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

18
wavelengths, however, its range of resolution is limited by the size of the primary mirror of
the parent telescope. Photometry is capable of very accurate flux measurements at different
wavelengths, but cannot distinguish between effects which would produce similar spectra
while having very different structures. Interferometry is by far the most flexible way of
measuring the diameters of stars. It is not limited to any area of the sky, position angle,
range of resolution, or wavelength. Thus, it is ideally suited for stellar size measurements.
The current technology in interferometry, however, does not yield straight-forward
diameter measurements. In practice, interferometry can measure only a small sample of the
available Fourier domain. A direct inversion of visibilities to a reasonably complete image
is nearly impossible and observations must be compared to a model in order for conclusions
to be drawn. This underscores the importance of making diameter measurements at a
wavelength where interpretation is as unambiguous as possible.
2.1 Diameter Measurements with the ISI
The stellar diameters obtained with the ISI represent the first 2 measurements of a
stellar disk at wavelengths longer than 3 µm. ISI measurements are limited to stars which
are bright enough both at 2 µm and at the observing wavelength 3 , and are not so obscured
by dust as to block all light from the stellar surface. Also, the angular diameter of the
stellar disk must be greater than ≈ 20 mas in order to be well enough resolved for a good
determination of its diameter. In practice, we are able to observe late-type stars within
≈ 200 parsecs. In this section, we discuss the diameter measurements of the Mira Variable
stars, o Cet, χ Cyg, and R Leo, and the supergiants, α Ori, and α Her.
The diameter is obtained from the measured data (visibility squared, V 2 i , with
error, σ V 2
i
, as a function of spatial frequency, x i ) by fitting it with the theoretical visibility
function for a disk of uniform intensity having a given radius, r. These late-type stars often
are surrounded by a dust shell at several stellar radii. The dust shell is resolved almost
completely at the spatial frequencies we consider (see Section 3.2) so it has the effect of
lowering the extrapolated visibility at low spatial frequencies by an amount equal to the
fraction of light emanating from the extended dust shell.
So, we allow in the fitting, a
2 There have been observations at radio wavelengths with resolutions high enough to resolve stars. They
do not actually “see” the stellar disk at these wavelengths. See Reid and Menten, 1997 [84].
3 See Hale et al. (2000) [37] for specific observing requirements including limiting magnitudes, sky coverage,
and available bandpasses.