In this paper , we address which sources contributed most of the reionizing photons .
Our argument assumes that the reionization ended around z \simeq 6 
and that it was a relatively quick process , i.e. , that there was a non-negligible fraction of neutral hydrogen in the Universe at somewhat earlier epochs .
Starting from our earlier estimate of the luminosity function ( LF ) of galaxies at z \simeq 6 , we quantitatively show that the major sources of reionization are most likely galaxies with L < L _ { * } .
Our approach allows us to put stronger constraints to the LF of galaxies at z \simeq 6 .
To have the Universe completely ionized at this redshift , the faint-end slope of the LF should be steeper than \alpha = -1.6 , which is the value measured at lower redshifts ( z \simeq 3 ) , unless either the normalization ( \Phi _ { * } ) of the LF or the clumping factor of the ionized hydrogen has been significantly underestimated .
If \Phi _ { * } is actually lower than what we assumed by a factor of two , a steep slope close to \alpha = -2.0 
is required .
Our LF predicts a total of 50 – 80 z \simeq 6 galaxies in the HST Ultra Deep Field ( UDF ) to a depth of AB = 28.4 mag , which can be used to constraint both \Phi _ { * } and \alpha .
We conclude that the least luminous galaxies existing at this redshift should reach as low as some critical luminosity in order to accumulate the entire reionizing photon budget .
On the other hand , the existence of significant amounts of neutral hydrogen at slightly earlier epochs , e.g . z \simeq 7 , requires that the least luminous galaxies should not be fainter than another critical value ( i.e. , the LF should cut-off at this point ) .