Literature Review: A Heated Disk
In this literature review I have decided to highlight a paper I only found by accident while searching for something else. This work, entitled "An accretion disk surrounding a component of Epsilon Aurigae" is written by M. Takeuti from the Konkoly Observatory in Budapest, Hungary. In this work, he explains that the disk isn't as smooth and round as is often suggested in literature, but instead is preferentially heated and probably distorted.
The beginning of Takeuti's paper discusses the possibility of a low-mass model from an evolutionary perspective. In this work it is proposed that both stars have recently been main sequence stars, with the F-star being the more massive component to start with. The F-star then evolved off the main sequence (i.e. finished burning hydrogen in it's core) first, which caused mass to flow onto the B-star companion. It is the remnants of this mass overflow that he speculates composes the disk. It is my intuition that such a mass overflow disk would not be composed of large particles like is mentioned in the Hoard, Howell and Stencel paper (called the "HHS paper" below) Dr. Bob just blogged about this week, but I haven't investigated this topic.
For simplicity, Takeuti assumes that the B-star is a main sequence star of approximately four solar masses separated from the F-star by 15 AU. He considers two heating scenarios, one in which the disk is heated internally by collisions (from accretion) and the other in which the disk is heated by the F-star's radiation. In the intrinsic heating case, he comes up with several accretion rates for various temperature profiles/scenarios. In the case that the F-star's radiation maintains the 550 K temperature of the disk, accretion is not a necessary source of energy.
In this scenario, he creates two tables of isothermal (one temperature) annuli (rings) as a function of radius from the F-star and B-star (see Tables 1 and 2). The quickest thing to notice is that the radius (R2) at which the temperature from the F-star's radiation equals the temperature from the B-star is around 1 AU from the B-star! Furthermore, if you work out the math, you will find that the F-star's radiation causes there to be a crescent-shaped zone of higher temperatures in the disk and possibly a cavity carved out on the edge of the disk by the F-star's radiation.
The proposed disk model from Takeuti's article.
As with all of my literature reviews, you might be wondering "why is this important?" Well, after the HHS publication, the biggest picture of the problem is solved, namely that there is an F-star, there is a B5V star, and that there is a disk. The obvious questions that remain are going to be related (1) to the out-of-eclipse variations of the F-star, (2) to the disk and it's composition, or (3) related to the evolutionary history for the system. Any discussion of the disk's composition will require that the temperature profile of the disk be solved because certain species of molecules or dust are destroyed in high temperatures. For instance, the CO molecules we're trying to observe with SPEX could come from carbon dioxide (CO2) condensed onto grains of dust which sublimate from the grains and are destroyed by radiation from the F-star. Also recall that we see CO appear after mid eclipse, that implies that the CO producing region passes between us and the F-star shortly before/during mid eclipse. Is that consistent with Takeuti's model? Perhaps, but involving rotation in a model with radiative transfer (the way heat/light moves through a medium) is a very complicated task. I'll probably undertake the simple 2D radiative transfer using a modified version of 2-Dust or something similar as part of my dissertation unless Dr. Bob insists a fully hydrodynamic case is required.
You may obtain a copy of the paper through ADS:
http://adsabs.harvard.edu/abs/1986Ap%26SS.121..127T