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.