Mass - metallicity relation and fundamental metallicity relation of metal-poor star-forming galaxies at $0.6<z<0.9$ from the eBOSS survey

The stellar mass-metallicity relation ($M_{\ast }-Z$, MZR) indicates that the metallicities of galaxies increase with increasing stellar masses. The fundamental metallicity relation (FMR) suggests that the galaxies with higher star formation rates (SFRs) tend to have lower metallicities for a given stellar mass. To examine whether the MZR and FMR still hold at poorer metallicities and higher redshifts, we compile a sample of 35 star-forming galaxies (SFGs) at $0.6<z<0.9$ using the public spectral database ($\rm v5_10_0$) of emission-line galaxies from the extended Baryon Oscillation Spectroscopic Survey (eBOSS). These galaxies are identified for their significant auroral $[\mathrm{O}\mathrm{I}\mathrm{I}\mathrm{I}]\lambda 4363$ emission line ($\mathrm{S}\mathrm{/}\mathrm{N}\ge 3$). With the electronic temperature metallicity calibration, we find nine SFGs are extremely metal-poor galaxies with $\rm 12 + log(O/H) \leq 7.69 \ (1/10
Z_\odot)$\mathrm{.}Themetallicityofthemostmetal-deficientgalaxyis$7.35\pm 0.09$(about1\mathrm{/}20$Z_{\odot}$). Compared with the SFGs with normal metallicities in local and high redshift universe, our metal-poor SFGs have more than ten times higher SFRs at a fixed stellar mass. We create a new mass – SFR relation for these metal-poor galaxies at $0.6<z<0.9$. Due to the higher SFRs and younger stellar ages, our metal-poor SFGs deviate from the MZR and FMR in the local universe toward lower metallicities, confirming the existence of FMR, as well as the cosmic evolution of MZR and FMR with redshift.