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Context. The combined use of carbon radio recombination lines (CRRLs) and the158 $\mu$m-[CII] line is a powerful tool for the study of the energetics andphysical conditions (e.g., temperature and density) of photodissociationregions (PDRs). However, there are few observational studies that exploit thissynergy. Aims. Here we explore the relation between CRRLs and the 158$\mu$m-[CII] line in light of new observations and models. Methods. We presentnew and existing observations of CRRLs in the frequency range 0.15--230 GHzwith ALMA, VLA, the GBT, Effelsberg 100m, and LOFAR towards Orion~A (M42). Wecomplement these observations with SOFIA observations of the 158 $\mu$m-[CII]line. We studied two PDRs: the foreground atomic gas, known as the Veil, andthe dense PDR between the HII region and the background molecular cloud.Results. In the Veil we are able to determine the gas temperature and electrondensity, which we use to measure the ionization parameter and the photoelectricheating efficiency. In the dense PDR, we are able to identify a layered PDRstructure at the surface of the molecular cloud to the south of the Trapeziumcluster. There we find that the radio lines trace the colder portion of theionized carbon layer, the C$^{+}$/C/CO interface. By modeling the emission ofthe $158$~$\mu$m-[CII] line and CRRLs as arising from a PDR we derive a thermalpressure $>5\times10^{7}$ K cm$^{-3}$ and a radiation field$G_{0}\approx10^{5}$ close to the Trapezium. Conclusions. This work providesadditional observational support for the use of CRRLs and the 158 $\mu$m-[CII]line as complementary tools to study dense and diffuse PDRs, and highlights theusefulness of CRRLs as probes of the C$^{+}$/C/CO interface.

Carbon radio recombination lines from gigahertz to megahertz frequencies towards Orion A