The LOFAR Two Metre Sky Survey Data Release 2: Probabilistic Spectral Source Classifications and Faint Radio Source Demographics: LoTSS DR2 Classifications

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 < 𝑧 < 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 H𝛼 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 which enables user-defined samples of radio sources with a reliability threshold suited to their science goal e.g. prioritising purity or completeness. Here we select high-confidence samples of radio sources (>90% reliability) to report: 38,588 radio-excess AGN 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 ∼ 4 percent 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.