[Paper Review] Top-heavy stellar mass distribution in galactic nuclei inferred from the universally high abundance ratio of [Fe/Mg]

Daisuke Toyouchi, Kohei Inayoshi+2 more|arXiv (Cornell University)|Dec 11, 2021

Gamma-ray bursts and supernovae93 references22 citations

TL;DR

This paper proposes that top-heavy initial mass functions (IMFs) with a power-law index of Γ ≳ −1 and a high-mass cutoff of Mmax ≃ 100–150 M⊙ (or Mmax ≳ 250 M⊙ for Γ ≳ 0) in active galactic nucleus (AGN) disks explain the universally high [Fe/Mg] ≳ 0.2 observed in high-redshift quasars. Such IMFs enhance iron production via massive core-collapse and pair-instability supernovae, enabling rapid chemical enrichment within <10 Myr, consistent with LIGO/Virgo binary black hole merger rates at z ≲ 3.

ABSTRACT

Recent observations of active galactic nuclei (AGNs) have shown a high Fe~II/Mg~II line-flux ratio in their broad-line regions, nearly independent of redshift up to $z \gtrsim 6$. The high flux ratio requires rapid production of iron in galactic nuclei to reach an abundance ratio of ${ m [Fe/Mg]} \gtrsim 0.2$ as high as those observed in matured galaxies in the local universe. We propose a possible explanation of rapid iron enrichment in AGNs by massive star formation that follows a top-heavy initial mass function (IMF) with a power-law index of $\Gamma$ larger than the canonical value of $\Gamma=-2.35$ for a Salpeter IMF. Taking into account metal production channels from different types of SNe, we find that the high value of ${ m [Fe/Mg]} \gtrsim 0.2$ requires the IMF to be characterized with $\Gamma \gtrsim -1$ ($\Gamma \gtrsim 0$) and a high-mass cutoff at $M_{ m max} \simeq 100$--$150~{ m M_\odot}$ $(M_{ m max} \gtrsim 250~{ m M_\odot})$. Given the conditions, core-collapse SNe with $M_\ast \gtrsim 70~{ m M_\odot}$ and pair-instability SNe give a major contribution for iron enrichment. Such top-heavy stellar IMFs would be a natural consequence from mass growth of stars formed in dense AGN disks under Bondi-like gas accretion that is regulated by feedback at $M_\ast \gtrsim 10~{ m M_\odot}$. The massive stellar population formed in AGN disks also leave stellar-mass black hole remnants, whose mergers associated with gravitational-wave emission account for at most 10 \% of the merger rate inferred from LIGO/Virgo observations to simultaneously explain the high ${ m [Fe/Mg]}$ ratio with metal ejection.

Motivation & Objective

• To explain the universally high [Fe/Mg] ≳ 0.2 abundance ratio observed in the broad-line regions (BLRs) of high-redshift quasars (z ≳ 6), which contradicts standard chemical evolution models.
• To determine the stellar IMF parameters (Γ and Mmax) that reproduce the observed [Fe/Mg] ratio through metal yields from massive stars.
• To investigate how such top-heavy IMFs could naturally arise in dense AGN accretion disks via Bondi-like accretion regulated by feedback.
• To assess the implications for gravitational-wave astronomy by calculating the cosmic merger rate of binary black holes formed in AGN disks under the top-heavy IMF hypothesis.

Proposed method

• The study uses stellar yield tables from NKT13 and UN08 for progenitor masses 10 ≤ M∗/M⊙ ≤ 260, focusing on Fe and Mg production from core-collapse and pair-instability supernovae (PISNe).
• It models the integrated mass-weighted yields across the IMF, varying the power-law index Γ and high-mass cutoff Mmax to reproduce [Fe/Mg] ≳ 0.2.
• A time-dependent stellar mass growth model is applied, assuming Bondi-like accretion regulated by radiative and mechanical feedback at M∗ ≳ 10 M⊙, leading to top-heavy IMFs.
• The cosmic merger rate of binary black holes is calculated by assuming a top-heavy IMF in the inner BLR (r < 0.1 pc) and a Salpeter IMF in the outer region (0.1 pc < r < 10 pc), with merger rates compared to LIGO/Virgo observations.

Experimental results

Research questions

• RQ1 What IMF parameters (Γ and Mmax) are required to reproduce the observed [Fe/Mg] ≳ 0.2 in high-redshift quasar BLRs?
• RQ2 How can top-heavy IMFs naturally form in the dense, self-gravitating disks of AGNs through accretion and feedback regulation?
• RQ3 To what extent do massive core-collapse and pair-instability supernovae contribute to iron enrichment under such top-heavy IMFs?
• RQ4 What is the predicted cosmic merger rate of binary black holes formed in AGN disks under the top-heavy IMF, and how does it compare to LIGO/Virgo observations?
• RQ5 Can the top-heavy IMF hypothesis be tested via future LSST observations of PISNe at z ≲ 2?

Key findings

• An IMF with a power-law index of Γ ≳ −1 and a high-mass cutoff of Mmax ≃ 100–150 M⊙ is required to reproduce the observed [Fe/Mg] ≳ 0.2 in quasar BLRs.
• A higher-mass IMF with Mmax ≳ 250 M⊙ and Γ ≳ 0 also satisfies the [Fe/Mg] constraint, indicating that very massive stars are essential for iron enrichment.
• Core-collapse SNe with M∗ ≳ 70 M⊙ and pair-instability SNe (PISNe) with M∗ ≃ 220–260 M⊙ are the dominant contributors to iron enrichment under these IMFs.
• The top-heavy IMF is naturally established in AGN disks via Bondi-like accretion regulated by feedback at M∗ ≳ 10 M⊙, leading to rapid stellar mass growth.
• The predicted binary black hole merger rate from AGN disks is consistent with LIGO/Virgo observations at z ≲ 3, accounting for up to 10% of the local merger rate.
• The model implies a high detection rate of PISNe at z ≲ 2, which could be tested by upcoming LSST surveys.