Astraeus V: The emergence and evolution of metallicity scaling relations during the Epoch of Reionization

In this work, we have implemented a detailed physical model of galaxy chemical enrichment into the ${\it Astraeus}$ (semi-numerical rAdiative tranSfer coupling of galaxy formaTion and Reionization in N-body dark matter simUlationS) framework which couples galaxy formation and reionization in the first billion years. Simulating galaxies spanning over 2.5 orders of magnitude in halo mass with $M_h \sim 10^{8.9-11.5} M_\odot$ ($M_h \sim 10^{8.9-12.8} M_\odot$) at $z \sim 10 ~ (5)$, we find: (i) smooth-accretion of metal-poor gas from the intergalactic medium (IGM) plays a key role in diluting the interstellar medium (ISM) metallicity which is effectively restored due to self-enrichment from star formation; (ii) a redshift averaged gas-mass loading factor that depends on the stellar mass as $\eta_g \approx 1.38 ({M_*}/{10^{10} M_\odot})^{-0.43}$; (iii) the mass-metallicity relation is already in place at $z \sim 10$ and shows effectively no redshift evolution down to $z \sim 5$; (iv) for a given stellar mass, the metallicity decreases with an increase in the star formation rate (SFR); (v) the key properties of the gas-phase metallicity (in units of 12+log(O/H), stellar mass, SFR and redshift are linked through a high-redshift fundamental plane of metallicity (HFPZ) for which we provide a functional form; (vi) the mass-metallicity-SFR relations are effectively independent of the reionization radiative feedback model for $M_* \geq 10^{6.5} M_\odot$ galaxies; (vii) while low-mass galaxies ($M_h \leq 10^9 M_\odot$) are the key contributors to the metal budget of the IGM at early times, higher mass halos provide about 50% of the metal budget at lower-redshifts.