1. AGB star model

There are two most important aspects in binary star simulation. One is the radiative transfer and the other is the AGB star model. The first one determine the large scale motion and morphology while the second one determine the robustness of inner boundary.

A sketch of the AGB star's structure is shown in the picture.

The hard pulsating sphere has velocity variation. Its amplitude is 5km/s and its period is 1 year.

The radius of the photosphere is also fixed. In reality, it must change but it is difficult to calculate. Within the photosphere, reduced gravity (80% of the original gravity) is being used. The reduced gravity has its physical stand - higher opacity inside the star but it is also because the resolution is poor. The simulation is resolving 2~3 order of magnitude density drop within 3 cells.

Between the photosphere and the dust formation zone, it is the gas opacity (2\times10^{-4}cm^{2}/g). The dust formation radii is calculated by

R_d=\sqrt{\frac{\alpha L \exp{(-\tau)}}{4 \pi \sigma T_{sub}^{4}}}

Where \tau=\int_rphotosphere^rmax \rho\kappa_{gas}dr is first calculated by assuming that there is only gas in the simulation. When the R_d is determined, I update the opacity where there is dust. The dust opacity is 8cm^{2}/g