WAVES mock survey simulations are generated using the Theoretical Astrophysical Observatory tool (TAO). Figure 1 shows the simulated light cones for WAVES-Wide and Deep.
4MOST observing times are estimated for each simulated source, using prior experience with the Anglo-Australian Telescope (AAT) + AAOmega (4m mirror + fibre-fed spectrograph - as such, a usefully comparison to VISTA + 4MOST). During GAMA observations a single 1deg2 deep test region was observed targeting sources down to r<22 and applying a nightly feedback observing strategy. In this strategy, spectra were reduced and redshifts calculated each night (in ~45min observing blocks). If a secure redshift was obtained, the source was removed from the target catalogue. In the following night, only sources without a secure redshift were re-observed and new sources added to the observations.
Using this method, sources are only observed for the minimum integration time required to obtain a secure redshift. In total ~2,000 secure redshifts were measured between 19.8<r<22.0, with varying integration times as a function of magnitude - largely dependant on source type/weather conditions. Using this the typical time required to obtain a redshift as a function of magnitude, irrespective of source type, may be estimated.
All integration times required to obtain a redshift are binned as a function of magnitude, and the upper 80% range in each bin calculated. A linear relation is fit to the upper 80% integration times and magnitude (which appears reasonable) and a function is derived for predicted integration times with the AAT. In order to account for the vastly better site and predicted throughput of VISTA + 4MOST, and for want of a more accurate formalism, all observing times are reduced by half. A minimum integration time of 20min is set for the brightest sources. Figure 2 displays the upper 80% integration times required to obtain a redshift for the G15-deep observations divided by two for improved site/throughput of 4MOST (blue) and the linear fit prediction for 4MOST with a 20min minimum integration time floor (red).
Using this derived function, a predicted integration time can be obtained for all TAO simulated sources based on their semi-analytically derived r-band magnitude.