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

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ature fall off continuously in the circumstellar regions. Consequently, the optical depth can
be very wavelength dependent and some spectral regions may see much larger continuum
photospheres than others. High resolution studies performed at radio and ultraviolet frequencies
have measured continuum radii more than twice as large as visible continuum radii
for some AGB stars. (Gilliland and Dupree (1996) [34] and Reid and Menten (1997) [84])
A comprehensive explanation of the data can be had by solving the radiative transfer problem
and obtaining the state of the gas everywhere around the star. A prediction of what
would be seen at any given wavelength could then be made. In practice, there are many
complications to such an idealized procedure.
For low effective temperature stars, the equation of state of the circumstellar
material can be very complicated. For instance the presence of molecules in the atmospheres
of stars can depend very sensitively on relative abundances of the chemical elements in the
parent star. These molecules, through their line opacity, can couple efficiently the radiation
pressure from the star to the (what would have been) transparent gases. Winds may
be formed and the extension of the stellar atmosphere increased significantly relative to
hydrodynamic equilibrium. This may result in more or different molecules or dust forming
and altering the star further. (Helling et al. (2000) [41]) In this way, small changes in
the initial stellar composition or luminosity may induce profound changes in its observable
properties.
Breaking of the spherical symmetry of a star may also occur in the outer regions
of its photosphere. Large convective cells may cause hotspots on the stellar surface capable
of lessening the apparent size of the star. (Predicted by Schwarschild (1975) [91] and
possibly observed in α Ori by Dupree and Gilliland (1995) [25]) Other asymmetries may
be caused by non-radial pulsational modes in Miras. The beginnings of a bi-polar planetary
nebula have even been suggested as the cause of an observed elongation in o Cet by
Josselin et al. (2000) [55].
Finally, the Miras and α Ori are known to exhibit dramatic temporal changes
in their luminosities. Changes at visible wavelengths of several magnitudes are common
for Miras. Strong shock waves also are observed in their line profiles. The complicated
dynamics of these large stars further obscures their properties. Pulsationally driven stellar
atmosphere models have progressed; however, no current model is capable of including
any but the simplest frequency dependence to the radiation field, much less non-spherical
dynamics. In the following sections we will attempt to address all of these concerns.