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Supermassive black holes from primordial black hole seeds

Norbert Duechting

TL;DR

The paper investigates whether supermassive black holes observed at high redshift can originate from primordial black hole seeds formed by collapsed primordial density fluctuations. It compares the required seed mass for rapid growth via Eddington-limited accretion, $M_i \gtrsim 1.3\times10^3\,M_\odot$, with PBH formation probabilities across several primordial fluctuation spectra, including scale-free, running tilt, and broken-scale-invariance (BSI) models. It finds that scale-free spectra cannot produce enough PBHs to seed SMBHs, while spectra with localized small-scale enhancements (e.g., tuned running tilts or BSI-like bumps) can, in principle, generate the needed PBH seeds but require nontrivial parameter choices and near-maximum normalizations; simple parameterizations are thus strongly constraining for PBH-seeded SMBHs. The work highlights specific observational tests (CMB/LSS constraints, future LISA measurements) that will help confirm or exclude PBHs as viable SMBH seeds and delineates the narrow conditions under which this scenario could operate.

Abstract

The observational evidence for a population of quasars powered by supermassive black holes of mass \geq 10^9 M_sun at redshifts z\geq 6 poses a great challenge for any model describing the formation of galaxies. Assuming uninterrupted accretion at the Eddington limit, seed black holes of at least 1000 M_sun are needed at z \approx 15. Here I study whether these seeds could be primordial black holes (PBHs) which have been produced in the very early universe by the collapse of primordial density fluctuations. In particular, I study the expected number densities of PBHs in the relevant mass range for several classes of spectra of primordial density fluctuations and confront the results with observational data. While it seems to be possible to produce the required PBHs with spectra showing large enhancements of fluctuations on a certain scale, our hypothesis can be clearly disproved for a scale free spectrum of primordial fluctuations described by a power-law slope consistent with recent observations.

Supermassive black holes from primordial black hole seeds

TL;DR

The paper investigates whether supermassive black holes observed at high redshift can originate from primordial black hole seeds formed by collapsed primordial density fluctuations. It compares the required seed mass for rapid growth via Eddington-limited accretion, , with PBH formation probabilities across several primordial fluctuation spectra, including scale-free, running tilt, and broken-scale-invariance (BSI) models. It finds that scale-free spectra cannot produce enough PBHs to seed SMBHs, while spectra with localized small-scale enhancements (e.g., tuned running tilts or BSI-like bumps) can, in principle, generate the needed PBH seeds but require nontrivial parameter choices and near-maximum normalizations; simple parameterizations are thus strongly constraining for PBH-seeded SMBHs. The work highlights specific observational tests (CMB/LSS constraints, future LISA measurements) that will help confirm or exclude PBHs as viable SMBH seeds and delineates the narrow conditions under which this scenario could operate.

Abstract

The observational evidence for a population of quasars powered by supermassive black holes of mass \geq 10^9 M_sun at redshifts z\geq 6 poses a great challenge for any model describing the formation of galaxies. Assuming uninterrupted accretion at the Eddington limit, seed black holes of at least 1000 M_sun are needed at z \approx 15. Here I study whether these seeds could be primordial black holes (PBHs) which have been produced in the very early universe by the collapse of primordial density fluctuations. In particular, I study the expected number densities of PBHs in the relevant mass range for several classes of spectra of primordial density fluctuations and confront the results with observational data. While it seems to be possible to produce the required PBHs with spectra showing large enhancements of fluctuations on a certain scale, our hypothesis can be clearly disproved for a scale free spectrum of primordial fluctuations described by a power-law slope consistent with recent observations.

Paper Structure

This paper contains 7 sections, 18 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Accretional growth of SMBHs
  3. Primordial black holes
  4. PBH formation
  5. Parametrizations of $\Delta^2_R(k)$
  6. Computation of PBH abundances
  7. Conclusions

Figures (3)

  • Figure 1: (Color online) Typical form of the BSI spectrum with jump parameter $p=0.07$. The jump scale $k_s$ is a free parameter and the large scale normalization may be chosen consistent with observational results.
  • Figure 2: (Color online) Expected comoving number density of PBHs per $e$-folding in $M$ for the spectrum of primordial curvature fluctuations (\ref{['si']}) with adopted parameters $n_0=0.98$, $n_1=-0.05$, $n_2=0.123$, $n_3=-0.022$, and all other $n_i$ equal to zero.
  • Figure 3: (Color online) Expected comoving number density of PBHs per $e$-folding in $M$ for the BSI-spectrum of primordial curvature fluctuations (\ref{['bsi']}) with adopted parameters $p=0.0004$, $M_s=2000M_\odot$, and large scale normalizationx $\Delta^2_0=3\times 10^{-9}$.