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

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It has been suggested (Bowen, private communication) that the 11 µm apparent
size of a Mira such as o Cet is actually a measure of the size of an optically thick dust
shell close to (∼1.75 R ∗ ) and surrounding the continuum photosphere. In this scenario, the
photospheric radius would be about half the 11 µm apparent size in much closer agreement
with the predictions of fundamental mode dynamic pulsation models. (See Section 4.1.)
The observed asymmetries and elongations in o Cet (See Sections 3.1 and 4.2.) also may
be more easily understood if they referred to a close dust shell rather than a photosphere.
However, this possibility can be ruled out by considering the whole of observations
of o Cet. First, the dust shell would need to be very opaque at 11 µm in order not to allow
any starlight through. Visibilities equalling zero have been recorded with a precision of
about 1% at spatial frequencies corresponding to the first null of the uniform disk implying
an optical depth of the hypothetical dust shell significantly greater than unity. The opacity
at visible and near-infrared wavelengths due to dust absorption is comparable (within an
order of magnitude, Figure 3.1) to the 11 µm opacity and due to scattering is orders of
magnitude greater. Hence, some dust would be evident around the smaller stellar disks
observed at these wavelengths. This is not the case. The 1.24 µm, 23 mas diameter
measurement of o Cet in Tuthill et al. (1999) [104] shows no dust shell contribution to the
flux to an accuracy of a few percent.
Finally, the mid-infrared flux is characteristic of a hot source, not a cool dust region.
A 12 µm flux of 4750 Jy was observed at phase 0.13 on o Cet. (Danchi et al. (1994) [22])
Assuming, as indicated by visibilities, that 25% of this flux originates from a region ∼48 mas
in diameter, the emitting region (in LTE) must have an average of temperature of 2000 K.
Due to the presence of a dust shell having optical depth, τ ≈ 0.12 in front of the emitting
region, we can estimate its flux to be ∼13% greater, or 5355 Jy, implying a temperature of
2185 K. This temperature is too hot for dust to exist according to any model. We thus conclude
that the 48 mas feature observed with the ISI is emission from hot gas characteristic
of a stellar photosphere and not dust.
As explained in Section 2.1, we take into account the dust shell in our uniform
disk fitting by allowing a single free parameter to represent the fraction of 11 µm intensity
coming from the dust shell and assuming that the dust shell is fully resolved at the lowest
spatial frequencies measured (∼ 20 × 10 5 rad −1 ). This procedure results in no errors if the
dust shell is very large in scale, but could potentially bias diameter measurements if the
dust were not fully resolved at the spatial frequencies used. To estimate how much of an