244 research outputs found
Universality of power law correlations in gravitational clustering
We present an analysis of different sets of gravitational N-body simulations,
all describing the dynamics of discrete particles with a small initial velocity
dispersion. They encompass very different initial particle configurations,
different numerical algorithms for the computation of the force, with or
without the space expansion of cosmological models. Despite these differences
we find in all cases that the non-linear clustering which results is
essentially the same, with a well-defined simple power-law behaviour in the
two-point correlations in the range from a few times the lower cut-off in the
gravitational force to the scale at which fluctuations are of order one. We
argue, presenting quantitative evidence, that this apparently universal
behaviour can be understood by the domination of the small scale contribution
to the gravitational force, coming initially from nearest neighbor particles.Comment: 7 pages, latex, 3 postscript figures. Revised version to be published
in Europhysics Letters. Contains additional analysis showing more directly
the central role of nearest neighbour interactions in the development of
power-law correlation
Renormalization Group Flow and Fragmentation in the Self-Gravitating Thermal Gas
The self-gravitating thermal gas (non-relativistic particles of mass m at
temperature T) is exactly equivalent to a field theory with a single scalar
field phi(x) and exponential self-interaction. We build up perturbation theory
around a space dependent stationary point phi_0(r) in a finite size domain
delta \leq r \leq R ,(delta << R), which is relevant for astrophysical applica-
tions (interstellar medium,galaxy distributions).We compute the correlations of
the gravitational potential (phi) and of the density and find that they scale;
the latter scales as 1/r^2. A rich structure emerges in the two-point correl-
tors from the phi fluctuations around phi_0(r). The n-point correlators are
explicitly computed to the one-loop level.The relevant effective coupling turns
out to be lambda=4 pi G m^2 / (T R). The renormalization group equations (RGE)
for the n-point correlator are derived and the RG flow for the effective
coupling lambda(tau) [tau = ln(R/delta), explicitly obtained.A novel dependence
on tau emerges here.lambda(tau) vanishes each time tau approaches discrete
values tau=tau_n = 2 pi n/sqrt7-0, n=0,1,2, ...Such RG infrared stable behavior
[lambda(tau) decreasing with increasing tau] is here connected with low density
self-similar fractal structures fitting one into another.For scales smaller
than the points tau_n, ultraviolet unstable behaviour appears which we connect
to Jeans' unstable behaviour, growing density and fragmentation. Remarkably, we
get a hierarchy of scales and Jeans lengths following the geometric progression
R_n=R_0 e^{2 pi n /sqrt7} = R_0 [10.749087...]^n . A hierarchy of this type is
expected for non-spherical geometries,with a rate different from e^{2 n/sqrt7}.Comment: LaTex, 31 pages, 11 .ps figure
Clustering in gravitating N-body systems
We study gravitational clustering of mass points in three dimensions with
random initial positions and periodic boundary conditions (no expansion) by
numerical simulations. Correlation properties are well defined in the system
and a sort of thermodynamic limit can be defined for the transient regime of
cluste ring. Structure formation proceeds along two paths: (i) fluid-like
evolution of density perturbations at large scales and (ii) shift of the
granular (non fluid) properties from small to large scales. The latter
mechanism finally dominates at all scales and it is responsible for the
self-similar characteristics of the clustering.Comment: 7 pages, 3 figures. Accepted for publication in Europhys. Let
The Galaxy Distribution Function from the 2MASS Survey
We determine the spatial distribution function of galaxies from a wide range
of samples in the 2MASS survey. The results agree very well with the form of
the distribution predicted by the theory of cosmological gravitational
many-body galaxy clustering. On large scales we find a value of the clustering
parameter b = 0.867 +/- 0.026, in agreement with b = 0.83 +/- 0.05 found
previously for the Pisces-Perseus supercluster. We measure b(theta) as a
function of scale, since this is a powerful test of the applicability of
computer simulations. The results suggest that when galaxies clustered they
were usually surrounded by individual, rather than by communal haloes.Comment: Astrophysical Journal, accepted: 14 pages with 23 embedded reduced
resolution Postscript figures & 2 table
Free streaming in mixed dark matter
Free streaming in a \emph{mixture} of collisionless non-relativistic dark
matter (DM) particles is studied by implementing methods from the theory of
multicomponent plasmas. The mixture includes Fermionic, condensed and non
condensed Bosonic particles decoupling in equilibrium while relativistic, heavy
non-relativistic thermal relics (WIMPs), and sterile neutrinos that decouple
\emph{out of equilibrium} when they are relativistic. The free-streaming length
is obtained from the marginal zero of the gravitational
polarization function, which separates short wavelength Landau-damped from long
wavelength Jeans-unstable \emph{collective} modes. At redshift we find ,where are the \emph{fractions} of the respective DM components of mass
that decouple when the effective number of ultrarelativistic degrees of
freedom is , and only depend on the distribution functions at
decoupling, given explicitly in all cases. If sterile neutrinos produced either
resonantly or non-resonantly that decouple near the QCD scale are the
\emph{only} DM component,we find (non-resonant), (resonant).If WIMPs with
decoupling at are present in the mixture with
, is \emph{dominated} by CDM. If a Bose Einstein condensate is a DM
component its free streaming length is consistent with CDM because of the
infrared enhancement of the distribution function.Comment: 19 pages, 2 figures. More discussions same conclusions and results.
Version to appear in Phys. Rev.
Inhomogeneous imperfect fluid spherical models without Big-Bang singularity
So far all known singularity-free cosmological models are cylindrically
symmetric. Here we present a new family of spherically symmetric non-singular
models filled with imperfect fluid and radial heat flow, and satisfying the
weak and strong energy conditions. For large anisotropy in pressure and
heat flux tend to vanish leading to a perfect fluid. There is a free function
of time in the model, which can be suitably chosen for non-singular behaviour
and there exist multiplicity of such choices.Comment: 8 pages, LaTeX versio
Clustering of Primordial Black Holes. II. Evolution of Bound Systems
Primordial Black Holes (PBHs) that form from the collapse of density
perturbations are more clustered than the underlying density field. In a
previous paper, we showed the constraints that this has on the prospects of PBH
dark matter. In this paper we examine another consequence of this clustering:
the formation of bound systems of PBHs in the early universe. These would
hypothetically be the earliest gravitationally collapsed structures, forming
when the universe is still radiation dominated. Depending upon the size and
occupation of the clusters, PBH merging occurs before they would have otherwise
evaporated due to Hawking evaporation.Comment: 23 pages, 1 figure. Submitted to PR
Gravitational Dynamics of an Infinite Shuffled Lattice: Particle Coarse-grainings, Non-linear Clustering and the Continuum Limit
We study the evolution under their self-gravity of infinite ``shuffled
lattice'' particle distributions, focussing specifically on the comparison of
this evolution with that of ``daughter'' particle distributions, defined by a
simple coarse-graining procedure. We consider both the case that such
coarse-grainings are performed (i) on the initial conditions, and (ii) at a
finite time with a specific additional prescription. In numerical simulations
we observe that, to a first approximation, these coarse-grainings represent
well the evolution of the two-point correlation properties over a significant
range of scales. We note, in particular, that the form of the two-point
correlation function in the original system, when it is evolving in the
asymptotic ``self-similar'' regime, may be reproduced well in a daughter
coarse-grained system in which the dynamics are still dominated by two-body
(nearest neighbor) interactions. Using analytical results on the early time
evolution of these systems, however, we show that small observed differences
between the evolved system and its coarse-grainings at the initial time will in
fact diverge as the ratio of the coarse-graining scale to the original
inter-particle distance increases. The second coarse-graining studied,
performed at a finite time in a specified manner, circumvents this problem. It
also makes more physically transparent why gravitational dynamics from these
initial conditions tends toward a ``self-similar'' evolution. We finally
discuss the precise definition of a limit in which a continuum (specifically
Vlasov-like) description of the observed linear and non-linear evolution should
be applicable.Comment: 21 pages, 8 eps figures, 2 jpeg figures (available in high resolution
at http://pil.phys.uniroma1.it/~sylos/PRD_dec_2006/
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