Revisiting the 150 MHz Radio Luminosity Function of Star-forming Galaxies with LOFAR Deep Fields through a Refined Statistical Framework

Abstract We present a comprehensive analysis of the 150 MHz radio luminosity function (LF) of star-forming galaxies (SFGs) using deep observations from the LOFAR Two-metre Sky Survey in the ELAIS-N1, Boötes, and Lockman Hole fields. Our sample comprises ∼56,000 SFGs over 0 < z < 5.7. We first analyze the deepest field (ELAIS-N1), then jointly model all three fields while accounting for their distinct flux limits and selection functions. Using adaptive kernel density estimation (KDE), we reconstruct the LF continuously across redshift and luminosity without binning or parametric assumptions. The KDE results reveal clear signatures of joint luminosity and density evolution (LADE). Motivated by this, we construct and fit three parametric models—pure luminosity evolution (PLE) and two LADE variants—using a full maximum-likelihood method that includes completeness corrections and constraints from the local radio LF and Euclidean-normalized source counts (SCs). Model selection using Akaike and Bayesian information criteria strongly favors LADE over PLE. For ELAIS-N1, the more flexible LADE model (Model C) provides the best fit, while for the combined fields, the simpler Model B balances fit quality and complexity more effectively. Both LADE models reproduce the observed LFs and SCs across luminosity and flux density ranges, whereas PLE underperforms. We also identify a mild excess at the bright end of the LF, likely due to residual active galactic nucleus contamination. This study demonstrates that combining KDE with parametric modeling offers a robust framework for quantifying the evolving radio LF of SFGs, paving the way for future work with next-generation surveys like the Square Kilometre Array.