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Published online by Cambridge University Press: 12 April 2016
Models for M and C giant stars differ from those for hotter stars by having complicated state equations and opacities dominated by lines from diatomic and polyatomic molecules. In addition many cool giants have atmospheres which are extended, and which cannot therefore be adequately modelled using a plane-parallel approximation. Mira variable stars have atmospheres which are even more extended due to the regular passage of shock waves through their atmosphere. In this review we will discuss recent modelling of such atmospheres and show comparisons with observations of variable and non-variable M stars.