  We investigate the synthesis of the Balmer and Paschen lines of the quiet
Sun, using both classical semi-empirical and theoretical model atmospheres,
modern line broadening theory and non-LTE line-formation. The computations
alleviate long-standing discrepancies between LTE predictions and the observed
lines. Theoretical and semi-empirical model atmospheres without a chromosphere
on the one hand and semi-empirical models with a chromosphere on the other
produce two physically disjoint solutions for the run of non-LTE level
populations, including HII, throughout the model stratification. The resulting
synthetic non-LTE line profiles are practically identical and reproduce the
observation in either case, despite large differences in the line-formation
depths, e.g., a chromospheric origin of the Halpha core (in concordance with
observation) versus a photospheric origin. The findings are of much broader
interest, assuming the Sun to be a prototype cool dwarf star. A consistent
account for chromospheres in cool star analyses is required, due to their
potential to change atmospheric structure via non-LTE effects on the ionization
balance of hydrogen and thus the free electron pool. The latter in turn affects
the main opacity source H-. This will in particular affect the atmospheres of
metal-poor and evolved stars, in which the contribution of hydrogen to the
electron pool becomes dominant.
