-limited and super-Eddington accretion, initiating at a redshift of z=30. Experiments show that the growth of SMBHs by z=10 is achievable via massive seeds, with masses exceeding 104 solar masses, across all tested cosmologies when limited by the Eddington rate.
Furthermore, super-Eddington accretion onto spinning black holes with masses of a few tens of solar masses can also result in SMBHs by z=10 in all cosmological models. The study establishes that the considered cosmologies are unable to significantly differentiate between the masses of the seed black holes, suggesting a common origin for these early SMBHs.
The seeds generated in this work are hypothesised to be of primordial origin, aligning with the criteria for the formation of massive galaxies at high redshifts. Calculations were performed to determine the fraction of primordial black holes (PBHs) contributing to dark matter (fPBH) and their corresponding number densities within a mass range of 105 to 108 solar masses, using both seed and Poisson effects.
Specifically, PBHs with masses greater than or equal to 107 solar masses contribute less than 10−2 to the overall dark matter fraction. The research also investigates the evolution of gas mass within PBH-seeded dark matter halos and evaluates the ratio of black hole to stellar mass for star formation efficiencies ranging from 0.1 to 1. The study generated seed black holes within various cosmological models, specifically ΛCDM, ωCDM, Dynamical Dark Energy (DDE), and braneworld cosmology, to examine growth timescales.
Researchers analysed SMBH growth through both Eddington-limited and super-Eddington accretion, initiating the process at a redshift of z=30. Findings indicate that growth to z=10 is achievable via massive seeds under Eddington-limited accretion across all tested cosmologies. Super-Eddington accretion onto spinning black holes, initially possessing masses of a few tens of solar masses, also facilitates SMBH formation by z=10 in all cosmological scenarios.
The team assumed primordial origins for these seeds to align with the formation criteria for high-redshift massive galaxies. Calculations determined the fraction of primordial black holes (PBHs) contributing to dark matter, denoted as fPBH, and their corresponding number densities for mass ranges between 10−2 and 108 solar masses, considering both seed and Poisson effects.
PBHs with a mass of 10−2 solar masses contribute to the dark matter fraction in the seed effect scenario. To model halo formation, the study employed a spherical top-hat collapse model, calculating virial temperatures using the equation Tvir= 1.98 × 104 μ 0.6 Mh 108h−1M⊙ 2/3 ΩmΔc Ωz m18π2 1 + z 10 K. The overdensity parameter, Δc, was determined using Δc= 18π2 + 82d−39d2, where d = Ωz m−1, evaluated at the collapse epoch z with Ωz m= Ωm(z) (1 + z)3 E2(z).
Cosmological models influenced seed mass calculations through the H(z) function within Ωz m. Researchers then calculated the baryonic overdensity, δb= 1 + 6Tvir 5 T 3/2, using μ≈1.22 for primordial neutral gas. The evolution of gas content within PBH-seeded dark matter halos was tracked using dMg dz = fb dMh dz, integrating from redshifts z2 to z1 to determine the total gas mass accumulated, expressed as ΔMg≈1.62 × 107 fbh−1M⊙ ∫ z 10 (1 + z)3/2 Mh 108M⊙ 1.06 dz E(z). This study generates seeds for these supermassive black holes within various cosmological backgrounds, examining cosmic timescales for black hole growth using three general relativistic cosmological models: ΛCDM, ωCDM, and Dynamical Dark Energy (DDE), alongside braneworld cosmology.
The team studied black hole growth through both Eddington-limited and super-Eddington accretion, initiating the process at a redshift of z=30. Experiments revealed that growth of supermassive black holes by redshift z=10 is possible via massive seeds in all tested cosmologies when using Eddington-limited accretion.
Super-Eddington accretion onto spinning black holes with masses of a few tens of solar masses can also result in supermassive black holes by z=10 across all cosmological models. Calculations show that the viable cosmologies considered cannot strongly differentiate between seed black hole masses. The seeds generated in this work are assumed to originate from primordial sources to satisfy the criteria for the formation of high-redshift massive galaxies.
Researchers calculated the fraction of primordial black holes contributing to dark matter, denoted as f, and their corresponding number densities for mass ranges between 1 and 100 solar masses, considering both seed and Poisson effects. In the seed effect, primordial black holes with a mass of 1 solar mass contribute to the dark matter fraction.
The evolution of gas mass within a primordial black hole seeded dark matter halo was also studied, yielding a black hole to stellar mass ratio of 0.01 for a star formation efficiency of 0.1 and a ratio of 0.1 for an efficiency of 1. Measurements confirm that the black hole to stellar mass ratio for massive galaxy formation, using both seed and Poisson effects, ranges from 0.01 to 0.1.
Scientists also estimated the black hole to stellar mass ratio for their seed black holes in all cosmologies. The timescale for seed growth, Δt, depends on the expansion rate of the universe and, therefore, the background cosmological model, with the Hubble parameter H(z) dictating this expansion history. For Eddington-limited accretion, the accretion ratio a, defined as the accretion rate divided by the Eddington accretion rate, is equal to 1, while deviations from unity indicate other models.
Supermassive black hole formation and early universe observations reconciled a long-standing astrophysical puzzle
Scientists have demonstrated the feasibility of forming supermassive black holes with masses between 10⁸ and 10⁹ solar masses through the growth of seed black holes within various cosmological models. This research investigates black hole growth via both Eddington-limited and super-Eddington accretion, starting at a redshift of 30, and considers the impact of different cosmological frameworks including CDM, ωCDM, dynamical dark energy, and braneworld cosmology.
The study finds that, across these cosmologies, sufficiently massive seeds can grow into supermassive black holes by a redshift of 10, particularly with super-Eddington accretion onto spinning black holes. The derived black hole to stellar mass ratios are broadly consistent with existing observational data.
The authors acknowledge that distinguishing between seed black hole masses is difficult within the considered cosmologies, and that the calculated dark matter fraction represents a lower bound. Future research could focus on further refining these models and exploring the potential for detecting gravitational waves from these seed black holes with instruments like LIGO-Virgo-KAGRA, potentially offering a means to differentiate between cosmological models and better constrain the properties of early black hole seeds.
👉 More information
🗞 Seeds of supermassive black holes in general relativistic and alternative cosmologies: Implications of massive seeds
🧠 ArXiv: https://arxiv.org/abs/2601.22991