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Ejected Black Holes and 3-Body Physics

by John G. Cramer

Alternate View Column AV-225

black hole, galaxy merger, 3-body, ejection
Published in the July-August-2023 issue of Analog Science Fiction & Fact Magazine;
This column was written and submitted 03/07/2023 and is copyrighted 2023 by John G. Cramer.
All rights reserved. No part may be reproduced in any form without
the explicit permission of the author.

The stately planetary orbits of our Solar System are, in a sense, deceptive.  Their regularity fails to convey the wild gyrations that can occur when three or more massive objects move in close gravitational orbits.  In our galaxy, low-mass stars tend to be isolated single stars, while the more massive stars tend to cluster in combinations of two or more participants, often moving in complicated orbits.  In particular, when three-star systems form close together, their orbits tend to be chaotic, and they usually stabilize with two stars in close orbit and the third star more distant or ejected altogether.  A nearby example is the Alpha Centauri system, in which the orbital distance between Alpha Centauri A and B varies from 11.2 to 35.6 astronomical units, while Proxima Centauri is still gravitationally bound to its siblings but orbits 3,000 astronomical units (0.21 light years) away from them.  An astronomer friend once told me that Nature doesn't like to solve the three-body problem, so She usually ejects one of the participants.

There are no general analytic solutions to the gravitational three-body problem, but with modern computers using numerical approximations we can accurately predict three-body dynamics in any specified three-body situation.  There are a few stable and quasi-stable three-body orbital configurations involving systems in which there is a very light object (e.g., an asteroid), a medium-weight object (e.g., a planet), and an object at least 25 times heavier (e.g., a star).  Probably the most familiar of these is the "trojan" configuration, in which the three orbiting objects form the vertices of a 60-degree equilateral triangle, with the lightest object at the Lagrange L4 or L5 point on the orbit of the second most massive object.  The best example in our Solar System is the Sun-Jupiter system, which has 7,508 trojan asteroids near Jupiter's L4 point and 4,044 trojan asteroids near its L5 point.  The Sun-Neptune system probably has even more trojan objects, but so far only 28 Neptunian trojan asteroids have been identified, 24 in its L4 region and 4 in its L5 region.  The gravitational perturbations of Jupiter prevent the inner planets from having many trojan objects in their orbits: Mercury has none, Venus has 1, Earth has 2, and Mars has 14.  For completeness, I should mention that there are also a few other semi-stable three-body orbital configurations like the "horseshoe," "Lissajous," and "tadpole" orbits.  However, there are no semi-stable close orbits in which the three orbiting objects have roughly equal masses.

It is now fairly well established that galaxies with stellar bulges have a super-massive (>106 solar mass) black hole at their centers.  We also know that on a billion-year time scale two galaxies often merge to form a single galaxy.  In 2007, astrophysicists Loren Hoffman and Abraham Loeb (H&L) of Harvard have used numerical three-body computer simulations to examine a broad range of initial conditions and predict the behavior and statistics of combinations of two and three super-massive black holes in such galactic mergers.  In these calculations they include the dynamic friction from interactions with the local medium of gas and stars.

They found that when two black-hole-bearing galaxies merge, the pair of black holes tends to settle into a roughly circular binary orbit separated by a few light years.  If interactions with local stars drive this binary to a much closer orbit (~17 times smaller), the merger of the two black holes will occur, generating the intense bursts of gravitational radiation that LIGO/VIRGO has been detecting.

Thus, many of the galaxies we observe should have a binary pair of super-massive black holes at their centers.  As the universe evolves, there is a distinct possibility that one of these binary-black-hole galaxies will merge with another galaxy to create a composite galaxy containing three black holes in unstable orbits.  The three-black-hole simulations of H&L lead to a range of different orbital outcomes, including at  one extreme those in which two or all three of the black holes are driven to merge into a single object, and at the other extreme those in which the single and double black holes pass each other "like ships in the night" and separate without further interaction.  Some of the other simulations result in a final binary black hole system with a very large orbital eccentricity, a situation that is predicted to produce low-frequency gravitational waves that should be detectable with the LISA space-based gravitational wave detector scheduled for launch in the early 2030s.  And finally, H&L calculate that around 14% to 22% (depending on initial conditions) of the colliding galaxies in their simulations show the violent ejection of a single black hole, leaving behind either a binary pair or a single merged object.

Now there is observational evidence that such an ejection event did occur long ago, in a distant merging galaxy.  An astronomy group based primarily at Yale University, using the Advanced Camera for Surveys (ACS) detector system of the Hubble Space Telescope, has reported the accidental observation of a very long linear structure (projected length about 202,000 light years) which seems to be the track of a black hole ejected from a compact star-forming galaxy around 11.7 billion light years (z=0.964) from Earth.  They calculate that the object that made the track was originally ejected about 39 million years before its present observed state and had a velocity with respect to the emitting galaxy of about 1,600 km/sec (~0.5% of lightspeed).  Along the track of the object, they observe optical spectra indicating the presence of both shock waves and star formation.  They conclude that the most likely explanation of their observation is that the track was made by an ejected super-massive black hole moving through the circumgalactic medium at a high speed, producing shock waves in the medium, and triggering much star formation.

On the reverse side of the galaxy, they also observe a shorter linear track with spectral evidence of shock waves but no indication of star formation, presumably indicating that it was made by a lower-velocity object.  Let us assume that the black hole making the long track was ejected after a chaotic three-body orbital encounter with a close binary of super-massive black holes of similar mass.  From momentum conservation, the binary system and single black hole would be expected to recoil in opposite directions with the same momentum magnitude.  If the recoiling binary system was two or three times more massive than the single ejected black hole, it would have a proportionately lower velocity and the track it would leave should be two or three times shorter, which is consistent with the back-side linear track observed.  Thus, the collision may have left the resulting composite galaxy with no black holes at all at its center, because three-body dynamics has sent one black hole out on one side and the other two out on the other side.

Stars normally form within galaxies, where interstellar gas is concentrated by gravitational attraction to a density sufficient for collapse and star formation.  However, astronomers observe intergalactic star-forming regions in galactic clusters that are well away from any host galaxy.  Such star formation in regions that should have low gas density is not understood.  It was suggested in 2008 by R. and C. de la Fuente Marcos that extra-galactic star formation could be the result of gas compression from shock waves generated by ejected supermassive black holes.  However, at the time there was no observational evidence in support of this conjecture.

But now, the idea of shockwave driven star formation has been corroborated, and the concept also supports the Yale group's supposition that the observed long track involving star formation traced the path of the ejected high-velocity super-massive black hole.

    Science fiction authors of stories involving interstellar civilizations usually assume that the home worlds of such civilizations are located within galaxies, because that is where most of the stars are.  However, these new observations indicate that there should also be chains of stars, all created in a linear sequence along the path of an ejected black hole.  Such stars should be fairly similar in size because they were created by the same black hole shock wave in a region of fairly uniform gas density.  They might be fairly close together in the direction along the track, but well isolated from other stars in the other two dimensions and also isolated from the sterilizing effects of supernova violence and orbit-changing gravitational perturbations that occur in the crowded region near the centers of galaxies.  This might make for interesting scenarios for the interactions of developing interstellar civilizations with home worlds along a straight line.

John G. Cramer's 2016 nonfiction book describing his transactional interpretation of quantum mechanics, The Quantum Handshake - Entanglement, Nonlocality, and Transactions, (Springer, January-2016) is available online as a hardcover or eBook at: or .

SF Novels:  John's 1st hard SF novel Twistor is available online at:   His 2nd and 3rd novels, Einstein's Bridge and its new sequel Fermi's Question, are now available as eBooks from Baen Books at: and .

Alternate View Columns Online: Electronic reprints of 226 or more of "The Alternate View" columns written by John G. Cramer and previously published in Analog are currently available online at: .


Parity Violation in Galaxy Locations:
Jiamin Hou, Zachary Slepian, and Robert N. Cahn, "Measurement of Parity-Odd Modes in the Large-Scale 4-Point Correlation Function of SDSS BOSS DR12 CMASS and LOWZ Galaxies," arXiv: 2206.03625v1 [astro-ph.CO] 8 Jun 2022;

Oliver H. E. Philcox, "Probing Parity-Violation with the Four-Point Correlation Function of BOSS Galaxies," arXiv:2206.04227v2 [astro-ph.CO] 29 Jul 2022.

Parity Violation in Galaxy Spin:
Lior Shamir, "Patterns of galaxy spin directions in SDSS and Pan-STARRS show parity violation and multipoles,"  Astrophysics and Space Science 365, 136 (2020); arXiv:2007.16116v1 [astro-ph.CO] 29 Jul 2020.

Chern-Simons Gravity Theory and CP Violations
Stephon H.S Alexander, Michael E. Peskin, and M. M. Sheikh-Jabbari, "Leptogenesis from Gravity Waves in Models of Inflation," Phys. Rev. Letters 96, 081301 (2006); arXiv:hep-th/0403069v4;

Arthur Lue, Limin Wang, and Marc Kamionkowski, "Cosmological Signature of New Parity-Violating Interactions," Phys. Rev. Letters 83, 1506 (1999); arXiv:astro-ph/9812088v2.

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