Properties of galaxies at the faint end of the H alpha luminosity function at z similar to 0.62

Context. Studies measuring the star formation rate density, luminosity function, and properties of star-forming galaxies are numerous. However, it exists a gap at 0.5 \textless z \textless 0.8 in H alpha-based studies. Aims. Our main goal is to study the properties of a sample of faint H alpha emitters at z similar to 0.62. We focus on their contribution to the faint end of the luminosity function and derived star formation rate density, characterising their morphologies and basic photometric and spectroscopic properties. Methods. We use a narrow-band technique in the near-infrared, with a filter centred at 1.06 mu m. The data come from ultra-deep VLT/HAWK-I observations in the GOODS-S field with a total of 31.9 h in the narrow-band filter. In addition to our survey, we mainly make use of ancillary data coming from the CANDELS and Rainbow Cosmological Surveys Database, from the 3D-HST for comparison, and also spectra from the literature. We perform a visual classification of the sample and study their morphologies from structural parameters available in CANDELS. In order to obtain the luminosity function, we apply a traditional V/V-max method and perform individual extinction corrections for each object to accurately trace the shape of the function. Results. Our 28 H alpha-selected sample of faint star-forming galaxies reveals a robust faint-end slope of the luminosity function alpha = 1.46(-0.08)(+0.16). The derived star formation rate density at z similar to 0.62 is rho(SFR) = 0.036(-0.008+0.012)M (circle dot) yr(-1) Mpc(-3). The sample is mainly composed of disks, but an important contribution of compact galaxies with Syyyrsic indexes n similar to 2 display the highest specific star formation rates. Conclusions. The luminosity function at z similar to 0.62 from our ultra-deep data points towards a steeper alpha when an individual extinction correction for each object is applied. Compact galaxies are low-mass, low-luminosity, and starburst-dominated objects with a light profile in an intermediate stage from early to late types.