A new determination using VLT/HAWK-I

We aim to place new, strengthened constraints on the luminosity function (LF )o f H-alpha (Hα) emitting galaxies at redshift z ≈ 2.2, and to further constrain the instantaneous star-formation rate density of the universe ( u ρ� ). We have used the new HAWK-I instrument at ESO-VLT to obtain extremely deep narrow-band (line; NB2090) and broad-band (continuum; Ks) imaging observations. The target field is in the GOODS-South, providing us with a rich multi-wavelength auxiliary data set, which we utilise for redshift confirmation and to estimate dust content. We use this new data to measure the faint-end slope (α )o fLF(Hα) with unprecedented precision. The data are well fit by a Schechter function and also a single power-law, yielding α = (−1.72±0.20) and (−1.77±0.21), respectively. Thus we are able to confirm the steepening of α from low- to high-z predicted by a number of authors and observed at other wavelengths. We combine our LF data-points with those from a much shallower but wider survey at z ∼ 2.2 (Geach et al. 2008), constructing a LF spanning a factor of 50 in luminosity. Re-fitting the Schechter parameters, we obtain logL� = (43.07 ± 0.22) erg s −1 ;l ogφ� = (−3.45 ± 0.52) Mpc −3 ; α = (−1.60 ± 0.15). We integrate over LF(Hα) and apply a correction for dust attenuation to determine the instantaneous cosmic star-formation rate density at z ∼ 2 without assuming α or extrapolating it from lower-z. Our measurement of u ρ�