New detections of (sub)millimeter hydrogen radio recombination lines towards high-mass star-forming clumps

Previous radio recombination line (RRL) observations of dust clumps identified in the APEX Telescope Large Area Survey of the Galaxy (ATLASGAL) have led to the detection of a large number of RRLs in the 3mm range. Here, we aim to study their excitation with shorter wavelength (sub)millimeter radio recombination line (submm-RRL) observations. We made observations of submm-RRLs with low principal quantum numbers ($n$ $\leq$ 30) using the APEX 12 m telescope, toward 104 HII regions associated with massive dust clumps from ATLASGAL. The observations covered the H25$\alpha$, H28$\alpha$, and H35$\beta$ transitions. Toward a small subsample the H26$\alpha$, H27$\alpha$, H29$\alpha$, and H30$\alpha$ lines were observed to avoid contamination by molecular lines at adjacent frequencies. We have detected submm-RRLs (signal-to-noise $\geq$ 3 $\sigma$) from compact HII regions embedded within 93 clumps. The submm-RRLs are approximately a factor of two brighter than the mm-RRLs and consistent with optically thin emission in local thermodynamic equilibrium (LTE). The average ratio (0.31) of the measured H35$\beta$/H28$\alpha$ fluxes is close to the LTE value of 0.28. No indication of RRL maser emission has been found. The Lyman photon flux, bolometric, and submm-RRL luminosities toward the submm-RRL detected sources present significant correlations. The trends of dust temperature and the ratio of bolometric luminosity to clump mass, $L_{\rm bol}/M_{\rm clump}$, indicate that the HII regions are related to the most massive and luminous clumps. By estimating the production rate of ionizing photons, $Q$, from the submm-RRL flux, we find that the $Q$(H28$\alpha$) measurements provide estimates of the Lyman continuum photon flux consistent with those determined from 5 GHz radio continuum emission.