WFOS: Wide-Field Optical Spectrometer Science Case Summary General description WFOS is a wide-field faint-object spectrometer and imager for wavelengths between the atmospheric UV cutoff at 0.31µm to at least 1.0µm (goal is 1.6µm). It is both one of the highest priority capabilities for TMT and one of the first instruments that will be commissioned. This instrument will have high throughout, spectral resolutions up to 4000 (1 slit) and multi-object capability (presumably with focal-plane slit masks to meet the imaging, throughput, and UV requirements). Although it is considered a seeing-limited instrument, some image correction may be desirable if it can be used to improve the overall efficiency and image quality over at least a significant portion of the full spectroscopic or imaging field of view. An atmospheric dispersion compensator will be required. Anticipated Science Areas WFOS will allow routine spectroscopic observations of very faint, V>24, sources throughout the Universe to z=7. Although some of the science with this instrument will require significant samples of objects, the ability to obtain spectra of extremely optically faint objects independent of multiplexing capabilities, is an important goal. The range of spectral resolution is designed to allow “identification” quality spectra for the faintest sources at the low end and to allow detailed astrophysical diagnostics (e.g. kinematics of low-mass galaxies, chemistry and kinematics from interstellar absorption line features in galaxy and AGN spectra, abundances for many elements in stellar spectra) at the high-R end. The high-resolution mode is also required for effective background (OH) suppression for wavelengths longward of 0.73 µm. The epoch of galaxy formation: 1< z<7. Identification of extremely faint sources, quantitative emission and absorption line measurements of optically faint galaxies and AGN using rest-frame UV diagnostics, three-dimensional mapping of hydrogen and metals in the z>1.6 intergalactic medium using absorption line techniques, kinematics and stellar populations in distant galaxies and galaxy clusters, and the physics of the reionization era. These general science areas are driving both the near-UV and near-IR capabilities as well as the requirements on spectral resolution and field size. Extensions of the wavelength coverage beyond 1 µm would allow multiplexed spectroscopy of faint objects beyond z~7, and will yield considerable additional diagnostic power for galaxies near the peak of the galaxy formation epoch near z~1-3. Spectroscopy of high redshift supernovae, gamma ray bursts, and other faint transient phenomena (some as yet not discovered). Science involving very faint, single interesting targets discovered by present and future facilities on the ground and in space. This type of application motivates the highest possible spectroscopic throughput, and the possibility of large simultaneous wavelength coverage. TMT will be certain to play a large role in new discoveries and physical understanding of the transient universe. Spectroscopy of very faint sources (V>25) in the local Universe. This is a broad range of science topics. Examples are studies of intrinsically very faint sources such as Galactic white dwarfs in clusters of all ages and opening up the field of optical photospheric emission from neutron stars. Intrinsically luminous stars (blue and red super giants) will be accessible at high S/N to the distance of the Virgo cluster, integrated light from globular clusters to the Coma cluster.