JADES: the mass-metallicity relation at $z=1-10$. New calibrations, extremely metal-poor galaxies, and chemical diversity

We present gas-phase metallicities of star-forming galaxies at $z=1$-10 with deep JWST/NIRSpec spectra from the JADES full data release, Dark Horse, and OASIS programmes. We stack $\sim$1500 medium-resolution spectra, yielding detections of the [OIII]$\lambda$4363 auroral line down to $12+\log(\mathrm{O/H})=7.0$ to derive stack-based strong-line calibrations over the metallicity range $12+\log(\mathrm{O/H})=7.0$-8.7. At a fixed metallicity, our stacks exhibit [OIII]$\lambda$5007/H$\beta$ and [OIII]$\lambda$5007/[OII]$\lambda\lambda$3726,3729 values generally lower than calibrations based on high-$z$ individual auroral-line emitters, suggesting an observational bias towards higher excitation introduced when requiring auroral line detections in individual spectra. Based on our new calibrations, we obtain canonical mass-metallicity relations (MZRs) at z$=$1-10, identifying a decrease in metallicities from $z\sim0$ to z$\sim$4-10, without significant change in slope. Moreover, we identify 50 promising candidates of extremely metal-poor galaxies (EMPGs) with $12+\log(\mathrm{O/H})=6.7$-7.3 (1-4\% solar metallicity) at $z=1.2$-9.1. The MZRs of EMPGs are characterised by a large scatter, with those having lower metallicities generally exhibiting lower sSFRs, opposite of what expected from the local Fundamental Metallicity Relation. These results support a stochastic star-formation history involving gas consumption/ejection and metal-poor inflow, strongly affecting metallicities of low-mass galaxies. Furthermore, we identify two Little Red Dots in our EMPG candidates, both exhibiting broad H$\alpha$ and prominent Ly$\alpha$, offering insights into the early black-hole growth in extremely metal-poor environments.