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.
