Binary star systems with asymmetrically heated disks: Thermal phase curves for the disk in epsilon Aurigae

Epsilon Aurigae is a long-period eclipsing binary that contains a warm F-star (~7750 K) and a circumstellar disk enshrouding a hidden companion, likely to be a hot B-star (≥15,000 K). The eclipse itself lasts just over two years---thanks, in part, to the size of the disk---and occurs every 27.1-years. Its evolutionary status is still debated, along with the true nature of each stellar component, due to the high uncertainty in its parallax. The disk is similarly debated from the near absence of solid state infrared spectral features indicating its composition, particle size distribution, and density. An investigation of a wide parameter space by means of analytic, Monte Carlo radiative transfer (MCRT), and thermal inertia-dependent methods are presented here in order to minimize the current parameter space. The first MCRT models including all of the epsilon Aurigae components (F-star, B-star, and disk) are included here.;Additional parameter constraints are found by melding MCRT outputs (e.g. dust temperatures) with a thermal inertia-based extrapolation. The so-called MCRT-TI 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 thirty-six independent models. Adding in the MCRT temperatures as possible solutions doubles the number of models to seventy-two.;Additionally, infrared observations at 7 epochs, spanning nearly 1/3 of the orbit of epsilon Aurigae, are evaluated in order to extract phase-dependent disk temperatures. The resulting temperatures create a thermal phase curve, or TPC, for the system. The TPC correlates the observed disk temperature with orbital phase or date of observation. Then, the best-case MCRT and MCRT-TI models are compared against two different mid-eclipse temperatures. If one considers the evolutionary constraints on the models---where a smaller distance denotes an older system with a disk composition identified as either silicate or carbon, and a large distance denotes a younger system with a disk more like the interstellar medium composition---the number of possible best-fit models becomes only nine. Further constraints leave two possible solutions for the epsilon Aurigae system: if epsilon Aurigae is almost a 1000 pc away, then the disk follows an MCRT temperature profile (indicative of a low thermal inertia) with small, ISM-like particles in an Earth-mass disk; if it is within approximately 700 pc, the disk follows the MCRT-TI temperature profile (indicative of a larger inertial effect) with medium-sized silicate particles in an Jupiter-mass disk.;Beyond the physical constraints on the disk, the TPC observations provide new disk temperature estimates at seven different orbital epochs, in addition to the two previously published results. These are used to navigate the nine best-fit models in search for a refined solution. A minimum disk temperature is found to be about 300 K, observed just after the most recent mid-eclipse of epsilon Aurigae.;The application of this thermal inertia effect to other binary disk systems is possible. First, though, observations must be made throughout the system's orbit. Any sort of irregularity in the disk's longitudinal temperatures is a target for application of this methodology. The proper application does require the heating and cooling rates of the system's material be less than the rotational rate of the disk. However, spatially resolved disk systems may be able to observe the effect without that prerequisite.