  The study of the Luminosity Function (LF) of Lyman Break Galaxies (LBGs) at
z=7 is important for ascertaining their role in the reionization of the
Universe. We perform a detailed and critical analysis of the statistical and
systematic errors in the z~7 LF determination: we have assembled a large sample
of candidate LBGs at z~7 from different surveys, spanning a large variety of
areas and depths. In particular, we have combined data from the deep (J<27.4)
and ultradeep (J<29.2) surveys recently acquired with the new WFC3 NIR camera
on HST, over the GOODS-ERS and the HUDF fields, with ground based surveys in
wide and shallow areas from VLT and Subaru. We have used public ACS images in
the z-band to select z-dropout galaxies, and other public data both in the blue
(BVI) and in the red bands to reject possible low-redshift interlopers. We have
compared our results with extensive simulations to quantify the observational
effects of our selection criteria as well as the effects of photometric
scatter, color selections or the morphology of the candidates. We have found
that the number density of faint LBGs at z~7 is only marginally sensitive to
the color selection adopted, but it is strongly dependent from the assumption
made on the half light distributions of the simulated galaxies, used to correct
the observed sample for incompleteness. The slope of the faint end of the LBGs
LF has thus a rather large uncertainty, due to the unknown distribution of
physical sizes of the z~7 LBGs. We conclude that galaxies at z~7 are unable to
reionize the Universe unless there is a significant evolution in the clumpiness
of the IGM or in the escape fraction of ionising photons or, alternatively,
there is a large population of z~7 LBGs with large physical dimensions but
still not detected by the present observations.
