Disks are among the most common of astrophysical systems. They
range in size from galaxies, through
protostellar/circumstellar disks, down to the rings
around planets.
A powerful technique for
observing disk systems is stellar occultations. This
method has been applied with great success to planetary rings (e.g.,
Lane et al.
1982, Holberg et al.
1982), the
best understood astrophysical disk systems. The
Aurigæ system allows us to apply this technique to an
entirely new class of disks.
Epsilon Aurigæ is an F0 Ia star with an enigmatic companion
which partially eclipses the visible star for 
2 years every 27.1 years.
The maximum fraction of the primary that is eclipsed is about 48%.
The eclipse light curve has a long, flat minimum
(Figure 
),
implying that the
secondary is not appreciably convex. The eclipse is fairly colorless
(hereafter ``gray'') over the
range of 4000 Å to 5 
m. The smaller eclipse depth that is
observed at longer wavelengths has been
attributed to thermal radiation from the secondary with a color
temperature of 
500 K (Backman et al.
1984).
During eclipse, absorption lines are seen, presumably due to cool,
optically thin material in the secondary passing in front of the
primary.
However, these lines are much more prominent after mid-eclipse than
prior to it (Lambert and Sawyer 1986, Hinkle and Simon 1987),
in contrast to the fairly symmetric light curve.
Huang (1965) suggested that
the secondary is a thick opaque disk which we view edge-on.
In most subsequent studies of 
Aurigæ,
the secondary has been modeled as a completely opaque disk viewed edge-on
or nearly so. Such a disk is unphysical. A realistic disk would have a
finite optical depth with a maximum value in the midplane (z = 0) and
decreasing values along lines of sight traversing the disk at larger
.
In this paper, we develop a hydrostatic/quasi-hydrodynamic model
of the secondary disk
which is constrained by the observational data.
Analysis of the 
Aurigæ system is complicated by diverse data
of varying quality.
The mass function, period and eclipse timing are well known, as is
the angular size of the primary. The solid angle subtended by the
secondary, the eccentricity of the orbit, the orbital velocity of material
at the edge of the secondary disk, and the distance of the system from Earth
have all been measured, but uncertainties are larger on these quantities.
We summarize the relevant system characteristics in Section D.2.
A rotating disk
supported by centrifugal force and gas pressure against gravitational
collapse will have a concave shape. That is, it will have greater vertical
(z)
extent at its outer radius than near its center
(Figure ).
For certain
density distributions, more blockage of light would occur at 2
and
3
contacts than at mid-eclipse. In principle, this effect may offer an
explanation for the small central brightening observed during the broad
light minimum. We develop hydrostatic models for the 
Aurigæ secondary in Section D.3 and present synthetic eclipse
light curves calculated using these models in Section D.4.
Thermal heating of the portion of the secondary exposed to the radiation field of the primary increases the secondary's z extent at the edge facing the primary. This thermal expansion from morning" (post-star ``rise'') to afternoon" offers an explanation for the observed temporal asymmetry in the strength of absorption line profiles relative to mid-eclipse. We study this hypothesis quantitatively using a quasi-hydrodynamic model of the disk edge in Section D.5. Our results are summarized in Section D.6.
