Predictions and Strategies for Integral-Field Spectroscopy of High-Redshift Galaxies

We investigate the ability of infrared integral-field spectrographs to mapthe velocity fields of high redshift galaxies, presenting a formalism which maybe applied to any telescope and imaging spectrograph system. We discuss the5-sigma limiting line fluxes which current integral-field spectrographs willreach, and extend this discussion to consider future large aperture telescopeswith cryogenically cooled adaptive reimaging optics. In particular, we simulateobservations of spectral line emission from star-forming regions at redshifts z= 0.5 to 2.5 using a variety of spatial sampling scales and give predictionsfor the signal-to-noise ratio expected as a function of redshift. Using valuescharacteristic of the W.M. Keck II telescope and the new OH-SuppressingInfraRed Imaging Spectrograph (OSIRIS) we calculate integral-fieldsignal-to-noise ratio maps for a sample of U_nGR color-selected star-forminggalaxies at redshift z ~ 2 - 2.6 and demonstrate that OSIRIS will be able toreconstruct the two-dimensional projected velocity fields of these galaxies onscales of 100 mas (~ 1 kpc at redshift z ~ 2). With signal-to-noise ratios perspatial sample up to ~ 20, OSIRIS will in some cases be able to distinguishbetween merger activity and ordered disk rotation. Structures on scales smallerthan 1 kpc may be detected by OSIRIS for particularly bright sources, and willbe easy targets for future 30m class telescopes.