  We investigate the intrinsic opacity of high-redshift galaxies to outgoing
ionising photons using high-quality photometry of a sample of 27
spectroscopically-identified galaxies of redshift 1.9<z<3.5 in the Hubble Deep
Field. Our measurement is based on maximum-likelihood fitting of model galaxy
spectral energy distributions-including the effects of intrinsic Lyman-limit
absorption and random realizations of intervening Lyman-series and Lyman-limit
absorption-to photometry of galaxies from space- and ground-based broad-band
images. Our method provides several important advantages over the methods used
by previous groups, including most importantly that two-dimensional sky
subtraction of faint-galaxy images is more robust than one-dimensional sky
subtraction of faint-galaxy spectra. We find at the 3sigma statistical
confidence level that on average no more than 4% of the ionising photons escape
galaxies of redshift 1.9<z<3.5. This result is consistent with observations of
low- and moderate-redshift galaxies but is in direct contradiction to a recent
result based on medium-resolution spectroscopy of high-redshift (z~3) galaxies.
Dividing our sample in subsamples according to luminosity, intrinsic
ultraviolet colour, and redshift, we find no evidence for selection effects
that could explain such discrepancy. Even when all systematic effects are
included, the data could not realistically accomodate any escape fraction value
larger than ~15%.
