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 \lower 2.0 pt \hbox { $ \buildrel { \scriptstyle < } \over { \scriptstyle \sim } $ } z % \lower 2.0 pt \hbox { $ \buildrel { \scriptstyle < } \over { \scriptstyle \sim } $ } 4.5 in the Hubble Deep Field ( HDF ) .
Eleven of these galaxies are confirmed to be at high redshift ( z _ { med } = 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 .
The spectra of the confirmed high-redshift galaxies show a diversity of features , including weak Ly \alpha emission , strong Ly \alpha breaks or damped Ly \alpha absorption profiles , and the stellar and interstellar rest-UV absorption lines common to local starburst galaxies and high-redshift star-forming galaxies reported recently by others .
The narrow profiles and low equivalent widths of C IV , Si IV , and N V absorption lines may imply low stellar metallicities .
Combined with the 5 high-redshift galaxies in the HDF previously confirmed with Keck spectra by Steidel et al . ( 1996b ) , the 16 confirmed sources yield a comoving volume density of n \geq 2.5 \times 10 ^ { -4 } h _ { 50 } ^ { 3 } { Mpc } ^ { -3 } for q _ { 0 } = 0.05 , or n \geq 1.2 \times 10 ^ { -3 } h _ { 50 } ^ { 3 } { Mpc } ^ { -3 } for q _ { 0 } = 0.5 .
These densities are 3 - 4 times higher than the recent estimates of Steidel et al . ( 1996a ) based on ground-based photometry with slightly brighter limits , and are comparable to estimates of the local volume density of galaxies brighter than L ^ { * } .
The high-redshift density measurement is only a lower limit , and could be almost three times higher still if all 29 of the unconfirmed candidates in our original sample , including those not observed , are indeed also at high redshift .
The galaxies are small but luminous , with half-light radii 1.8 < r _ { 1 / 2 } < 6.5 h _ { 50 } ^ { -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 h _ { 50 } ^ { -2 } M _ { \odot } yr ^ { -1 } for q _ { 0 } = 0.05 and q _ { 0 } = 0.5 , respectively .
These rates overlap those for local spiral and H II galaxies today , although they could be more than twice as high if dust extinction in the UV is significant .
If the objects at z = 3 were simply to fade by 5 magnitudes ( assuming a 10 ^ { 7 } yr burst and passive evolution ) without mergers in the 14 Gyr between then and now ( for q _ { 0 } = 0.05 ,h _ { 50 } = 1.0 ) , they would resemble average dwarf elliptical/spheroidal galaxies in both luminosity and size .
However , 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 .