Simulation and Visualization of Selfgravitating
N-particle System
Mladen Martinis and Marin Šošić
Theoretical Physics Division
Ruđer Bošković Institute, Zagreb, Croatia
When we observe the universe we see structures
on essentially all scales. The large distribution of
matter in the universe as traced by visible (red shift surway) galaxy
structures shows a complex irregular pattern, characterized by clusters of
galaxies which are organized in filaments and walls around large voids.The most widely used tool to study these structures is by means of
gravitational N-body simulations1.
During simulation, the structures form and evolve from
a given initial state (generally unknown) according to the law of Newtonian
gravity. The long-range character of the gravity, however, produces several
peculiarities in statistical behaviors of the
system that are totally different from usual systems.These are the ensembles inequivalence, negative specific
heat, non-extensive thermodynamics, strong dependence on N, large fluctuations, self-consistent
chaos, slow relaxation, and formation of
structures. Some years ago a detailed two
point correlation analysis of galaxy clustering2 showed that galaxy
correlation properties are similar to
those of a fractal, self-similar object with fractal dimension D ~ 2. Since the
evidence for scale-invariance of highly irregular galaxy distributions with
large structures and voids strongly depends on the appropriate choice of two
point correlation analysis, we studied various two point correlation estimators
to find that only Ripley's K-function minus estimator gives the correct fractal dimension of an arbitrary 3-d
disrtibution of point particles. The test
is performed first on the Menger's sponge
model with a known fractal distribution of point particles, for which we also developed
a small 3-d visualization program RoPo (Rotate Points)3. K-minus
estimator was then applied to 2dF
(Two-Degree Field) catalogue data.
1
S. J.
Aarseth: Gravitational N-Body
Simulations. Tools and Algorithms. Cambridge University Press, 2003
3 Available upon request from martinis@irb.hr. Bugs should be reported to marin.sosic@zg.htnet.hr