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

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Figure 3.2: Intensity Distribution of a Star with Dust Shell Forming at 2R ∗
effect a radially symmetric dust shell would have on our diameter fits, we construct a model
dust shell forming at some radius at 1300 K with a temperature distribution proportional
to r −1/2 around a spherical blackbody star of temperature 2500 K. (The temperature of
formation of 1300 K is somewhat of an upper limit and would affect the fit more than a
lower value.) We assume the dust is of uniform make-up and in LTE and that there is no
scattering of 11 µm light. Finally, we impose a density distribution proportional to r −2
characteristic of a uniform outflow. The total optical thickness of the dust is adjusted so
that a constant 65% of the 11 µm radiation emerging is from the dust (based on observed
o Cet visibilities, and a decent approximation for the other stars.) Next, we calculate the
intensity distribution for such a model. A plot of the emergent intensity distribution for a
star of radius 25 mas having a dust shell with radius of formation 2R ∗ is shown in Figure 3.2.
The sharp peak at 50 mas comes about from viewing the inner edge of the dust shell from
the side. A more realistic model would assume that the dust does not form instantaneously,
but the above should serve as a valid approximation. The visibilities corresponding to such
an intensity distribution are shown as the individual points in Figure 3.3. The uniform