1. Runs

The normal state of the pulsating AGB star is the same. The mass of the AGB star is always 1M_{\odot}

model number	q	z	burst	separation	link	\dot{m_1}(M_{\odot}/yr)	\dot{m_2}(M_{\odot}/yr)	j_{g}/j_{0}	accretion/circumbinary disk	total gas mass around the binary(M_{\odot})	gas mass around the secondary(M_{\odot})
1	0.5	0.031	no	4AU	​model1	3.414\times10^{-7}	1.157\times10^{-7}	2.577	Y/Y	4.3\times10^{-6}	9.69\times10^{-7}
2	0.5	0.031	yes	4AU	​model2	3.526\times10^{-7}	1.546\times10^{-7}	2.25	Y/Y	4.3\times10^{-6}	9.69\times10^{-7}
3	0.1	0.016	no	3AU	​model3	1.278\times10^{-7} ？	2.998\times10^{-9}	0.62	Y?/Y	1.3\times10^{-6}	3.27\times10^{-9}
4	0.5	0.008	no	6AU	​model4	2.673\times10^{-7}	4.330\times10^{-8}	1.563	Y/Y	3.4\times10^{-6}	3.10\times10^{-7}
6	0.5	0.008	no	8AU	​model6	2.673\times10^{-7}	4.330\times10^{-8}	1.563	Y/Y	3.4\times10^{-6}	3.10\times10^{-7}
5	0.5	0.002	no	10AU	​model5	2.263\times10^{-7}	7.613\times10^{-9}	1.072	N/N	NA	9.27\times10^{-9}

q is the mass ratio of the two stars, defined by M_{com}/M_{AGB}

z is the tidal force coefficient, defined by (\frac{M_{com}}{(d-r_{AGB})^2}-\frac{M_{com}}{(d+r_{AGB})^2})/\frac{M_{AGB}}{d^2} where d is the binary separation.

j_0 is the initial average angular momentum per unit mass in the binary system.

j_g is the average angular momentum per unit mass of the escaping gas.

2. 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.

A questionable number is \alpha=0.3.

The velocity profile of the AGB wind.

Mass loss rate vs time.

3. On physics

3a. Currently, I am using electron excitation as high temperature cooling source ​Mastrodemons & Morris (1998) and H2 and water as low temperature cooling source ​Neufeld & Kaufman (1993). The defect of these method is: it admits the chemical interaction but did not fully take them into account. For example, HII can interact with electron to form HI. This chemical reaction will release heat thus making the gas's specific heat change (\Gamma\sim1). In ​Tomida et al. (2013) and ​Tomida et al. (2015) use statistical mechanics to derive \Gamma table as a function of \rho and T. I will use their model in future simulation. A color plot of the table can be found here ​Pejcha, Metzger & Tomida (2016). Besides, there is new data for high temperature cooling (>10000 K) ​Gnat & Sternberg (2007).

3b. Opacity is another key aspect of this problem. MESA has some subroutines that can derive opacity tables.

3c. Implicit cooling scheme is useful when t_{cool}<t_{dynamical}. ​Townsend R.H.D. (2009) and the reference therein are useful.