Multi-Wavelength Constraints on the Cosmic Star Formation History from Spectroscopy: the Rest-Frame UV, H-alpha, and Infrared Luminosity Functions at Redshifts 1.9<z<3.4

We use a sample of rest-frame UV selected and spectroscopically observed galaxies at redshifts 1.9<z<3.4, combined with ground-based spectroscopic H-alpha and Spitzer MIPS 24 micron data, to derive the most robust measurements of the rest-frame UV, H-alpha, and infrared (IR) luminosity functions (LFs) at these redshifts. Our sample is by far the largest of its kind, with over 2000 spectroscopic redshifts in the range 1.9<z<3.4 and ~15000 photometric candidates in 29 independent fields covering a total area of almost a square degree. Our method for computing the LFs takes into account a number of systematic effects, including photometric scatter, Ly-alpha perturbations to optical colors, and contaminants. Taking into account the latter, we find no evidence for an excess of UV-bright galaxies over what was inferred in early z~3 LBG studies. The UV LF appears to undergo little evolution between z~4 and z~2. Corrected for extinction, the UV luminosity density (LD) at z~2 is at least as large as the value at z~3 and a factor of ~9 larger than the value at z~6, primarily reflecting an increase in the number density of bright galaxies between z~6 and z~2. Our analysis yields the first constraints anchored by extensive spectroscopy on the IR and bolometric LFs for faint and moderately luminous (L[bol]<10^12 L_sun) galaxies. Adding the IR to the emergent UV luminosity, incorporating independent measurements of the LD from ULIRGs, and assuming realistic dust attenuation values for UV-faint galaxies, indicates that galaxies with L[bol]<10^12 L_sun account for ~80% of the bolometric LD and SFRD at z~2-3. Our multi-wavelength constraints on the global SFRD indicate that approximately one-third of the present-day stellar mass density was formed in sub-ultraluminous galaxies between redshifts z=1.9-3.4. [Abridged]