  We have obtained spectra with the 10-m Keck telescope of a sample of 24
galaxies having colors consistent with star-forming galaxies at redshifts
2<z<4.5 in the Hubble Deep Field (HDF). Eleven of these galaxies are confirmed
to be at high redshift (median z=3.0), one is at z=0.5, and the other 12 have
uncertain redshifts but have spectra consistent with their being at z>2.
Combined with 5 previously confirmed high-redshift galaxies in the HDF, the 16
confirmed sources yield a comoving volume density of n>2.5^-4 h50^3 Mpc^-3 for
q0=0.05, or n>1.2^-3 h50^3 Mpc^-3 for q0=0.5. These densities are comparable to
estimates of the local volume density of galaxies brighter than L*, and could
be almost three times higher still if all 29 of the unconfirmed candidates in
our original sample are indeed also at high redshift. The galaxies are small
but luminous, with half-light radii 1.8 < r(1/2) < 6.5 h50^-1 kpc and absolute
magnitudes -21.5 > M_B > -23. The HST images show a wide range of morphologies,
including several with very close, small knots of emission embedded in wispy
extended structures. Using rest-frame UV continuum fluxes with no dust
correction, we calculate star formation rates in the range 7 - 24 or 3 - 9
h50^-2 Msun/yr for q0=0.05 and q0=0.5, respectively. The variety of
morphologies and the high number density of z=3 galaxies in the HDF suggest
that they represent a range of physical processes and stages of galaxy
formation and evolution, rather than any one class of object, such as massive
ellipticals. A key issue remains the measurement of masses. These high-redshift
objects are likely to be the low-mass, starbursting building blocks of more
massive galaxies seen today.
