The Roche Potential

Now we will show another feature of Binary Maker which will show us the Roche Potential of the binary.

When two point orbit one another in a circular path their gravitational fields merge and form a specific pattern. If we were to trace out the places which have the same gravitational potential we would see something like this:

(Make my own roche potential figure from binary maker)

This is called the Roche potential, named after its discoverer Edouard Roche.

The most important aspect is the figure of eight line. This is called the Roche lobe. If a test particle were on this line it could travel between the gravitational potential of one body to the other.

Binary stars have Roche potentials. If the stars are smaller than their Roche lobes then they will evolve as if they would if they were isolated stars. Binaries of this type are called "detached binaries".

Stars evolve and grow, however, and if the stars of a binary are close enough they will swell to their Roche lobe. When this happens the star takes on the shape of the Roche lobe, which is the tear-drop shape we saw in the last binary in Binary Maker. These binaries are called "semi-detached binaries".

Let's see what the Roche potential looks like for our binary.

In Binary Maker, go to starting screen and choose Surface Outlines under the Run menu.

Type Enter for all values.

The screen should now show part of the Roche potential of the binary as lightly dotted lines. The heavy dotted lines show the star surfaces. The smaller crosses are the center of mass of the individual stars and the larger cross is the center of mass of the binary.

Type Esc and N for the rest.

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