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

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3.5 Explanation of Variations in Measured Diameter with
Wavelength
The focus of the preceding sections has been the systematic consideration of processes
which may have affected the apparent size of AGB stars near 11 µm. The necessary
corrections for dust, spectral contamination, and continuum center to limb variations were
estimated. The result is a set of upper limits for the error in ISI diameter measurements
relative to near-IR “continuum” monochromatic and apparent diameters. The theoretical
Rosseland diameter is inaccessable from the simple continuum models considered in Section
3.4.3, however it is thought to be close to near-IR monochromatic diameters since most
of the stellar flux is emitted in this region. With a good degree of confidence, for the supergiants,
α Ori and α Her, we estimate corrections to the ISI measured diameters relative to
near-IR continuum and symmetric model apparent diameters to be about -1%. For lower
mass, pulsating Miras, such as o Cet, R Leo, and χ Cyg, the extra atmospheric extension
increases those corrections to between -3% and -14% depending on phase with an additional
±3% error if dust forms within 2.5R ∗ . Corrections due to spectral lines within the
ISI bandpass are predicted to be less than 1% for all stars measured with the ISI continuum
P20 bandpass.
Having investigated many of the phenomenon responsible for altering the apparent
sizes of AGB stars, it should be possible to re-examine the variety of stellar size measurements
from Tables 2.2-2.4 in the context of atmospheric morphology. The visible diameter
measurements of α Ori displayed in Table 2.2 span the range of 44-58 mas. A systematic
increase in apparent size is observed in the strongest TiO bands, and a decrease due to limb
darkening may be evident in weaker bands. In addition, dust is a fairly efficient absorber
and scatterer in the visible, and very small variations in surface temperature can produce
pronounced changes in emitted intensity. (At 500 nm and 3000 K, a 1% change in temperature
will change the intensity by 10%.) As a result, there are many ways that the roughly
30% variations in size can be accounted for. A molecular shell of TiO at 1.3R ∗ having varying
transparency with wavelength is not unlikely and is capable of reproducing the varying
apparent diameters observed. The near-IR diameters are somewhat less variable. Other
than the 3.09 µm Keck diameter which is located in an H 2 O band, they span the range of
40-44 mas. They are roughly a lower bound to the visible sizes. Since the TiO molecular
lines are weaker in the near-IR, there appears to be no inconsistency between these sizes