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

The exploration of the relation between galaxy sizes and other physical parameters has provided important clues for understanding galaxy formation. We use the 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\sim7. We select 153 z-band drop-out galaxies in six different fields characterized by a wide combination of depth and areal coverage, ideally suited to sample without biases the observed size-magnitude plane. Detailed simulations allow us to derive the completeness as a function of size and magnitude and to quantify measurements errors/biases. We find that the half light radius distribution function of z\sim7 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 ~0.15 arcsec. We also find a well defined size-luminosity relation, Rh\simL^1/2. We compute the Luminosity Function 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\pm0.1 for the luminosity function of LBGs at this redshift. Using this LF, we find that the amount of ionizing photons 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). With future CANDELS data, we can put severe limits to the role of galaxies in the reionization of the Universe.