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A multi-object spectrograph on the forthcoming European Extremely LargeTelescope will be required to operate with good sky coverage. Many of theinteresting deep cosmological fields were deliberately chosen to be free ofbright foreground stars, and therefore are potentially challenging for adaptiveoptics (AO) systems. Here we investigate multi-object AO performance usingsub-fields chosen at random from within the Great Observatories Origins DeepSurvey (GOODS)-S field, which is the worst case scenario for five deep fieldsused extensively in studies of high-redshift galaxies. Our AO system model isbased on that of the proposed MOSAIC instrument but our findings are equallyapplicable to plans for multi-object spectroscopy on any of the plannedExtremely Large Telescopes. Potential guide stars within these sub-fields areidentified and used for simulations of AO correction. We achieve ensquaredenergies within 75~mas of between 25-35\% depending on the sub-field, which issufficient to probe sub-kpc scales in high-redshift galaxies. We alsoinvestigate the effect of detector readout noise on AO system performance, andconsider cases where natural guide stars are used for both high-order andtip-tilt-only AO correction. We also consider how performance scales withensquared energy box size. In summary, the expected AO performance issufficient for a MOSAIC-like instrument, even within deep fields characterisedby a lack of bright foreground stars.

Wide-field adaptive optics performance in cosmological deep fields for multi-object spectroscopy with the European Extremely Large Telescope