Sky subtraction at the Poisson limit with fibre-optic multiobject spectroscopy

We report on the limitations of sky-subtraction accuracy for long-duration fibre-optic multiobject spectroscopy of faint astronomical sources during long-duration exposures. We show that while standard sky subtraction techniques yield accuracies consistent with the Poisson noise limit for exposures of 1 h duration, there are large-scale systematic defects that inhibit the sensitivity gains expected on the summation of longer duration exposures. For the AAOmega system at the Anglo-Australian Telescope, we identify a limiting systematic sky-subtraction accuracy, which is reached after integration times of 4-10 h. We show that these systematic defects can be avoided through the use of the fibre nod-and-shuffle (N+S) observing mode, but with a potential cost in observing efficiency. Finally, we demonstrate that these disadvantages can be overcome through the application of a Principal Components Analysis (PCA) sky-subtraction routine. Such an approach minimize systematic residuals across long-duration exposures, allowing deep integrations.We apply the PCA approach to over 200 h of on-sky observations and conclude that for the AAOmega system, the residual error in long-duration observations falls at a rate proportional to τ^-0.32 in contrast to the τ^-0.5 rate expected from theoretical considerations. With this modest rate of decline, the PCA approach represents a more efficient mode of observation than the N+S technique for observations in the sky limited regime with durations of 10-100 h (even before accounting for the additional signal-to-noise ratio and targeting efficiency losses often associated with the N+S technique).This conclusion has important implications for the observing strategies of the next generation of fibre-optics redshift surveys with existing facilities as well as design implications for fibre-optic systems destined for new facilities. It argues against the use of the inherently inefficient N+S technique for faint object fibre-optic survey spectroscopy.