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

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 greater than or similar to 6. The high flux ratio requires rapid production of iron in galactic nuclei to reach an abundance ratio of [Fe/Mg] greater than or similar to 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 [Fe/Mg] greater than or similar to 0.2 requires the IMF to be characterized with Gamma greater than or similar to -1 (Gamma greater than or similar to 0) and a high-mass cutoff at M-max similar or equal to 100-150 M-circle dot (M-max greater than or similar to 250 M-circle dot). Given the conditions, core-collapse SNe with M-* greater than or similar to 70 M-circle dot 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 discs under Bondi-like gas accretion that is regulated by feedback at M-* greater than or similar to 10 M-circle dot. The massive stellar population formed in AGN discs also leave stellar-mass black hole remnants, whose mergers associated with gravitational-wave emission account for at most 10 per cent of the merger rate inferred from LIGONirgo observations to simultaneously explain the high [Fe/Mg] ratio with metal ejection.