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Context. Hydrogen recombination lines (HRLs) are valuable diagnostics of the physical conditions in ionized regions surrounding high-mass stars. Understanding these lines, including broadening mechanisms and intensity trends, can provide insights into HII region densities, temperatures, and kinematics. Aims. This study aims to investigate the physical properties of ionized gas around massive protostars by analysing the HRLs (Hαand Hβ) in the Q band. Methods. We carried out observations using the Yebes 40m radio telescope in the Q band (30.5–50 GHz) towards six high-mass protostars selected from the SOMA Survey (G45.12+0.13, G45.47+0.05, G28.20−0.05, G35.20−0.74, G19.08−0.29, and G31.28+0.06). The observed line profiles were analysed to assess broadening mechanisms, and electron densities and temperatures were derived. The results were compared with available Q-band data from the TianMa 65-m Radio Telescope (TMRT) that have been reported in the literature, and ALMA Band 1 (35–50 GHz) Science Verification observations towards Orion KL, analysed in this study. Results. A total of eight Hα(n = 51 to 58) and ten Hβ(n = 64 to 73) lines were detected towards G45.12+0.13, G45.47+0.05, and G28.20−0.05; there were no detections in other sources. We derived electron densities of ~1−5 × 10⁶cm⁻³and temperatures of 8000–10 000 K for the sources. However, for Orion KL, we obtained an electron density one order of magnitude lower, while its temperature was found to be more similar. Interestingly, G45.12 and G28.20 show an increasing intensity trend with frequency for both Hαand Hβtransitions, contrary to the decreasing trend observed in Orion KL. Conclusions. The line widths of the detected HRLs indicate contributions from both thermal and dynamical broadening, suggesting the presence of high-temperature ionized gas that is likely kinematically broadened (e.g. due to turbulence, outflows, rapid rotation, or stellar winds). Pressure broadening caused by electron density may also have a minor effect. We discuss different scenarios to explain the measured line widths of the HRLs. The contrasting intensity trends between the sources may reflect variations in local physical conditions or radiative transfer effects, highlighting the need for further investigation through higher-resolution observations and detailed modelling. 

Observations at (sub-)millimeter wavelengths offer a complementary perspective on our Sun and other stars, offering significant insights into both the thermal and magnetic composition of their chromospheres. Despite the fundamental progress in (sub-)millimeter observations of the Sun, some important aspects require diagnostic capabilities that are not offered by existing observatories. In particular, simultaneously observations of the radiation continuum across an extended frequency range would facilitate the mapping of different layers and thus ultimately the 3D structure of the solar atmosphere. Mapping large regions on the Sun or even the whole solar disk at a very high temporal cadence would be crucial for systematically detecting and following the temporal evolution of flares, while synoptic observations, i.e., daily maps, over periods of years would provide an unprecedented view of the solar activity cycle in this wavelength regime. As our Sun is a fundamental reference for studying the atmospheres of active main sequence stars, observing the Sun and other stars with the same instrument would unlock the enormous diagnostic potential for understanding stellar activity and its impact on exoplanets. The Atacama Large Aperture Submillimeter Telescope (AtLAST), a single-dish telescope with 50m aperture proposed to be built in the Atacama desert in Chile, would be able to provide these observational capabilities. Equipped with a large number of detector elements for probing the radiation continuum across a wide frequency range, AtLAST would address a wide range of scientific topics including the thermal structure and heating of the solar chromosphere, flares and prominences, and the solar activity cycle. In this white paper, the key science cases and their technical requirements for AtLAST are discussed.