Sky subtraction at the Poisson limit with fibre-optic multi-object spectroscopy

We report on the limitations of sky subtraction accuracy for long duration fibre-optic multi-object 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 hour 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 hours. We show that these systematic defects can be avoided through the use of the fibre nod-and-shuffle observing mode, but with potential cost in observing efficiency. Finally we demonstrate that these disadvantages can be overcome through the application of a Principle Components Analysis sky subtraction routine. Such an approach minimise systematic residuals across long duration exposures allowing deep integrations. We apply the PCA approach to over 200 hours of on-sky observations and conclude that for the AAOmega system the residual error in long duration observations falls at a rate proportional to t^-0.32 in contrast to the t^-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 nod-and-shuffle technique for observations in the sky limited regime with durations of 10-100 hours (even before accounting for the additional signal-to-noise and targeting efficiency losses often associated with the N+S technique).[abridged]