Universal conditional distribution function of [OII] luminosity of galaxies, and prediction for the [OII] luminosity function at redshift $z<3$

The star-forming emission line galaxies (ELGs) with strong [OII] doublet are one of the main spectroscopic targets for the ongoing and upcoming fourth generation galaxy redshift surveys. In this work, we measure the [OII] luminosity $L_{\mathrm{[OII]}}$ and the near-ultraviolet band absolute magnitude $M_{\mathrm{NUV}}$ for a large sample of galaxies in the redshift range of $0.6\leq z <1.45$ from the Public Data Release 2 (PDR-2) of the VIMOS Public Extragalactic Redshift Survey (VIPERS). We aim to construct the intrinsic relationship between the $L_{\mathrm{[OII]}}$ and $M_{\mathrm{NUV}}$ through Bayesian analysis. In particular, we develop two different methods to properly correct for the incompleteness effect and observational errors in the [OII] emission line measurement. Our results indicate that the conditional distribution of $L_{\mathrm{[OII]}}$ at a given $M_{\mathrm{NUV}}$ can be well described by a universal probability distribution function (PDF), which is independent of $M_{\mathrm{NUV}}$ or redshift. Convolving the $L_{\mathrm{[OII]}}$ conditional PDF with the NUV Luminosity function (LF) available in the literature, we make a prediction for [OII] LFs at $z<3$. The predicted [OII] LFs are in good agreement with the observational results from the literature. Finally, we utilize the predicted [OII] LFs to estimate the number counts of [OII] emitters for the Subaru Prime Focus Spectrograph (PFS) survey. This universal conditional PDF of $L_{\mathrm{[OII]}}$ provides a novel way to optimize the source targeting strategy for [OII] emitters in future galaxy redshift surveys, and to model [OII] emitters in theories of galaxy formation.