Matter ghost matter astrophysics.6:
Spiral structure.(p5)
- An attempt to convert
these analytical results into numerical simulation machinery.
The following pictures shows a
non-rotating system, with initial conditions as given by a solution of this
Eddington-like solution. F.Lhanseat checked that it remained steady. For a
given choice of parameters ( 
= 1
, 
= 3, 
= 1,
= 1 ) we get the following solution (figures 8 and 9). The figure 5 shows the mass
densities 
(
)
and - 
(),
versus radial (adimensional) distance
(the unity corresponds to the Jeans
length). The figure 9 gives the corresponding gravitational potential, in
arbitrary units.
Fig. 8 : Steady-state
solution. Mass-densities
r
and r*.
Fig. 9 : Gravitational
potential
The characteristic thermal velocities
in the two sub-systems 2d galaxy and 2d anti-galaxy, are chosen equal
(
= 1 ). The characteristic lengths
of the two coupled solutions, are both chosen equal to the Jean's length Lj
of the first population (positive masses), which corresponds to the choice
= 1, = 1
The chosen ratio of the mass
densities is :
About the boundary problem see
references [1] and [2].
Fig. 10-a : In the first
2d fold, positive mass distribution,
according to the chosen analytical
solution (see above)
F.Lhanseat checked, through numerical
solution, that it corresponded to acceptable initial quasi steady-state conditions.
He used two populations of 10,000 mass-points, sprayed over space, in order
to fit analytical data. The first describes the positive mass distribution
and the second the negative mass distribution. As the number of masses were
basicly equal in his program, he introduced :
m* = - m
The intial
situation corresponds to the figures 10-a, 10-b and 10-c.
