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A sample of low-mass H$\alpha$ emission line sources (ELS) at $z\,\sim\,0.4$was studied in the context of the mass-metallicty relation (MZR) and itspossible evolution. We drew our sample from the OSIRIS Tunable Emission LineObject (OTELO) survey, which exploits the red tunable filter of OSIRIS at theGran Telescopio Canarias to perform a blind narrow-band spectral scan in aselected field of the Extended Groth Strip. We were able to directly measureemission line fluxes and equivalent widths from the analysis of OTELOpseudo-spectra. This study aims to explore the MZR in the very low-mass regime.Our sample reaches stellar masses ($M_*$) as low as $10^{6.8}\,M_\odot$, where63\% of the sample have $M_*\,<10^9\,M_\odot$. We also explore the relation ofthe star formation rate (SFR) and specific SFR (sSFR) with $M_*$ and gas-phaseoxygen abundances, as well as the $M_*$-size relation and the morphologicalclassification. The $M_*$ were estimated using synthetic rest-frame colours.Using an $\chi^2$ minimization method, we separated the contribution of\Nii$\lambda$6583 to the H$\alpha$ emission lines. Using the N2 index, weseparated active galactic nuclei from star-forming galaxies (SFGs) andestimated the gas metallicity. We studied the morphology of the sampledgalaxies qualitatively (visually) and quantitatively (automatically) usinghigh-resolution data from the \textit{Hubble Space Telescope}-ACS. The physicalsize of the galaxies was derived from the morphological analysis using\texttt{GALAPAGOS2/GALFIT}, where we fit a single-S\'ersic 2D model to eachsource.

The OTELO survey: Nature and mass-metallicity relation for H$\alpha$ emitters at $z\sim\,0.4$