| Abstract
| - Aims. Ly α emitters (LAEs) can be detected out to very high redshifts during the epoch of reionization. The evolution of the LAE luminosity function with redshift is a direct probe of the Ly α transmission of the intergalactic medium (IGM), and therefore of the IGM neutral-hydrogen fraction. Measuring the Ly α luminosity function (LF) of Ly α emitters at redshift z = 7.7 therefore allows us to constrain the ionizing state of the Universe at this redshift. Methods. We observed three 7 '.5 × 7 '.5 fields with the HAWK-I instrument at the VLT with a narrow band filter centred at 1.06 μm and targeting Ly α emitters at redshift z ~ 7.7. The fields were chosen for the availability of multiwavelength data. One field is a galaxy cluster, the Bullet Cluster, which allowed us to use gravitational amplification to probe luminosities that are fainter than in the field. The two other fields are subareas of the GOODS Chandra Deep Field South and CFHTLS-D4 deep field. We selected z = 7.7 LAE candidates from a variety of colour criteria, in particular from the absence of detection in the optical bands. Results. We do not find any LAE candidates at z = 7.7 in ~2.4 × 10 4 Mpc 3 down to a narrow band AB magnitude of ~26, which allows us to infer robust constraints on the Ly α LAE luminosity function at this redshift. Conclusions. The predicted mean number of objects at z = 6.5, derived from somewhat different luminosity functions of Hu et al. (2010, ApJ, 725, 394), Ouchi et al. (2010, ApJ, 723, 869), and Kashikawa et al. (2011, ApJ, 734, 119) are 2.5, 13.7, and 11.6, respectively. Depending on which of these luminosity functions we refer to, we exclude a scenario with no evolution from z = 6.5 to z = 7.7 at 85% confidence without requiring a strong change in the IGM Ly α transmission, or at 99% confidence with a significant quenching of the IGM Ly α transmission, possibly from a strong increase in the high neutral-hydrogen fraction between these two redshifts.
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