INTRODUCTION
Some theories posit that water was delivered to the Earth by long period comets that collided with the planet earlier in its history. We assume that terrestrial planets orbit the two stars (see the work done by Javiera Guedes and Erica Davis) and that the binary system is surrounded by its own analogous cloud of comets. The alpha Centauri system is especially interesting because of the presence of a third star, Proxima, which is currently located about 15000 AU from the binary. We are running N-body simulations to examine Proxima's role in perturbing the orbits of these comets inward toward the binary system.

In our simulations, we assume that the comets are massless test particles that only interact with the three stars: alpha Centauri A/B and Proxima.

ONE ORBIT: PARTICLE 56
We first determined that the particles most susceptible to perturbations from Proxima were located between about 5000 and 8000 AU. This corresponded to Proxima's distance from the binary when it crossed the binary plane. (Proxima's orbit is inclined about 151 degrees from the binary plane.) In order to understand what was happening to the particles, we looked at one particular orbit in detail. Particle 56 started out with a semi-major axis of 6990.77 AU and after 8.5 million years it was ejected from the system. Its closest approaches were 42.79 AU (alpha Centauri A, at 6.3 million years) and 18.42 AU (alpha Centauri B, at 7.05 million years). Since we are interested in Earth-like planets (terrestrial planets located in the habitable zones of either of the stars), this closest approach is much too far (about the orbit of Uranus in the solar system). Below is a movie showing the 3-dimensional orbit of Particle 56. The orbit of Proxima is in blue, and the orbit of Particle 56 is in green.

Here is a zoomed-in, top-view version. The orbit of alpha Centauri B is in red, and alpha Centauri A is located in the center (not marked).

Although it looks like the comet crosses the orbit of alpha Centauri B more than once, a 3-dimensional examination of the orbit shows that those apparent crosses are not located in the binary plane.

The plots below show that the irregularities in the orbit of Particle 56 are a direct consequence of its close encounters with Proxima. The particle's distance from Proxima is shown in both plots: second from top on the left, and bottom on the right. In the plot on the left, the particle's two closest encounters with Proxima (marked with vertical dotted lines) occur right before significant changes in the distance to the binary system (top), the eccentricity of the orbit (third from top), and the inclination of the orbit (bottom). In the plot on the right, the particle's closest encounters with alpha Centauri A (top) and alpha Centauri B (second from top) occur right after the second close encounter with Proxima. Click on the plots to larger versions.

One thing to note, however, is that the particle never gets close enough to either of the two stars in the binary pair to be able to collide with a terrestrial planet in the habitable zone. Of all of the test particles that we have input into our simulation, the closest approach was about 5 AU, which is about the orbit of Jupiter in our solar system and outside of the habitable zone.

MANY ORBITS: THE RING
Though we could not find any evidence that Proxima was sending comets into the A/B binary system, it was clear that the third star was having an effect on the orbits of the particles. We found that if we began with an ordered set of particles, like a ring (a very unhomogeneous distribution), Proxima's motion around the binary pair would homogenize the comets, turning the ring into more of an isotropic cloud. A movie of one of our simulations is shown below. We constructed a ring at 7500 AU (the distance where Proxima crosses the binary plane) and let Proxima orbit about five times. The red plus sign in the center indicates the location of the A/B pair, the red dot orbiting A/B is Proxima, and the blue symbols represent the 80 test particles in the simulation.

CONCLUSION
Proxima's main interaction with the comets around A/B appears to be the homogenization of the distribution of particles. It does not appear to be sending comets into the A/B system as initially guessed. That does not mean, however, that no comets are being delivered to the terrestrial planets around alpha Centauri A and B. There are many other potential perturbers that may cause comet showers: giant molecular clouds, brown dwarfs and other nearby stars, and even the galactic potential. The presence of habitable, wet, terrestrial planets is still very much a possibility.

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