Extended atmospheres of AGB stars: modeling and measurement

Encoded in the time- and wavelength dependent properties of pulsating AGB stars are the underlying fundamental parameters of mass, composition and evolutionary state. However, the standard technique of placing stars on a HR diagram, even with the aid of pulsation periods, can not be done easily for extended AGB stars, because of the difficulty of defining a radius or temperature. The atmospheres of Mira variables are so extended that the optical depth unity radius can vary by a factor of ~3 over the energetically important region of the spectrum. Many important constituents in the radiative transfer are far from local thermodynamic equilibrium, and for the coolest stars, the process of dust formation and destruction requires a time-dependent model of grain growth. I will describe the challenges and some of the solutions to modeling these atmospheres, and describe the utility of different kinds of observations in helping understand both fundamental parameters and chaotic processes in complex AGB atmospheres.