Binary-induced collapse of a compact, collisionless cluster

Matthew D. Duez
Eric T. Engelhard
John M. Fregeau
Kevin M. Huffenberger
Stuart L. Shapiro

We evolve a compact cluster consisting of 20,000 test particles orbiting a Schwarzschild black hole in randomly oriented circular orbits. This system is stable in isolation. We then place the system in the tidal field of a binary companion point mass which spirals in toward the black hole due to gravitational wave emission. The tidal field of the companion is treated as a small perturbation in the background Schwarzschild geometry. We find that this configuration can be driven dynamically unstable by the time the companion has reached 30 M, and that 70% of the test particles have fallen in by 26 M. This simulation shows that the "crushing instability" does occur for compact binaries of collisionless particles.

Setting It Up

The black hole and the companion point mass both have a mass M. The test particles each have mass m, where m << M. The combined mass of the 20,000 test particles is still much less than M.

The black hole's horizon is at r/M = 1.0 (All values given in harmonic coordinates).

The innermost stable circular orbit, inside of which no test particle can stably orbit, is at r/M = 5.0.

The radius of the initial circular orbits of the spherical swarm of test particles is at r/M = 5.9.

The distance from the black hole (here covered with the swarm of 20,000 test particles, indicated by white dots) to the companion point mass is r/M = 60 initially.

Scene 1: Binary Induced Collapse of Cluster (top view)

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We join this simulation after a long time has passed, i.e., after the companion has spiraled in to approximately 30 M. The test particles would orbit forever if there were no companion present, but the companion's inspiral drives the configuration unstable by this point. We view the collapse from directly above the plane of the companion's orbit around the black hole.

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We join this simulation after a long time has passed, i.e., after the companion has spiraled in to approximately 30 M. The test particles would orbit forever if there were no companion present, but the companion's inspiral drives the configuration unstable by this point. We view collapse from a point just above the orbital plane of the companion.

We now rotate around the final configuration to ascertain its shape. The particles that are near the orbital plane of the companion are the most stable against the tidal perturbation, hence the 'donut' shape.

This image shows the location at the end of the simulation.

Scene 3: Orbit of a test particle

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Here, we study a typical test particle around the black hole, and trace out its orbit throughout the entire simulation. The test particle begins with an orbit oriented 45 degrees to the plane of the companion's orbit. We start tracing the orbit when the companion is at 60 M, the beginning of our simulation, and then fade to a time near 26 M when this particle is about to fall in. We then rotate around the black hole to see the final shape of the test particle trajectory.

Scientific visualization by

Matt Duez
Eric Engelhard
John Fregeau
Kevin Huffenberger

University of Illinois at Urbana-Champaign last updated 1 Mar 00 by jjm