Epsilon Aurigae is a long-period eclipsing binary that likely contains an F0Ia star and a circumstellar disk enshrouding a hidden companion, assumed to be a main-sequence B star. High uncertainty in its parallax has kept the evolutionary status of the system in question and, hence, the true nature of each component. This unknown, as well as the absence of solid state spectral features in the infrared, requires an investigation of a wide parameter space by means of both analytic and Monte Carlo radiative transfer (MCRT) methods. The first MCRT models of epsilon Aurigae that include all three system components are presented here. We seek additional system parameter constraints by melding analytic approximations with MCRT outputs (e.g., dust temperatures) on a first-order level. The MCRT models investigate the effects of various parameters on the disk-edge temperatures; these include two distances, three particle size distributions, three compositions, and two disk masses, resulting in 36 independent models. Specifically, the MCRT temperatures permit analytic calculations of effective heating and cooling curves along the disk edge. These are used to calculate representative observed fluxes and corresponding temperatures. This novel application of thermal properties provides the basis for utilization of other binary systems containing disks. We find degeneracies in the model fits for the various parameter sets. However, the results show a preference for a carbon disk with particle size distributions ≥10 μm. Additionally, a linear correlation between the MCRT noon and basal temperatures serves as a tool for effectively eliminating portions of the parameter space.
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