a204 A cosmological model: The twin big bang. (p.4)
Gravitational instability could be illustrated by a single population (of weight balls), placed on a soft mattress. If some heavy balls form a clump, at any point, they create a depression in the mattress and tend to attract their neighbors. This phenomenon is called accretion.
...Similarly, a system composed of a single population of ping-pong balls would be unstable. If some form a clump at any point, they rise on the sheet and attract their neighbors.
...With these two populations (heavy balls and ping-pong balls), we simulate joint gravitational instabilities. They can produce either matter clumps or ghost matter clumps. On figure (156 ter), the simulation of joint instabilities gives a ghost matter clump (a clump of ping-pong balls), with reinforced confinement (by heavy black balls).
...In 1994, we began to study the behavior of this system using 2D numerical simulations. In the articles:
- J.P. Petit & P. Midy: Repulsive dark matter. Geometrical Physics A, 3, section 3, figure 5.
- J.P. Petit & P. Midy: Repulsive dark matter. Geometrical Physics A, 4 Astrophysics of matter-ghost matter. 1. The geometrical framework. The matter era and the Newtonian approximation.
...Our cosmological model shows that the matter density r and the ghost matter density r* are different, due to the instability of the expansion process of the two universes (r* @ 64 r). Moreover, the thermal velocity Vth in the twin fold F was found to be four times greater than that in ours. We used two sets of 5000 interacting mass points. To manage this mass density contrast, we "weighted" our mass points according to: m* = 65 m.
...3D simulations would require more points: beyond the capabilities of our system (currently, in April 1998, the situation is different: we have no system at all...).
...These results obtained are only a qualitative exploration of the system, with mass density contrast and different thermal velocities. We find that ghost matter, the denser population, runs the show. As the accretion times are:
(156d)
ghost matter, owning the smaller one, forms clumps. The regular matter then occupies the remaining space. The following figures come from:
J.P. Petit, P. Midy and F. Landsheat: Astrophysics of matter-ghost matter. 5: Results of numerical 2D simulations. VLS. About a possible scheme for galaxy formation. Geometrical Physics A, 8, 1998.
*(157)
The two populations, together:
(158)
...Compared to Mellot's simulations, based on Zel'dovich's "pancake" theory, our structure is remarkably stable over time. The lacunar distribution tends to keep the clumps in place. Conversely, the clumps fix the lacunar structure in space. Each acts on the other as a potential barrier. They mutually stabilize each other.
...Returning to the heavy balls and ping-pong balls model, we can schematize it, as shown on figure (158 bis). In order to simulate the mass density contrast, we have placed small lead shots on the linen.
...We can imagine a different configuration, where the ghost matter is so hot that its "Jeans' length" is larger than the tank's characteristic length. Then the shots form a clump. See the depression on figure (158 ter). The presence of the surrounding ping-pong balls modifies the side of the depression (its slope) and reinforces the confinement effect.
...This is a didactic model of a galaxy surrounded by hot ghost matter, which confines it.