We present the largest search to date for Y-band dropout galaxies ( z \sim 8 Lyman break galaxies , LBGs ) based on 350 arcmin ^ { 2 } of HST observations in the V- , Y- , J- and H-bands from the Brightest of Reionizing Galaxies ( BoRG ) survey .
In addition to previously published data , the BoRG13 dataset presented here includes approximately 50 arcmin ^ { 2 } of new data and deeper observations of two previous BoRG pointings , from which we present 9 new z \sim 8 LBG candidates , bringing the total number of BoRG Y-band dropouts to 38 with 25.5 \leqslant m _ { J } \leqslant 27.6 ( AB system ) .
We introduce a new Bayesian formalism for estimating the galaxy luminosity function , which does not require binning ( and thus smearing ) of the data and includes a likelihood based on the formally correct binomial distribution as opposed to the often used approximate Poisson distribution .
We demonstrate the utility of the new method on a sample of 97 Y-band dropouts that combines the bright BoRG galaxies with the fainter sources published in ( 9 ) from the Hubble Ultradeep Field ( HUDF ) and Early Release Science ( ERS ) programs .
We show that the z \sim 8 luminosity function is well described by a Schechter function over its full dynamic range with a characteristic magnitude M ^ { \star } = -20.15 ^ { +0.29 } _ { -0.38 } , a faint-end slope of \alpha = -1.87 ^ { +0.26 } _ { -0.26 } , and a number density of \log _ { 10 } \phi ^ { \star } [ \textrm { Mpc } ^ { -3 } ] = -3.24 ^ { +0.25 } _ { -0.24 } .
Integrated down to M = -17.7 this luminosity function yields a luminosity density , \log _ { 10 } \epsilon [ \textrm { erg } / \textrm { s / Hz / Mpc } ^ { 3 } ] = 25.52 ^ { +0.05 } _ { -0.05 } .
Our luminosity function analysis is consistent with previously published determinations within 1 \sigma .
The error analysis suggests that uncertainties on the faint-end slope are still too large to draw firm conclusion about its evolution with redshift .
We use our statistical framework to discuss the implication of our study for the physics of reionization .
By assuming theoretically motivated priors on the clumping factor and the photon escape fraction we show that the UV luminosity density from galaxy samples down to M = -17.7 can ionize only 10-50 % of the neutral hydrogen at z \sim 8 .
Full reionization would require extending the luminosity function down to M = -15 .
The data are consistent with a substantial fraction of neutral hydrogen at z > 7 , in agreement with recent suggestions based on deep spectroscopy of redshift 8 LBGs .