The LOFAR two metre sky survey data release 2: probabilistic spectral source classifications and faint radio source demographics

We present an analysis of 152 355 radio sources identified in the second data release of the LOFAR Two Metre Sky Survey (LoTSS-DR2) with Sloan Digital Sky Survey (SDSS) spectroscopic redshifts in the range $0.00 \lt z \lt 0.57$. Using Monte Carlo simulations, we determine the reliability of each source exhibiting an excess in radio luminosity relative to that predicted from their H $\alpha$ emission, and, for a subset of 124 023 sources we combine this measurement with a full BPT analysis. Using these two independent diagnostics, we determine the reliability of each source hosting a supermassive black hole of high or low Eddington-scaled accretion rate, and combine the measurements to determine the reliability of sources belonging to each of four physical classes of objects: star-forming galaxies (SFGs), radio-quiet active galactic nuclei (RQAGN), and high- or low-excitation radio galaxies (HERGs or emission-line LERGs). The result is a catalogue that enables user-defined samples of radio sources with a reliability threshold suited to their science goal, for example prioritizing purity or completeness. Here, we select high-confidence samples of radio sources (>90 per cent reliability) to report: 38 588 radio-excess AGNs in the LoTSS-DR2 sample (362 HERGs, and 12 648 emission-line LERGs), together with 38 729 SFGs, and 18 726 RQAGN. We validate these results through comparison to literature using independent emission-line measurements, and to widely adopted WISE photometric selection techniques. While our use of SDSS spectroscopy limits our current analysis to $\sim 4$ per cent of the LoTSS-DR2 catalogue, our method is directly applicable to data from the forthcoming WEAVE-LOFAR survey, which will obtain over a million spectra of 144 MHz selected sources.