2D Monte-Carlo Radiative transfer modeling of the disk shaped secondary of Epsilon Aurigae

We present two dimensional Monte-Carlo radiative transfer models for the disk of the eclipsing binary $\epsilon$ Aur by fitting its spectral energy distribution from optical to the far-IR wavelengths. We also report new observations of $\epsilon$ Aur made by AKARI in its five mid and far-IR photometric bands and were used to construct our SED. The disk is optically thick and has flared disk geometry containing gas and dust with a gas to dust mass ratio of 100. We have taken the primary of the binary to be a F0Iae-type post-AGB star and the disk is heated by a B5V hot star with a temperature of 15,000 K at the center of the disk. We take the radius of the disk to be 3.8 AU for our models as constrained from the IR interferometric imaging observations of the eclipsing disk. Our models imply that the disk contains grains which are much bigger than the ISM grains (grain sizes 10$\mu$ to 100$\mu$). The grain chemistry of the disk is carbonaceous and our models show that silicate and ISM dust chemistry do not reproduce the slope of the observed SED in the mid-IR to far-IR regions. This implies that the formation of the disk shaped secondary in $\epsilon$ Aur system could be the result of accretion of matter and or mass transfer from the primary which is now a F0Iae post-AGB star. It is not a proto-planetary disk. The disk is seen nearly edge on with an inclination angle larger than 85$^{o}$. We propose from our radiative transfer modeling that the disk is not solid and have a void of 2AU radius at the center within which no grains are present making the region nearly transparent. The disk is not massive, its mass is derived to be less than 0.005M$_{\odot}$.