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

104
30 km/s causes the spectrum to change position slightly relative to the fixed laser line. The
dates shown are the extrema of the motion, and observations performed at intermediate
dates can be interpolated in a straightforward 6 manner. The 11.0856 and 11.1713 µm
bandpasses in α Ori don’t appear to contain any observable H 2 O spectral lines and any
other lines present have a depth of less than 5%. The 11.1713 µm bandpass in R Leo also
avoids strong water lines and an upper limit of about 5% can be placed on any spectral
features within it. The 10.8844 µm bandpass in o Cet contains a very strong H 2 O line in
the summer, and the 01-08Aug01 diameter measurement of o Cet at this wavelength would
likely be effected by the presence of H 2 O. The 25,26Oct01 o Cet observation at 11.0856 µm
also includes a strong H 2 O spectral line. The 11.1713 µm bandpass appears to contain a
moderately strong spectral line in the summer, but not in the winter. The 10-16Nov01 observation
at this wavelength lies between these extrema and would have included only part
of this spectral feature within its bandpass. The increase in size of the alternate bandpass
diameter measurements relative to the P20 continuum diameter (at a nearby date) is listed
in Table 5.1. The α Ori and R Leo sizes were seen to be only about 2% larger than their
respective continuum values. Given that the error in these diameter measurements were
almost 1%, it is not entirely clear if the difference is due to the presence of a spectral line, a
small time-like change in the star, or possibly a statistical fluctuation. The o Cet diameters
show a marked increase, however. The greater than 14% increases in size are much too
large to be caused by the time-like change of only a week or so between continuum and
non-continuum observations.
The increases in apparent size when a spectral line was present within the bandpass
contain some information of the radii where H 2 O exists. If one assumes that the gas
responsible for the emission line is optically thick, and that the absorption line doesn’t
affect the apparent size very much, we can estimate that the size change is due to a large
apparent size on the emission line, averaged with the continuum size in the rest of the
bandpass. For simplicity, let us assume that the intensity profile at the wavelength of the
emission line is uniform disk-like, the temperature of the gas is 1500 K and the star is
2500 K, and that the emission line fills one-fourth of the bandpass. In this case, the radius
of the gas on the emission line would need to be 1.66R ∗ in order to increase the apparent
size of the star by 14.5%. This implies that H 2 O densities on the order of 10 11 m −3 are
6 The relative doppler shift of the earth varies nearly sinusoidally over its yearly cycle.