The bright end of the z  ~ 7 UV luminosity function from a wide and deep HAWK-I survey

Aims. We perform a deep search for galaxies in the redshift range 6.5 ≤ z ≤ 7.5 to measure the evolution of the number density of luminous galaxies in this redshift range and derive useful constraints on the evolution of their luminosity function. Methods. We present here the second half of an ESO Large Programme, which exploits the unique combination of area and sensitivity provided in the near-IR by the camera Hawk-I at the VLT. We have obtained ~30 observing hours with Hawk-I in the Y-band of two high galactic latitude fields. We combined the Y-band data with deep J and K Hawk-I observations, as well as FORS1/FORS2 U, B, V, R, I, and Z observations to select z-drop galaxies with Z − Y > 1, no optical detection, and flat Y − J and Y − K colour terms. Results. We detect eight high-quality candidates in the magnitude range Y = 25.5−26.5 that we add to the z-drop candidates selected in two Hawk-I pointings over the GOODS-South field. We use this full sample of 15 objects found in ~161 arcmin2 of our survey to constrain the average physical properties and the evolution of the number density of z ~ 7 LBGs. A stacking analysis yields a best-fit SED with photometric redshift $z=6.85^{+0.20}_{-0.15}$z=6.85-0.15+0.20 and an $E(B-V)=0.05^{+0.15}_{-0.05}$E(B−V)=0.05-0.05+0.15. We compute a binned estimate of the z ~ 7 LF and explore the effects of photometric scatter and model uncertainties on the statistical constraints. After accounting for the expected incompleteness through MonteCarlo simulations, we strengthen our previous finding that a Schechter luminosity function constant from z = 6 to z = 7 is ruled out at a ≳ 99% confidence level, even including the effects of cosmic variance. For galaxies brighter than M1500 = −19.0, we derive a luminosity density $\rho_{UV}= 1.5^{+2.1}_{-0.8}\times 10^{25}\rm ~erg ~ s^{-1} ~ Hz^{-1} ~ Mpc^{-3} $ρUV=1.5-0.8+2.1×1025 erg s-1 Hz-1 Mpc-3, implying a decrease by a factor 3.5 from z = 6 to z ≃ 6.8. We find that under standard assumptions, the emission rate of ionizing photons coming from UV bright galaxies is lower by at least a factor of two than the value required for reionization. Finally, we exploit deep Hawk-I J and K band observations to derive an upper limit on the number density of M1500 ≲ −22.0 LBGs at z ~ 8 (Y-dropouts).