Multiline observations of hydrogen, helium, and carbon radio-recombination lines toward Orion A: A detailed dynamical study and direct determination of physical conditions

We present a study of hydrogen, helium, and carbon millimeter-wave radio-recombination lines (RRLs) toward ten representative positions throughout the Orion Nebula complex, using the Yebes 40m telescope in the Q band (31.3 GHz to 50.6 GHz) at an angular resolution of about $45\arcsec$ ($\sim$0.09\,pc). The observed positions include the Orion Nebula (M42) with the Orion Molecular Core 1, M43, and the Orion Molecular Core 3 bordering on NGC 1973, 1975, and 1977. While hydrogen and helium RRLs arise in the ionized gas surrounding the massive stars in the Orion Nebula complex, carbon RRLs stem from the neutral gas of the adjacent photo-dissociation regions (PDRs). The high velocity resolution ($0.3\,\mathrm{km\,s^{-1}}$) enables us to discern the detailed dynamics of the RRL emitting neutral and ionized gas. We compare the carbon RRLs with SOFIA/upGREAT observations of the [CII] $158\,\mu\mathrm{m}$ line and IRAM 30m observations of the $^{13}$CO (J=2-1) line. Using the [CII] and [$^{13}$CII] intensities with the carbon RRL intensities, we can infer physical conditions (electron temperature and electron density) in the PDR gas using non-LTE excitation models. Our observations are sensitive enough to detect faint lines toward two positions in OMC1, that may be attributed to RRLs of C$^+$ or O$^+$. In general, the RRL line widths of both the ionized and neutral gas, as well as the [CII] and $^{13}$CO line widths, are broader than thermal, indicating significant turbulence in the interstellar medium, which transitions from super-Alfv\'enic and subsonic in the ionized gas to sub-Alfv\'enic and supersonic in the molecular gas. At the scales probed by our observations, the turbulent pressure dominates the pressure balance in the neutral and molecular gas, while in the ionized gas the turbulent pressure is much smaller than the thermal pressure.