  We present and discuss the mean rest-frame ultraviolet spectrum for a sample
of 81 Lyman Break Galaxies (LBGs) selected to be B-band dropouts with a mean
redshift of z=3.9 and apparent magnitudes z_AB<26. Most of the individual
spectra are drawn from our ongoing survey in the GOODS fields with the Keck
DEIMOS spectrograph, and we have augmented our sample with published data taken
with FORS2 on the VLT. In general we find similar trends in the spectral
diagnostics to those found in the earlier, more extensive survey of LBGs at z=3
undertaken by Shapley et al (2003). Specifically, we find low-ionization
absorption lines which trace the presence of neutral outflowing gas are weaker
in galaxies with stronger Lyman-alpha emission, bluer UV spectral slopes, lower
stellar masses, lower UV luminosities and smaller half-light radii. This is
consistent with a physical picture whereby star formation drives outflows of
neutral gas which scatters Lyman-alpha and gives rise to strong low-ionization
absorption lines, while increasing the stellar mass, size, metallicity, and
dust content of galaxies. Typical galaxies are thus expected to have stronger
Lyman-alpha emission and weaker low-ionization absorption at earlier times
(higher redshifts). Indeed, our mean spectrum at z=4 shows somewhat weaker
low-ionization absorption lines than at z=3 and available data at higher
redshift indicates a rapid decrease in low-ionization absorption strength with
redshift. We argue that the reduced low-ionization absorption is likely caused
by a decrease in the covering fraction and/or velocity range of outflowing
neutral gas at earlier epochs. Our continuing survey will enable us to extend
these diagnostics more reliably to higher redshift and determine the
implications for the escape fraction of ionizing photons which governs the role
of early galaxies in cosmic reionization. [Abridged]
