Correcting for Fibre Assignment Incompleteness in the DESI Bright Galaxy Survey

The Dark Energy Spectroscopic Instrument (DESI) Bright Galaxy Survey (BGS) will be a survey of bright, low redshift galaxies, which is planned to cover an area of ~14,000 sq deg in 3 passes. Each pass will cover the survey area with ~2000 pointings, each of area ~8 sq deg. The BGS is currently proposed to consist of a bright high priority sample to an r-band magnitude limit r ~ 19.5, with a fainter low priority sample to r ~ 20. The geometry of the DESI fibre positioners in the focal plane of the telescope affects the completeness of the survey, and has a non-trivial impact on clustering measurements. Using a BGS mock catalogue, we show that completeness due to fibre assignment primarily depends on the surface density of galaxies. Completeness is high (>95%) in low density regions, but very low (<10%) in the centre of massive clusters. We apply the pair inverse probability (PIP) weighting correction to clustering measurements from a BGS mock which has been through the fibre assignment algorithm. This method is only unbiased if it is possible to observe every galaxy pair. To facilitate this, we randomly promote a small fraction of the fainter sample to be high priority, and dither the set of tile positions by a small angle. We show that inverse pair weighting combined with angular upweighting provides an unbiased correction to galaxy clustering measurements for the complete 3 pass survey, and also after 1 pass, which is highly incomplete.