Breaking the sound barrier in recombination fronts

We exploit a generic instability in the integration of steady, sonic, near-isothermal flows to find the complete transition diagram for recombination fronts (for a model system of equations). The instability requires the integration of the flow equations for speeds between the isothermal and adiabatic sound speeds to be performed with particular care. As a result of this, the previous work of Newman & Axford on the structure of recombination fronts neglected an important class of solution, that of transonic fronts; our method is readily extensible to a more complete treatment of the ionization structure. Future papers will apply these results in models of the structure of ultracompact HII regions.