Dynamical opacity-sampling models of Mira variables - I. Modelling description and analysis of approximations

We describe the Cool Opacity-sampling Dynamic EXtended (codex) atmosphere models of Mira variable stars, and examine in detail the physical and numerical approximations that go in-to the model creation. The codex atmospheric models are obtained by computing the temperature and the chemical and radiative states of the atmospheric layers, assuming gas pressure and velocity profiles from Mira pulsation models, which extend from near the H-burning shell to the outer layers of the atmosphere. Although the code uses the approximation of Local Thermodynamic Equilibrium (LTE) and a grey approximation in the dynamical atmosphere code, many key observable quantities, such as infrared diameters and low-resolution spectra, are predicted robustly in spite of these approximations. We show that in visible light, radiation from Mira variables is dominated by fluorescence scattering processes, and that the LTE approximation likely underpredicts visible-band fluxes by a factor of 2.