  We present a study into the capabilities of integrated and spatially resolved
integral field spectroscopy of galaxies at z=2-4 with the future HARMONI
spectrograph for the European Extremely Large Telescope (E-ELT) using the
simulation pipeline, HSIM. We focus particularly on the instrument's
capabilities in stellar absorption line integral field spectroscopy, which will
allow us to study the stellar kinematics and stellar population
characteristics. Such measurements for star-forming and passive galaxies around
the peak star formation era will provide a critical insight into the star
formation, quenching and mass assembly history of high-z, and thus present-day
galaxies. First, we perform a signal-to-noise study for passive galaxies at a
range of stellar masses for z=2-4, assuming different light profiles; for this
population we estimate integrated stellar absorption line spectroscopy with
HARMONI will be limited to galaxies with M_star > 10^10.7 solar masses. Second,
we use HSIM to perform a mock observation of a typical star-forming 10^10 solar
mass galaxy at z=3 generated from the high-resolution cosmological simulation
NutFB. We demonstrate that the input stellar kinematics of the simulated galaxy
can be accurately recovered from the integrated spectrum in a 15-hour
observation, using common analysis tools. Whilst spatially resolved
spectroscopy is likely to remain out of reach for this particular galaxy, we
estimate HARMONI's performance limits in this regime from our findings. This
study demonstrates how instrument simulators such as HSIM can be used to
quantify instrument performance and study observational biases on kinematics
retrieval; and shows the potential of making observational predictions from
cosmological simulation output data.
