Direct Measurements of the Stellar Continua and Balmer/4000 Å Breaks of Red z > 2 Galaxies: Redshifts and Improved Constraints on Stellar Populations^{* ** ***}

We use near-infrared (NIR) spectroscopy obtained with the GNIRS on Gemini, NIRSPEC on the Keck, and ISAAC on the VLT to study the rest-frame optical continua of three "distant red galaxies" (with J_s - K_s > 2.3) at z > 2. All three galaxy spectra show the Balmer/4000 Å break in the rest-frame optical. The spectra allow us to determine spectroscopic redshifts from the continuum with an estimated accuracy of Δz/(1 + z) ~ 0.001-0.04. These redshifts agree well with the emission-line redshifts for the two galaxies with Hα emission. This technique is particularly important for galaxies that are faint in the rest-frame UV, as they are underrepresented in high-redshift samples selected in optical surveys and are too faint for optical spectroscopy. Furthermore, we use the break, continuum shape, and equivalent width of Hα, together with evolutionary synthesis models, to constrain the age, star formation timescale, dust content, stellar mass, and star formation rate of the galaxies. Inclusion of the NIR spectra in the stellar population fits greatly reduces the range of possible solutions for stellar population properties. We find that the stellar populations differ greatly among the three galaxies, ranging from a young dusty starburst with a small break and strong emission lines to an evolved galaxy with a strong break and no detected line emission. The dusty starburst galaxy has an age of 0.3 Gyr and a stellar mass of 1 × 10¹¹ M_☉. The spectra of the two most evolved galaxies imply ages of 1.3-1.4 Gyr and stellar masses of 4 × 10¹¹ M_☉. This large range of properties strengthens our previous, more uncertain results from broadband photometry. Larger samples are required to determine the relative frequency of dusty starbursts and (nearly) passively evolving galaxies at z ~ 2.5.