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.
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
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
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.
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
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.
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:
http://www.springer.com/gp/book/9783319246406 or https://www.amazon.com/dp/3319246402 .
John's 1st hard SF novel Twistor
is available online at:
View Columns Online: Electronic reprints of 226 or more of "The
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;
H. E. Philcox, "Probing Parity-Violation with the Four-Point Correlation
Function of BOSS Galaxies," arXiv:2206.04227v2
[astro-ph.CO] 29 Jul 2022.
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;
Lue, Limin Wang, and Marc Kamionkowski, "Cosmological Signature of New
Parity-Violating Interactions," Phys. Rev. Letters 83, 1506