Studies measuring the star formation rate density, luminosity function, andproperties of star-forming galaxies are numerous. However, it exists a gap at$0.5<z<0.8$ in H$\alpha$-based studies. Our main goal is to study theproperties of a sample of faint H$\alpha$ emitters at $z\sim0.62$. We focus ontheir contribution to the faint end of the luminosity function and derived starformation rate density, characterising their morphologies and basic photometricand spectroscopic properties. We use a narrow-band technique in thenear-infrared, with a filter centred at 1.06 $\mu$m. The data come fromultra-deep VLT/HAWK-I observations in the GOODS-S field with a total of 31.9 hin the narrow-band filter. We perform a visual classification of the sample andstudy their morphologies from structural parameters available in CANDELS. Our28 H$\alpha$-selected sample of faint star-forming galaxies reveals a robustfaint-end slope of the luminosity function $\alpha=-1.46_{-0.08}^{+0.16}$. Thederived star formation rate density at $z\sim0.62$ is $\rho_\mathrm{SFR} =0.036_{-0.008}^{+0.012} M_{\odot}~\mathrm{yr^{-1}~Mpc^{-3}}$. The sample ismainly composed of disks, but an important contribution of compact galaxieswith S\'ersic indexes $n\sim2$ display the highest specific star formationrates. The luminosity function at $z\sim0.62$ from our ultra-deep data pointstowards a steeper $\alpha$ when an individual extinction correction for eachobject is applied. Compact galaxies are low-mass, low-luminosity, andstarburst-dominated objects with a light profile in an intermediate stage fromearly to late types.

Observationally, the quenching of star-forming galaxies appears to dependboth on their mass and environment. The exact cause of the environmentaldependence is still poorly understood, yet semi-analytic models (SAMs) ofgalaxy formation need to parameterise it to reproduce observations of galaxyproperties. In this work, we use hydrodynamical simulations to investigate thequenching of disk galaxies through ram-pressure stripping (RPS) as they fallinto galaxy clusters with the goal of characterising the importance of thiseffect for the reddening of disk galaxies. Our set-up employs a live model of agalaxy cluster that interacts with infalling disk galaxies on different orbits.We use the moving-mesh code AREPO, augmented with a special refinement strategyto yield high resolution around the galaxy on its way through the cluster in acomputationally efficient way. Our direct simulations differ substantially fromstripping models employed in current SAMs, which in most cases overpredict themass loss from RPS. Furthermore, after pericentre passage, as soon as rampressure becomes weaker, gas that remains bound to the galaxy is redistributedto the outer parts, an effect that is not captured in simplified treatements ofRPS. Star formation in our model galaxies is quenched mainly because the hotgas halo is stripped, depriving the galaxy of its gas supply. The cold gas diskis only stripped completely in extreme cases, leading to full quenching andsignificant reddening on timescale of ~200 Myr. On the other hand, galaxiesexperiencing only mild ram pressure actually show an enhanced star formationrate that is consistent with observations and are quenched on timescales > 1Gyr. Stripped gas in the wake is mixed efficiently with intracluster gasalready a few tens of kpc behind the disk, and this gas is free of residualstar formation.