Epsilon Aurigae is an F supergiant in a spectroscopic binary system th
at undergoes a flat-bottomed partial eclipse of 2 yr duration every 27
yr. The spectrum appears to be single-lined, aside from extra absorpt
ion features detected during and shortly after eclipse. Eclipse charac
teristics indicate that the secondary is a very elongated object 5-10
AU in dimension parallel to its orbit. Orbital characteristics and the
spectral properties of the primary are consistent with two different
models of the system, with the secondary having a mass of either simil
ar to 15 M(.) or similar to 4 M(.). We have modeled the cool, dark sec
ondary in the epsilon Aurigae system as a geometrically thin circumste
llar disk of gas and dust (surrounding one or two unseen stars, at or
near its center), which is rotationally supported about its short axis
and pressure supported perpendicular to its midplane. We assume that
the midplane of the disk is coplanar with the orbital plane of the sys
tem. The gross features of the eclipse light curve observed at any sin
gle wavelength are easily reproduced, using a variety of disk scale he
ights and optical depths, provided that we are viewing within similar
to 3 degrees of the symmetry plane of the system. Central holes in the
disk only affect the eclipse profile for models with low optical dept
h (and correspondingly large pressure scale height). The observed gray
ness of the eclipse in the visible and near-IR implies that the partic
les in the disk are significantly larger than those in the typical ISM
. Either particles of radius less than or similar to 5 mu m are almost
completely absent, or the disk must be very opaque. If the disk is ve
ry opaque, then the observed eclipse depth implies a small scale heigh
t for the disk, equal to roughly 3% of the disk's radius at the outer
edge. This is a factor of similar to 1.5-2 smaller than the value expe
cted for the low-mass model from hydrostatic balance with the disk tem
perature measured in the thermal-IR, suggesting that the high-mass mod
el of the system is correct and/or the dust particles have settled int
o a thinner disk than the pressure-supported gas. We have also constru
cted a quasi-hydrodynamic model of the expansion of the material in th
e outermost edge of the disk secondary in response to the heating that
it receives as it rotates into view of the luminous primary. Light cu
rves computed using this model reproduce the basic features of absorpt
ion lines, which are observed to be deepest subsequent to the middle o
f the continuum eclipse and to persist after fourth contact.