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Appendix A: Weights

This appendix describes the details of the weighting scheme.

	Fig. A.1 Predictions from the CMC for magnitude vs. color (in the CFHT system) and observed [Oii] luminosity for the CFHT magnitude redshift bins described in Table 5 and Fig. 12.
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	Fig. A.2 LF(d)/LF(0.15) ratio for d = 0.11, 0.12, 0.13, 0.14, 0.16, 0.17, 0.18 divided by the LF determined with 0.15. The vertical red line is the luminosity completeness limit. The error on the LF is shown by black dashes. The LFs with radius 0.14 and 0.16 stay well within the uncertainty on the LF, while larger or smaller radii approach the limit of the uncertainty of the LF.
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The theoretical relation between the magnitude containing [Oii], the color before this magnitude, redshift, and the [Oii] luminosity is shown using the Cosmo Mock Catalog (Jouvel et al. 2009) in Fig. A.1. This representation does not take into account the dust present in the galaxies that will induce scatter in this figure. For a constant magnitude, the most luminous galaxies have a blue color. This simulation is based on the Kennicutt laws, an extrapolation of the DEEP2 [Oii] LF, and ignores dust effects. Therefore, this test cannot be used at face value, not even to determine the completeness limit of our sample. This analysis provides an idea on the relation between the magnitude limit and the luminosity completeness limit we can reach with a sample.

In the text, we quote as best value for the tree search a distance of 0.15. This distance corresponds to a maximum distance in each direction of 0.088, and constrains the search for neighbors within about ~±0.5 mag around the magnitude, about ~±0.25 mag around the colors, and about ~±0.15 around the redshift. These values approximately correspond to the area a given galaxy population occupies (see Fig. A.1).

We tested the LF estimation for different distance values and found that a limit at 0.15 ± 0.01 was stable and variations in the measurement of the LF would be smaller than the uncertainty on the LF. Figure A.2 shows the variation in the LF compared to the LF estimate using the tree search distance 0.15. For tree searches that are too wide (>0.17) the weighting scheme begins to fail; i.e., the LF is inconsistent at 1σ with the fiducial LF. For tree searches that are too narrow (<0.13), the weights become inaccurate, the weight error increases, and the LF is less accurate.

© ESO, 2015