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4AU binary simulation with great pulsation in the co-rotating frame.

This post analyze the 4 AU binary simulation with great pulsation in the co-rotating frame. The pulsation is from t=15yrs to t=25yrs which last for 10 years. The wind speed during the pulsation is 20km/s and the escape speed is 40km/s at that radii.

This image shows the density looking from top. There is a spiral structure that extends outward indefinitely. This structure may be a consequence of the great pulse or just the normal AGB pulsation. But a direct reason for this structure is that the secondary can not accrete all the gas that has been pulled to it. Therefore the secondary will periodically release some gas and absorb the rest.

I do not think the spiral structure is starting from the L2 point. Because the L2 point is not located on the high density arm that extends outward. As I can see, the gas that leaking from the L2 point is gravitationally bound.

This image shows another information. First I will define a quantity, angular momentum per unit mass:

j_{b}=\frac{m_{agb}v_{agb}d_{agb}+m_{com}v_{com}d_{com}}{m_{agb}+m_{com}}

where subscript b stands for binary. d is the distance to the center of mass and v is the velocity with respect to the center of mass in the lab frame. This value for such system is 2.425\times10^{19}g\cdot cm^{2}/s.

Then we calculate the actual angular momentum per unit mass in the simulation and name it j_{g}. This image shows the value of s1=j_{g}/j_{b}. The greater the s1 the higher the angular momentum per unit mass. We can see that this value is above 4 in most area in this image.

Next I calculated the mass of the gas that leave this system, it is \dot{M}_{runaway}=2.16652\times10^{-7}M_{\odot}/yr. The accretion rate of the secondary is \dot{M}_{sec}=1.037\times10^{-7}M_{\odot}/yr. Therefore the massloss rate of the AGB star is M_{agb}=3.2\times10^{-7}M_{\odot}/yr. In the single AGB star case, the massloss rate is around 1.6\times10^{-7}M_{\odot}/yr. So the existence of the secondary double the massloss rate of the AGB star.

I also calculated the angular momentum loss rate, that is, the angular momentum in the z direction that is carrying away by the runaway gas per unit time. It is \dot{J}_{z}=1.52845\times10^{39}g\cdot cm^{2}/s^{2}. Hence the angular momentum per unit mass in the z direction in the runaway gas is:

j_{g}=\frac{\dot{J}_{z}}{\dot{M}_{runaway}}

compared to j_{b}, it is:

\frac{j_{g}}{j_{b}}=4.613

Now, we can see that the runaway gas is carrying more angular momentum than the average angular momentum in the binary system. More specifically, it is 4.613 times of the average angular momentum per unit mass.

If we write j_{b} in terms of m_{agb},m_{sec} and d, it is:

j_{b}=\frac{m_{agb}m_{sec}sqrt(Gd)}{(m_{agb}+m_{sec})^{3/2}}(1)

On the other hand, by the conservation of angular momentum:

j_{b}(m_{agb}+m_{sec})+j_{g}m_{g}=j_{b0}(m_{agb0}+m_{sec0})

where 0 stands for the initial values.

If we let this angular momentum and accretion run for 5\times10^{5}yrs under such condition, then j_{b}=0.727 j_{b0} at that time. Use equation (1) and substitute the correct numbers we can get that the separation will be 2 AU.

Researchers have put much attention to the angular momentum carried away by the gas leaking from the L2 point. The angular momentum loss in this simulation is different from that and it is more effective. However, I can not tell if this situation is going to last because it has only been 9 years after the pulsation. However, considering that the massloss rate for the single AGB star is low. I would argue that if the massloss rate of the AGB star is very high, such expulsion may last because the secondary can not accrete that much of gas. I will run the 4 AU simulation without the great pulsation and check whether if will also be there.

I think when there is no formation of circumbinary disk, there is strong orbital decay.

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