The size-luminosity relation at z=7 in CANDELS and its implication on reionization

Context. The exploration of the relation between galaxy sizes and other physical parameters (luminosity, mass, star formation rate) has provided important clues for understanding galaxy formation, but such exploration has until recently been limited to intermediate redshift objects. Aims. We use the currently available CANDELS Deep+Wide surveys in the GOODS-South, UDS and EGS fields, complemented by data from the HUDF09 program, to address the relation between size and luminosity at z similar to 7. Methods. The six different fields used for this study are characterized by a wide combination of depth and areal coverage, well suited for reducing the biases on the observed size-magnitude plane. From these fields, we select 153 z-band dropout galaxies. Detailed simulations have been carried out for each of these six fields, inserting simulated galaxies at different magnitudes and half light radius in the two dimensional images for all the Hubble Space Telescope (HST) bands available and recovering them as carried out for the real galaxies. These simulations allow us to derive precisely the completeness as a function of size and magnitude and to quantify measurements errors/biases, under the assumption that the 2D profile of z = 7 galaxies is well represented by an exponential disk function. Results. We find in a rather robust way that the half light radius distribution function of z similar to 7 galaxies fainter than J = 26.6 is peaked at <= 0.1 arcsec (or equivalently 0.5 kpc proper), while at brighter magnitudes high-z galaxies are typically larger than similar to 0.15 arcsec. We also find a well defined size-luminosity relation, Rh proportional to L-1/2. We compute the luminosity function (LF) in the HUDF and P12HUDF fields, finding large spatial variation on the number density of faint galaxies. Adopting the size distribution and the size-luminosity relation found for faint galaxies at z = 7, we derive a mean slope of -1.7 +/- 0.1 for the LF of LBGs at this redshift. Conclusions. Using this LF, we find that the number of ionizing photons emitted from galaxies at z similar to 7 cannot keep the Universe re-ionized if the IGM is clumpy (C-HII >= 3) and the Lyman continuum escape fraction of high-z LBGs is relatively low (f(esc) <= 0.3). If these results are confirmed and strengthened by future CANDELS data, in particular by the forthcoming deep observations in GOODS-South and North and the wide field COSMOS, we can put severe limits to the role of galaxies in the reionization of the Universe.