(abridged) Non-ionizing stellar continua are a source of photons for continuum pumping in the hydrogen Lyman transitions. In the environments where these transitions are optically thick, deexcitation occurs through higher series lines, so that the flux in these lines has a fluorescent contribution in addition to recombination; in particular, Balmer emissivities are systematically enhanced above case B. The effectiveness of such mechanism in HII regions and the adequacy of photoionization models as a tool to study it are the two main focuses of this work. We find that photoionization models of H II regions illuminated by low-resolution population synthesis models significantly overpredict the fluorescent contribution to the Balmer lines. Conversely, photoionization models in which the non-ionizing part of the continuum is omitted or is not transferred underpredict the fluorescent contribution to the Balmer lines, producing a bias of similar amplitude in the opposite direction. In this paper, we carry out realistic estimations of the fluorescent Balmer intensity and discuss the variations to be expected as the simulated observational setup and the stellar populations parameters are varied. In all the cases explored, we find that fluorescent excitation provides a significant contribution. We also show that differential fluorescent enhancement may produce line-of-sight differences in the Balmer decrement, mimicking interstellar extinction. Fluorescent excitation emerges from our study as a small but important mechanism for the enhancement of Balmer lines, which should be taken into account in the abundance analysis of photoionized regions, particularly in the case of high-precision applications such as the determination of primordial helium.
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