Matter
ghost matter astrophysics. 5 :
Results
of numerical 2d simulations.
VLS. About a possible
schema for galaxies' formation. (p3)
If we put on such a sphere an uniform
distribution of matter, the behaviour of the system depends on the initial value
of the mean 2d "thermal velocity" Vth . If this last 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 : Vth =
0.2 Vth cr
.
Fig. 9b : Matter alone.
Vth = 10 Vth cr
When a clump of matter forms (fig.9a),
the larger is the initial value of Vth, the larger is irs 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 2p 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
is the initial mass density r the faster is the process. Now
we consider a mixture of two species, normal matter (that we simply call matter)
and ghost matter, according to the interaction schema 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 matter plus ghost matter
V
th = 0.25 Vth cr : Joint gravitational
instability.
.
Fig.10b: Mixture matter plus ghost matter
Vth = 15 Vth cr**. The two species remain closely
mixed.**
