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

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they form farther out in the atmosphere at lower densities. Thus, the spectrum is rather
clean. Conversely, in the 2000 K star, the water vapor bands are 80–90% deep, indicating
that at these wavelengths, one would observe outer atmospheric layers of the star almost
entirely.
There is ample evidence that the spectra of real stars, including the AGB stars
considered here, are greatly affected by TiO and H 2 O line opacity. (See Tsuji, 2000 [99],
Wing (1997) [113], and references therein.) H 2 O lines were observed in α Ori by Jennings
and Sada (1998) [52] and an H 2 O column density of 3 × 10 18 cm −2 was measured.
Tsuji (2001) [100] argues that there exists an observable “warm molecular region” with a
temperature around 1500 K in the atmospheres of most or all late-type stars containing
a chemically active soup of diatomic and polyatomic molecules. There is also significant
evidence to support the claim that the measured sizes of stars are affected by the presence of
molecules. Diameter measurements were made for a number of stars with the Mark III interferometer
at both 712 and 754 nm. (Quirrenbach et al. , 2001 [79]) The 712 nm sizes were
systematically larger, presumably due to the strong TiO bands present at this wavelength.
Moreover, the relative increase in size between the two wavelengths increased for decreasing
effective temperature. The effect of spectral lines is evident in the stellar diameters of
Tuthill et al. (1999) [104]. A uniform disk was fit to visibilities taken from Keck telescope
aperture masking at a variety of near-IR wavelengths. A reproduction of Figure 3 from that
paper showing the best fit diameters vs. wavelength is shown in Figure 3.6. Between 1.3
and 3.1 µm, the apparent size of α Ori increases from 42 mas to 48 mas, while for o Cet,
it increases from 21 mas to 60 mas! Presumably, this is due to the presence of strong TiO
and H 2 O bands.
The prevalence of these polyatomic molecules in AGB stars, and the large opacities
of their spectral lines may explain many of the observed variations in diameter measurements
with wavelength (and possibly with time, as well.) Although very model dependent,
variations in the apparent diameters of late-type stars in the visible due to TiO are predicted
to be as large as a factor of 2.5 (see Jacob et al. , 2000 [50]). In most cases, the extra
opacity at radii greater than the photosphere’s produces extension in the stellar profile and
a larger diameter would be measured such as is shown in the measurements of Quirrenbach
et al. (2001) [79]. In some cases, the line can darken the star around its edges and a
smaller value for its radius can be recorded. This “extreme limb-darkening” is discussed in
Hofmann et al. (1998) [46] and for some Mira models can result in a factor of ∼2 smaller