Matter
ghost matter astrophysics. 5 :
Results
of numerical 2d simulations.
VLS. About a possible
schema for galaxies' formation.(p4)
If we study intermediate initial
configuration we find the result shown on figures 11 and 11bis, i.e. some sort
of an emulsion, stable over long time. The relative stability of such pattern
could comes from the fact that any mass concentration of one species forms a
potential barrier with respect to the other, and vice versa. Notice this method
could be extended to a 3d hypersphere, whose metric is :
(5)
ds2 = dr2 + R2 ( dq2
- sin2q dj2)
Given two points
M1 (r1 , q1
, j1) and
M2 (r2 , q2
, j2)
we may compute the two geodesic arc lengths d and d� which join them and the
gravitational force. But these spherical or hyperspherical descriptions induce
curvature effects. If we want to study a phenomenon, whose characteritic span
is L, in a portion of such 2d or 3d closed universes, expecting curvature
effects can be neglected, we must deal with very large 2d or 3d spheres
(R >> L), which requires a large
number of mass-points, far beyond the possibilities of today�s existing systems.
Fig.11: An emulsion corresponding to Vth = Vth
cr.
Fig
11bis : the same with two different greys.
Following [11]
and [12] let us return to the simpler classical method, introducing space
truncature : we limit the interaction computation to the neighour mass
points located is the dotted square (figure 12) whose side is equal to
the side of the basic cell.
Fig.
12 : Space truncature for
spatially periodic system.
The results are similar. If we
fill the unit square with a single self-attractive species, with uniform mass-density
r and
uniform thermal velocity field, corresponding to a 2d Maxwell-Boltzmann distribution
:
(6)
we refind a critical value Vth
. See figures 13a and 13b .
Fig.
13 : 2d gravitational instability
with space truncation and
unique species.
