A 0.1339 solar mass object is located at origin and emitting wind. Although parameters change in the following simulations, the functional form of time dependent variables behave alike.

The initial velocity of the wind and The density of the wind vary as:

Red line indicate the escape velocity at the radius where the wind is launched.

\triangle t time duration of pulsation

t_f free fall time of the wind with lowest velocity

v_{esc} escape velocity from the starting radius of the wind

v_w lowest wind velocity

\dot{M}_{pulse}v_{pulse} highest mass loss rate times lowest velocity during pulsation (they happen at the same time)

\dot{M}_{postp}v_{postp} asymptotic mass loss rate times asymptotic velocity after the pulsation

\frac{\triangle t}{t_f}	0.5	0.367
	color1.gif​	color4.gif​
	1.gif​	4.gif​
\frac{v_w}{v_{esc}}	0.768	0.670
	color1.gif​	color0.gif​
	1.gif​	0.gif​
\frac{\dot{M}_{pulse}v_{pulse}}{\dot{M}_{postp}v_{postp}}	58	29
	color1.gif​	color5.gif​
	1.gif​	5.gif​

Conclusions:

1. Fall back radius is sensitive to the value of post pulse wind momentum.

2. I guess the time of fractal of dense shell is relevant to the time duration of pulsation (given the same other conditions).