[Paper Review] The Race to Build Supermassive Black Holes

Craig Tyler, Brent Janus+1 more|arXiv (Cornell University)|Aug 30, 2003

Pulsars and Gravitational Waves Research2 references3 citations

TL;DR

This paper evaluates mechanisms for forming supermassive black holes (SMBHs) within the first 880 million years of the universe, focusing on the challenge posed by a z=6.41 quasar hosting a 3×10⁹ M☉ black hole. It finds that merger-driven growth is too slow, and continuous Eddington-limited accretion from small seeds is implausible; instead, the authors conclude that unconventional processes—such as primordial black holes from large overdensities, extreme population III starbursts, or supermassive stars—are required to explain the rapid SMBH formation observed.

ABSTRACT

The high redshifts of the most distant known quasars, and the best estimates of their black hole masses, require that supermassive black holes (SMBHs) must have formed very early in history. Several mechanisms for creating and growing these holes have been proposed. Here we present an evaluation of the timescales needed for various critical processes in order to discriminate between the proposed scenarios. We find in particular that mergers alone are not able to grow the black holes at a sufficient rate. Accretion models offer a solution and we use accretion timescales to constrain the manner in which the black hole was first formed. This analysis implies, but does not require, the action of some unconventional process.

Motivation & Objective

• To assess whether known astrophysical processes can grow a 3×10⁹ M☉ black hole within 880 million years after the Big Bang.
• To evaluate the viability of merger-driven growth versus accretion-based growth for supermassive black holes.
• To determine the minimum initial black hole mass required for Eddington-limited accretion to produce the observed quasar mass by z=6.41.
• To identify whether standard formation scenarios—such as population III stars or primordial black holes—can satisfy the timing constraints.
• To conclude whether unconventional mechanisms are necessary to explain the early formation of supermassive black holes.

Proposed method

• The authors calculate accretion timescales for black holes growing at the Eddington limit, using the standard Eddington accretion rate formula: Ṁ_Edd = 4πGM/c²F, where F is the Eddington flux.
• They model black hole growth via mergers using outputs from a cold dark matter (CDM) simulation, tracking subhalo infall and dynamical friction timescales to determine merger efficiency.
• They assess dark matter accretion growth, assuming a self-similar dark matter halo forms around the black hole, with growth scaling linearly with time due to angular momentum suppression.
• They compare growth rates from different seed formation scenarios: primordial black holes, population III stellar remnants, and supermassive stars.
• They apply cosmological parameters from the WMAP ΛCDM model (H₀=71 km s⁻¹ Mpc⁻¹, Ωₘ=0.27, ΩΛ=0.73) to compute the age of the universe at z=6.41 as 880 Myr.
• They evaluate the consistency of each growth pathway with the observed M•–σ relation and the lack of mass evolution in quasars over cosmic time.

Experimental results

Research questions

• RQ1 Can black hole growth via mergers alone account for the formation of a 3×10⁹ M☉ black hole by z=6.41?
• RQ2 Is continuous Eddington-limited accretion from a small seed black hole (e.g., 100 M☉) sufficient to grow a supermassive black hole within 880 million years?
• RQ3 What initial black hole mass is required for Eddington-limited accretion to produce the observed quasar mass by the time the universe was 880 Myr old?
• RQ4 How does accretion from dark matter compare in growth efficiency to baryonic accretion, and can it explain the observed SMBH masses?
• RQ5 Are standard formation pathways—such as population III stars or primordial black holes—sufficient, or is an unconventional mechanism required?

Key findings

• Merger-driven growth is too slow to produce a 3×10⁹ M☉ black hole within 880 million years, as dynamical friction limits the mass of subhalos that can merge in time.
• Continuous Eddington-limited accretion from a 100 M☉ seed black hole requires unreasonably high and sustained gas infall, making this scenario implausible.
• A seed black hole of at least ~900 M☉ is required for Eddington-limited accretion to produce the observed mass in the available time, implying a need for a massive initial seed.
• Accretion from dark matter grows linearly with time due to angular momentum suppression, making it too slow to explain SMBH formation without an initial large seed.
• The authors conclude that standard formation pathways are insufficient, and unconventional mechanisms—such as primordial black holes from large overdensities, extreme population III starbursts, or supermassive stars—are likely required.
• The analysis implies that some non-standard process is necessary to explain the early formation of supermassive black holes, as neither mergers nor standard accretion from small seeds suffice.