The Size, Structure, and Variability of Late-Type Stars Measured ...

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3.4.2 The Effect of Dynamic Phenomena on Stellar Atmospheres
The hydrostatic theory of stellar atmospheres, although quite successful when
applied to main-sequence stars, neglects the effects of all time-dependent processes. A
pulsating stellar interior, such as those likely to exist in mira variables, is believed to have
profound effects on the morphology of the stellar atmosphere and circumstellar environment.
These dynamic phenomena can depend quite sensitively on the magnitude of variation with
time, and can produce structures which have no counterpart in hydrostatic theory. The
origin of variability in mira variables is thought to be a resonance which occurs in the
energy generating stellar core. Some of the energy from this interior periodic expansion
and contraction is transmitted through the photosphere to the stellar atmosphere. Here,
as the pressure wave propagates through the decreasing densities near the stellar surface,
it steepens, increases in speed and may become a shock front. As the shock passes through
the atmosphere, it alters the state of the gas dramatically, producing strong recombination
radiation, and allowing molecules and dust to form in the cool region in the wake of the
shock. This dust may in turn drive a stellar wind causing mass loss, increasing circumstellar
densities, and enriching the interstellar medium.
In order to calculate the amount of dust formed, molecular species present, and
temperatures surrounding the photosphere, a model needs to be developed to adequately
treat the dynamic processes involved. The emitted intensity distribution of radiation is, of
course, dependent upon these quantities and interpretation of our diameter measurements
necessitates a complete description. Several time dependent models exist which take into
account the dynamics of stellar pulsation. Most of these models take as a starting point the
results of a hydrostatic model. Gradually, some layer below the photosphere is forced to pulsate.
This “piston” oscillates with some velocity amplitude (typically ∼4 km/s) and drives
outward propagating waves which define the mira variable’s atmospheric environment. The
time-like iteration of the atmosphere involved in a dynamic model is very expensive in
computer time, however, and the dynamic models of today are incapable of taking into account
complicated frequency-dependent radiative transfer. Hence, a grey radiative transfer
is performed and some mean opacity function is used.
In addition to mira variables, other AGB stars exhibit weak and/or non-regular
variability. Previous studies on α Ori with the ISI reveal changes in its effective temperature
and the formation of a new dust shell close to the star. (Bester et al. ,1996 [12]) Evidence for