Partially Ionized Gas at Equilibrium Powered by Ultraviolet Irradiation

We study the formation of a partially ionized zone behind the usual H II zone in photo-ionized gas for gas density intermediate between ordinary H II regions and AGN BLRs and without X-rays. While Lyman continuum photons are depleted before reaching this zone, Balmer continuum photons can ionize the $n=2$ hydrogen atoms as those are pumped by scattering-trapped Ly$\alpha$ photons. Ly$\alpha$ photons need to be replenished in a steady state, but fast radiative cooling at high gas temperature makes replenishment through electron collisional excitation of $n=2$ inefficient. Independently of the temperature, Raman scattering of incident continuum photons on the Lyman-series damping wings injects Ly$\alpha$ photons in the line core and pumps the $n=2$ state, which helps realize a partially ionized equilibrium at $5000$--$7000\,$K. Since the ratio between the incident radiation flux and gas density is limited by the dynamic effects of radiation pressure, significant ionization fraction is only realized at densities $n_{\rm H} \gtrsim 10^7\,{\rm cm}^{-3}$. A large H$\alpha$/H$\beta$ line ratio results from such partially ionized gas as large Balmer line optical depths enhance the $n=3$ population relative to higher $n$ states. Partial ionization also provides the ideal condition for internally forming an intense and very broad Ly$\alpha$ line, which can power strong fluorescent metal emission lines observed from the Weigelt blobs of $\eta$ Carinae in the Galaxy, and from a candidate young super star cluster in the Cosmic Noon Sunburst galaxy. This phenomenon may also have implications for understanding the spectra of high-$z$ galaxies that show unusually dense ionized gas.