ALMA-IMF XIV: Free-Free Templates Derived from H$41\alpha$ and Ionized Gas Content in Fifteen Massive Protoclusters

We use the H$41\alpha$ recombination line to create templates of the millimeter free-free emission in the ALMA-IMF continuum maps, which allows to separate it from dust emission. This method complements spectral-index information and extrapolation from centimeter wavelength maps. We use the derived maps to estimate the properties of up to 34 HII regions across the ALMA-IMF protoclusters. The hydrogen ionizing-photon rate $Q_0$ and spectral types follow the evolutionary trend proposed by Motte et al. The youngest protoclusters lack detectable ionized gas, followed by protoclusters with increasing numbers of OB stars. The total $Q_0$ increases from $\sim 10^{45}$ s$^{-1}$ to $> 10^{49}$ s$^{-1}$. We used the adjacent He$41\alpha$ line to measure the relative number abundances of helium, finding values consistent with the Galactic interstellar medium, although a few outliers are discussed. A search for sites of maser amplification of the H$41\alpha$ line returned negative results. We looked for possible correlations between the electron densities ($n_e$), emission measures (EM), and $Q_0$ with HII region size $D$. The latter are the better correlated, with $Q_0 \propto D^{2.49\pm0.18}$. This favors interpretations where smaller ultracompact HII regions are not necessarily the less dynamically evolved versions of larger ones, but rather are ionized by less massive stars. Moderate correlations were found between dynamical width $\Delta V_\mathrm{dyn}$ with $D$ and $Q_0$. $\Delta V_\mathrm{dyn}$ increases from about one to two times the ionized-gas sound speed. Finally, an outlier HII region south of W43-MM2 is discussed. We suggest that this source could harbor an embedded stellar or disk wind.