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 $z\gtrsim 6$. The high flux ratio requires rapid production of iron in galactic nuclei to reach an abundance ratio of ${\rm [Fe/Mg]} \gtrsim 0.2$ 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 $\mathrm{\Gamma }$ larger than the canonical value of $\mathrm{\Gamma }=-2.35$ for a Salpeter IMF. Taking into account metal production channels from different types of SNe, we find that the high value of $[\mathrm{F}\mathrm{e}\mathrm{/}\mathrm{M}\mathrm{g}]\gtrsim 0.2$ requires the IMF to be characterized with $\mathrm{\Gamma }\gtrsim -1$ ($\Gamma \gtrsim 0$)andahigh-masscutoffat$M_{\rm max} \simeq 100$--$150~{\rm M_\odot}$ $(M_{\mathrm{m}\mathrm{a}\mathrm{x}}\gtrsim 250{\mathrm{M}}_{\odot })$. Given the conditions, core-collapse SNe with $M_{\ast }\gtrsim 70{\mathrm{M}}_{\odot }$ 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 $M_\ast \gtrsim 10~{\rm M_\odot}$. 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 ${\rm [Fe/Mg]}$ ratio with metal ejection.