The tiling algorithm for the 6dF Galaxy Survey

The 6-degree Field Galaxy Survey (6dFGS) is a spectroscopic survey of the southern sky, which aims to provide positions and velocities of galaxies in the nearby Universe. When completed the survey will produce approximately 170 000 redshifts and 15 000 peculiar velocities. The survey is being carried out on the UK Schmidt telescope at the Anglo Australian Observatory (AAO), using the 6dF robotic fibre positioner and spectrograph system. We present here the adaptive tiling algorithm developed to place 6dFGS fields on the sky, and allocate targets to those fields. Optimal solutions to survey field placement are generally extremely difficult to find, especially in this era of large-scale galaxy surveys, as the space of available solutions is vast (2N-dimensional) and false optimal solutions abound. The 6dFGS algorithm utilizes the Metropolis (simulated annealing) method to overcome this problem. By design the algorithm gives uniform completeness independent of local density, so as to result in a highly complete and uniform observed sample. The adaptive tiling achieves a sampling rate of approximately 95 per cent, a variation in the sampling uniformity of less than 5 per cent, and an efficiency in terms of used fibres per field of greater than 90 per cent. We have tested whether the tiling algorithm systematically biases the large-scale structure in the survey by studying the two-point correlation function of mock 6dF volumes. Our analysis shows that the constraints on fibre proximity with 6dF lead to underestimating galaxy clustering on small scales (<1 h(-1) Mpc) by up to similar to 20 per cent, but that the tiling introduces no significant sampling bias at larger scales. The algorithm should be generally applicable to virtually all tiling problems, and should reach whatever optimal solution is defined by the user's own merit function.