astrophysical twin universe and cosmology Ghost matter astrophysical matter. 5: Results of 2D numerical simulations.
VLS. About a possible scheme for galaxy formation. (p3)
If we place a uniform distribution of matter on such a sphere, the behavior of the system depends on the initial value of the mean 2D "thermal velocity" Vth. If this is weak or null, matter forms a clump (figure 9-a). If this velocity is very large, the clump does not form and the medium remains uniform. The transition corresponds to some critical value Vth cr.
**Fig.**9a: 2D Jeans instability on a sphere S2. Matter alone: V th = 0.2 V th cr
. **Fig.**9b: Matter alone. V th = 10 V th cr
When a clump of matter forms (fig.9a), the larger the initial value of Vth, the larger its final span. This is similar to the Jeans problem. We may compute some sort of 2D Jeans length and say that the clump forms when this characteristic length is smaller than the perimeter 2π R of the sphere. If it is larger, the thermal agitation tends to dissipate any mass concentration. When a clump forms, as in 3D Jeans instability, the larger the initial mass density r, the faster the process. Now we consider a mixture of two species, normal matter (that we simply call matter) and ghost matter, according to the interaction scheme defined above. We start from uniform initial conditions defined by the four parameters:
(4)
r r* Vth Vth*
If we choose (r = r* ; Vth = Vth* ), the result depends on the initial common value Vth. Here again, we find some critical value Vcr. We have two extreme configurations, corresponding to figures 10-a and 10-b.
**Fig.**10a : Mixture of matter and ghost matter V th = 0.25 V th cr : Joint gravitational instability.
. **Fig.**10b : Mixture of matter and ghost matter V th = 15 V th cr . The two species remain closely mixed.
