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 ($M_* - Z$, 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 $\rm [OIII]\lambda4363$ emission line ($\rm S/N \geq 3$).
With the electronic temperature metallicity calibration, we find nine SFGs are
extremely metal-poor galaxies with $\rm 12 + log(O/H) \leq 7.69 \ (1/10 \
Z_\odot)$. The metallicity of the most metal-deficient galaxy is $7.35\pm 0.09$
(about 1/20 $Z_{\odot}$). 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.
