fall back disk

Assume a third star with mass between 0.001 SM to 0.05 SM (hot Jupiter to Brown Dwarf) around the primary fall into the primary during common envelop phase evolution from an orbit of 1 AU to 0. So it will induce an equatorial outflow J. Nordhaus and E. Blackman 2006. The angular momentum, the potential energy and the kinetic energy of the planet will partially be transferred to the outflow. A detailed calculation will not be presented here.

Let's assume the equatorial outflow is , lasting for 1 - 10 yrs, so the total mass of the outflow is .

Below are some parameters:

: Binary separation, can vary from 4 AU to 20 AU. A close binary will transfer more angular momentum to emitted gas but will also challenge the small planet around the primary. Because they are basically three body system. (Boldly assume the small planet is 0.8 - 1 AU from the primary such that the secondary will impose so much effect.)

: Primary mass, let's fix it to be 1 SM and low metallicity. Metallicity is important in AGB evolution since it will provide dust thus drive the wind away from the primary.

: Ratio of secondary's mass to primary's mass. It can be 0.2 to 1, varies in correspond to the binary separation. The greater the ratio the less the orbital period thus the more angular momentum will be transferred to the gas emitted from the primary. Note here when the gas is emitted from the primary, it receives some angular momentum from the primary because the primary has orbital motion.

: Open angle of the equatorial outflow. Let it vary from . The more mass the planet (or Brown Dwarf), the wider the open angle. This open angle is closely associated with turbulence driven by the in falling planet rather than viscosity. companion driven dynamo happens in this process.

: Spinning angular velocity of the primary. The envelop of the primary is spun up by the in fall of the third planet and may induce a dynamo. This may also come from its own spinning (though very small, data missing here). A value to be noticed is the orbital angular velocity at the radii which the outflow will be emitted. .

Given that:

\[\omega=\sqrt{G M/r3}\]

\[l_z=r\times v=r2 \omega = \sqrt{G M r}\]

This means, any object with angular momentum larger than 0 can find its orbit, mathematically, if the radial velocity is 0.

: Actual temperature can be around 2000 K, like the temperature in the envelop. In the test simulations, we can choose 200 K simply because it reduce the pressure and the sound speed.

: Radial velocity of the outflow. The best scenario is we can depict its angular dependence. Here we can use step function due to low angular resolution in test runs. This speed should below escaping velocity. Let's say, ¾ of the escaping velocity.

: The radius which the outflow is emitted. It is set to be 1 AU.

A recent simulation:

Primary star has a constant alpha of 0.1339 throughout space. Simulation temp is 100 K.

density.gif​

Attachments (3)

Comments

No comments.