The DESI View of the Faint Radio Source Population in LoTSS DR2

The faint radio-source population includes galaxies dominated by both star formation (SF) and active galactic nuclei (AGN), which are two key processes shaping galaxy evolution. To investigate this population, we probabilistically classified 251,413 radio sources from the second data release of the LOFAR Two-metre Sky Survey (LoTSS DR2) using spectroscopic data from the first release of the Dark Energy Spectroscopic Instrument (DESI DR1). Our classification method includes: (i) the identification of radio excess relative to SF, (ii) the Baldwin, Philips & Terlevich (BPT) diagram, (iii) a modified Mass Excitation (MEx) diagram, and (iv) the [OIII]5007 equivalent width. These are combined with Monte Carlo methods to estimate the probability that each source is a star-forming galaxy (SFG), a radio-quiet AGN (RQ AGN), or a low- or high-excitation radio galaxy (LERG or HERG), allowing various thresholds to be applied depending on science goals. Considering classifications above a 90 per cent probability threshold, we identify 68,820 SFGs, 32,288 RQ AGN, 35,210 LERGs and 3,085 HERGs, representing the largest radio sample to date with high-confidence spectroscopic classifications. Using this sample, we show with higher statistical power than previous studies that LERGs typically accrete below 1 per cent of the Eddington limit and HERGs above it. We also identify a small subset of high-accreting LERGs whose stacked spectra reveal prominent star-forming features, highlighting difficulties in interpreting their accretion properties. Our results demonstrate the power of large spectroscopic samples to characterise the radio-source population, providing a foundation for studies in the SKA era.