twin universe cosmology Matter ghost matter astrophysics. 4 :
Joint gravitational instabilities. (p2)
- Didactic image of the phenomenon.
There is a classical image of the Jeans instability. Consider the following "machine":
Fig. 2 : A foam mattress with vibrating plates covered with small buckshot.
...We could fabricate something of this type with certain flat loudspeakers. We could also put a plate of glass on top, to prevent the shot from jumping overboard. Having done this, we could regulate at will the "temperature" of this kind of two-dimensional gas. It would simply be proportional to the square of the shot's average agitation speed.
...Agitating the shot in every direction would have the effect of opposing their tendency to assemble themselves in the basins. Heating this "gas" would make the basins disappear. But reducing the shot's state of agitation would make them reappear.
...A certain amount of time is needed for basins to be formed, for shot to assemble there and then to attract their little comrades. The heavier the shot, or the more numerous, the faster will basins appear (2D simulation of the accretion phenomenon). It does not depend on the size of the depressions which tend to form.
...We cover the mattress with shot corresponding to a certain density of matter r in grams per square inch. The basins will form in a time t which depends on this density. (In astrophysics, this accretion time is proportional to the inverse of the square root of the density of matter r. See annex.)
Let us take a depression having a diameter D. The shot has a speed of agitation V. Therefore, it crosses the basin in a time:
t = D/V.
...This is also the time which the shot takes to leave this type of basin, or, if we prefer, the time all accidental condensation of matter takes to disperse naturally by simple thermal agitation.
...If this time is less than the time t of basin formation, the depression cannot be formed. Even before it had begun to be formed, the shot which would have served to create it would be gone to set up the same structure elsewhere. Therefore, for a given density of shot r on the mattress, and for their equally fixed agitation speed V, the basins which can form will be those such that:
t < D/V.
This is to say that only those basins will form having a diameter superior to:
V t.
Fig. 3 : 2D simulation of Jeans gravitational instability.
...The diameter of such a condensation of matter depends on the equilibrium between the force of gravity, tending to contract it, and the force of pressure, tending to dilate it. Calculations show that this happens when the diameter is very close to the Jeans distance.
...We now show how to simulate joint gravitational instabilities. We have to shift to another model. Consider a swimming pool, filled with water. Put an horizontal plane of fabric, at mid depth. Above: some balls, denser than water. Below: ping-pong balls. The first objects tend to weigh on the fabric, the second to lift it. Initially, the two forces balance each other. We must add some turbulence of the water, sustained by fans, to simulate the thermal agitation state on both sides. We take it equal (but it could be different).
Fig. 4 : 2D simulation of joint gravitational instability. 1 : a clump of heavy balls forms.
...On figure 4, the formation of a clump of heavy balls. But the problem is symmetrical. In some places the ping-pong balls may form their own clump, and repel the heavy balls. See figure 5.
Fig. 5 : 2D simulation of joint gravitational instability. 2 : a clump of ping-pong balls forms.
