This study presents Keck optical and infrared spectroscopy of the rest-frame ultraviolet and optical emission lines in two Lyman alpha emitting galaxies at z>2. These data provide insight on the evolution of fundamental galaxy scaling relations at early epochs, especially the luminosity-velocity and luminosity-metallicity relations. Lynx 2-9691 exhibits extended [O III] emission over a diameter of >28 kpc, reminiscent of the Lyman alpha nebulae discovered near Lyman-drop galaxies [Steidel et al 2000]. The ratios of strong nebular emission lines indicate sub-solar oxygen abundances in the range 8.2<12+log(O/H)<8.8 (Z = 0.25-0.95 Z_sun). Interestingly, Galactic metal-rich globular clusters have similar metallicities, consistent with the idea that we could be seeing the formation of galaxies like the Milky Way at $zsim3$. The measured gas phase oxygen abundances are >4-10 times higher than the Z < 0.1 Z_sun metallicities found in damped Lyman alpha (DLA) absorbers at similar redshifts, indicating that DLA systems trace different environments than the vigorously star-forming objects observed here. Star-forming galaxies at $zsim3$ are 2-4 magnitudes more luminous than local spiral galaxies of similar metallicity, and thus, are offset from the local luminosity-metallicity relation. Their kinematic linewidths are sigma_v=65-130 km/s, making this sample 1-3 magnitudes more luminous than local galaxies of similar linewidth and mass. [Abridged]
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