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

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Figure 3.3: Visibilities Corresponding to the Intensity Distribution from Figure 3.2 (Individual
Points) and the Best Fit Uniform Disk Curve for the Spatial Frequencies Between
20 and 45 ×10 5 rad −1 (Solid Line)
disk which best fits these data between 20 and 45 ×10 5 rad −1 is plotted as the solid line
in Figure 3.3. In this case, the best fit uniform disk had a radius of 24.125 mas (instead
of 25 mas) and the simulated model visibilities at spatial frequencies greater than 20 × 10 5
rad −1 are almost indistinguishable from that of a uniform disk.
This procedure was repeated several times varying the radius of formation and
the best fit uniform disk radius was recorded. The relative apparent increase of the stellar
diameter as a function of dust formation radius is plotted in Figure 3.4. The oscillation which
occurs in Figure 3.4 results from the “hard” inner edge to the dust shell. This produces
“ringing” in the visibility with respect to spatial frequency. We see that for stars like α Ori,
α Her, and χ Cyg, no correction to the measured diameters will be needed. For o Cet, a
correction of +3% ± 1% may be needed if the dust shell measured by Danchi et al. (1994) [22]
is still present. For R Leo, the correction would be +0.8% ± 1% based on the 1.3–2.3 R ∗
dust formation radii given by Danchi et al. (1994) [22]. (Note: to calculate the corrections