THE LUMINOSITY FUNCTION AT z ∼ 8 FROM 97 Y-BAND DROPOUTS: INFERENCES ABOUT REIONIZATION

We present the largest search to date for Y-band dropout galaxies (z similar to 8 Lyman break galaxies, LBGs) based on 350 arcmin(2) of Hubble Space Telescope 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 data set presented here includes approximately 50 arcmin2 of new data and deeper observations of two previous BoRG pointings, from which we present 9 new z similar to 8 LBG candidates, bringing the total number of BoRG Y-band dropouts to 38 with 25.5 <= m(J) <= 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 Bouwens et al. from the Hubble Ultra Deep Field and Early Release Science programs. We show that the z similar to 8 luminosity function is well described by a Schechter function over its full dynamic range with a characteristic magnitude M-star = -20.15(-0.38)(+0.29), a faint-end slope of alpha = -1.87(-0.26)(+0.26), and a number density of log(10) phi(star) [Mpc(-3)] = -3.24(-0.24)(+0.25). Integrated down to M = -17.7, this luminosity function yields a luminosity density log(10) is an element of[erg s(-1) Hz(-1) 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 a 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 similar to 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 z similar to 8 LBGs.