The OTELO survey: Nature and mass-metallicity relation for H$\alpha$
  emitters at $z\sim\,0.4$
  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 its
possible evolution. We drew our sample from the OSIRIS Tunable Emission Line
Object (OTELO) survey, which exploits the red tunable filter of OSIRIS at the
Gran Telescopio Canarias to perform a blind narrow-band spectral scan in a
selected field of the Extended Groth Strip. We were able to directly measure
emission line fluxes and equivalent widths from the analysis of OTELO
pseudo-spectra. This study aims to explore the MZR in the very low-mass regime.
Our sample reaches stellar masses ($M_*$) as low as $10^{6.8}\,M_\odot$, where
63\% of the sample have $M_*\,<10^9\,M_\odot$. We also explore the relation of
the star formation rate (SFR) and specific SFR (sSFR) with $M_*$ and gas-phase
oxygen abundances, as well as the $M_*$-size relation and the morphological
classification. 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, we
separated active galactic nuclei from star-forming galaxies (SFGs) and
estimated the gas metallicity. We studied the morphology of the sampled
galaxies qualitatively (visually) and quantitatively (automatically) using
high-resolution data from the \textit{Hubble Space Telescope}-ACS. The physical
size of the galaxies was derived from the morphological analysis using
\texttt{GALAPAGOS2/GALFIT}, where we fit a single-S\'ersic 2D model to each
source.
