The PAU Survey: The $i$-band galaxy luminosity function from the present-day to $z = 2$

Abstract

We present a measurement of the $i$-band galaxy luminosity function from the present-day to $z = 2$, using over 1.1 million galaxies from the Physics of the Accelerating Universe Survey (PAUS). PAUS combines broad-band imaging from the Canada-France-Hawaii Telescope Lensing Survey with narrow-band photometry from PAUCam, enabling high-precision photometric redshifts with an accuracy of $\sigma_{68} (\Delta z) = 0.019$ down to $i_{\textrm{AB}} = 23$. A synthetic lightcone mock catalogue built using the \texttt{GALFORM} semi-analytic model is used to simulate PAUS selection effects and photometric uncertainties, and to derive a machine-learning based estimate of the $k$-correction. We recover rest-frame $i$-band luminosities using a random forest regressor trained on simulated $ugriz$ photometry and redshifts. Luminosity functions are estimated using the $1/V_{\textrm{max}}$ method, accounting for photometric redshift and magnitude errors, and validated against mock data. We find good agreement between observations and models at $z < 1$, with increasing discrepancies at higher redshifts due to photometric redshift outliers. The bright-end of the luminosity function becomes flatter at high redshift, primarily driven by redshift errors. We show that the faint-end of the luminosity function becomes more incomplete with increasing redshift, but is still useful for constraining models. We analyze the red and blue galaxy populations separately, observing distinct evolutionary trends. The model overpredicts the number of both faint red and blue galaxies. Our study highlights the importance of accurate redshift estimation and selection modeling for robust luminosity function recovery, and demonstrates that PAUS can characterise the galaxy population with photometric redshifts across a wide redshift baseline.