Direct Measurements of the Stellar Continua and Balmer/4000 Angstrom Breaks of Red z>2 Galaxies: Redshifts and Improved Constraints on Stellar Populations

We use near-infrared (NIR) spectroscopy obtained with GNIRS on Gemini, NIRSPEC on KECK, and ISAAC on the VLT to study the rest-frame optical continua of three `Distant Red Galaxies' (having Js - Ks > 2.3) at z>2. All three galaxy spectra show the Balmer/4000 Angstrom break in the rest-frame optical. The spectra allow us to determine spectroscopic redshifts from the continuum with an estimated accuracy dz/(1+z) ~ 0.001-0.04. These redshifts agree well with the emission line redshifts for the 2 galaxies with Halpha 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 Halpha 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*10^11 Msun. The spectra of the two most evolved galaxies imply ages of 1.3-1.4 Gyr and stellar masses of 4*10^11 Msun. The large range of properties seen in these galaxies strengthens our previous much 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.