4
Below is a didactic model designed to illustrate the phenomenon of joint gravitational instabilities. Imagine a kind of pool. At mid-height, underwater, we place a horizontal, flexible, weightless sheet. Above it, we place heavy balls, which will therefore press down on the sheet. Above that, we arrange an equal number of ping-pong balls, of the same volume. These, being sensitive to Archimedes' buoyancy, will also exert pressure on the sheet, but in the opposite direction. We can also arrange things so that all the balls have the same diameter.
If there is a uniform distribution of heavy balls and ping-pong balls on both sides, the net force exerted on the sheet will be zero everywhere, and the sheet will remain horizontal (its curvature will be zero). But chance might cause some heavy balls to gather in one spot. They will then depress the sheet, pushing the ping-pong balls away. Schematically, making a cross-section, the surface would take the following shape:
Heavy balls gather and depress the sheet.
They push the ping-pong balls outward, which then gather around the depression.
Intuitively, one can imagine that these two phenomena, rather than opposing each other, reinforce one another. The presence of this ring of excess ping-pong balls around the depression will deepen the hollow, thus enhancing the "confinement" of the dense balls.
Gravitational instability could also be illustrated with a single population by placing heavy balls on a sufficiently soft foam mattress. If a few of them happen to gather by chance somewhere, they will create a depression in which neighboring balls will tend to fall. This is known as an accretion phenomenon.
If we took a sheet and placed only ping-pong balls underneath it, this system would also be unstable. If some ping-pong balls gather in one spot on the sheet, they will encourage their neighbors to join them.
With this two-population model—heavy balls and ping-pong balls—we have two coupled effects, which evoke the phenomenon of
joint gravitational instabilities.
This model also has the advantage of illustrating the symmetry between the two subsystems.
If we reconsider the two-population system, it would look like this:
Ping-pong balls gather and bulge the sheet upward.
They push the heavy balls outward.
Thus, we sought to test this idea by starting from two distributions:
- Cold matter, density
r
- Ghost matter, density
r *
@ 64 r
, hotter: The average thermal agitation velocity in the ghost universe
V*th being four times higher than in our own, parameters derived from studies of the joint expansions of the two universes [see on the website:
Geometrical Physics,
3
, section 3 and figure 5
].
Calculations were performed through 2D numerical simulations using two sets of 5,000 point masses. These are only indicative. 3D calculations would be needed, requiring the handling of a much larger number of point masses—something our system was unable to do. Therefore, these 2D results should not be taken literally.
Qualitatively, ghost matter leads the process. It quickly gives rise to clumps (its accretion time, inversely proportional to the square root of the density, is shorter). These clumps then push our own matter into the remaining space, giving it its lacunar configuration. See: J.P. Petit, P. Midy, and F. Landsheat: Matter, ghost matter astrophysics. 5: Results of numerical 2D simulations. VLS. About a possible schema for galaxy formation. [See on the website:
Geometrical Physics A,
8
, 1998.
]
The two superimposed:
The interest lies in the fact that this distribution is then stable. The clumps of ghost matter stabilize the lacunar matter distribution, and conversely, the matter distribution traps these clumps within its "meshes." This could explain the high stability achieved (on the order of the age of the universe). The "meshes" of matter thus act as potential barriers against ghost matter elements, originating from the clumps and accelerated during collisions (in the Anglo-Saxon sense of "encounter," meaning binary interaction between two ghost matter point masses).
Note
(February 2000):
All these calculation results are six years old. How could anyone learn about them? Those who have read my books will know that these quite interesting and promising simulations were carried out in 1993–94, first by my colleague and friend Pierre Midy on an old Cray computer, and later by "Fred," a young researcher who preferred to remain anonymous—something I fully understand and respect. The calculations were then performed "in disguise" on a powerful computer managing data from a European particle accelerator. Later, Fred changed labs, and such computations were no longer feasible in his new unit. Thus, the numerical simulation approach was abandoned for six long years. But recently, a new development has occurred. First, computers have advanced tremendously over the past six years (in speed and especially in memory capacity), so that calculations previously possible only on powerful research-grade machines are now accessible to... ordinary individuals. Two retired engineers, passionate about astrophysics and cosmology, have therefore stepped forward. By programming their own machines, they produced fairly impressive simulations, perturbing a "2D numerical galaxy" made of 3,000 point masses with a "passing companion" made of 300 points. In short, the classic scenario leading to the spiral shape of the Whirlpool Galaxy, also known as M51. When one sees these images, one immediately thinks: "This is exactly what could be done ten years ago in research environments with powerful computing resources." Of course, the spiral structure did not persist—it disappeared when the perturbing companion moved away (an aspect long known). Our two engineers, encouraged by these promising results, approached six well-known astrophysicists, asking for guidance—but none had the courtesy to respond. I was thus the seventh astrophysicist they contacted. You can imagine how delighted I was to receive this unexpected support, and I immediately connected these new collaborators to new simulations. Apparently, they are doing very well, and if all goes well, we will have "fresh results" in the coming months. An exciting prospect, as the goal is nothing less than simulating the birth of a galaxy. Watch this space.
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