The SDSS-IV extended Baryon Oscillation Spectroscopic Survey: selecting emission line galaxies using the Fisher discriminant

We present a new selection technique of producing spectroscopic target catalogues for massive spectroscopic surveys for cosmology. This work was conducted in the context of the extended Baryon Oscillation Spectroscopic Survey (eBOSS), which will use ~200 000 emission line galaxies (ELGs) at 0.6<zspec<1.0 to obtain a precise baryon acoustic oscillation measurement. Our proposed selection technique is based on optical and near-infrared broad-band filter photometry. We used a training sample to define a quantity, the Fisher discriminant (linear combination of colours), which correlates best with the desired properties of the target: redshift and [OII] flux. The proposed selections are simply done by applying a cut on magnitudes and this Fisher discriminant. We used public data and dedicated SDSS spectroscopy to quantify the redshift distribution and [OII] flux of our ELG target selections. We demonstrate that two of our selections fulfil the initial eBOSS/ELG redshift requirements: for a target density of 180 deg^2, ~70% of the selected objects have 0.6<zspec<1.0 and only ~1% of those galaxies in the range 0.6<zspec<1.0 are expected to have a catastrophic zspec estimate. Additionally, the stacked spectra and stacked deep images for those two selections show characteristic features of star-forming galaxies. The proposed approach using the Fisher discriminant could, however, be used to efficiently select other galaxy populations, based on multi-band photometry, providing that spectroscopic information is available. This technique could thus be useful for other future massive spectroscopic surveys such as PFS, DESI, and 4MOST.