The InfraRed Imaging Spectrograph (IRIS) is a first-light instrument being designed for the Thirty Meter Telescope (TMT). IRIS is a combination of an imager that will cover a 16.4 field of view at the diffraction limit of TMT (4 mas sampling), and an integral field unit spectrograph that will sample objects at 4-50 mas scales. IRIS will open up new areas of observational parameter space, allowing major progress in diverse fields of astronomy. We present the science case and resulting requirements for the performance of IRIS. Ultimately, the spectrograph will enable very well-resolved and sensitive studies of the kinematics and internal chemical abundances of high-redshift galaxies, shedding light on many scenarios for the evolution of galaxies at early times. With unprecedented imaging and spectroscopy of exoplanets, IRIS will allow detailed exploration of a range of planetary systems that are inaccessible with current technology. By revealing details about resolved stellar populations in nearby galaxies, it will directly probe the formation of systems like our own Milky Way. Because it will be possible to directly characterize the stellar initial mass function in many environments and in galaxies outside of the the Milky Way, IRIS will enable a greater understanding of whether stars form differently in diverse conditions. IRIS will reveal detailed kinematics in the centers of low-mass galaxies, allowing a test of black hole formation scenarios. Finally, it will revolutionize the characterization of reionization and the first galaxies to form in the universe.
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