Gravitational Wave Signals from Chaotic System: A Point Mass with A Disk

We study gravitational waves from a particle moving around a system of a point mass with a disk in Newtonian gravitational theory. A particle motion in this system can be chaotic when the gravitational contribution from a surface density of a disk is comparable with that from a point mass. In such an orbit, we sometimes find that there appears a phase of the orbit in which particle motion becomes to be nearly regular (the so-called ``stagnant motion'') for a finite time interval between more strongly chaotic phases. To study how these different chaotic behaviours affect on observation of gravitational waves, we investigate a correlation of the particle motion and the waves. We find that such a difference in chaotic motions reflects on the wave forms and energy spectra. The character of the waves in the stagnant motion is quite different from that either in a regular motion or in a more strongly chaotic motion. This suggests that we may make a distinction between different chaotic behaviours of the orbit via the gravitational waves.Comment: Published in Phys.Rev.D76:024018,200

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

A new algorithm for anisotropic solutions

We establish a new algorithm that generates a new solution to the Einstein field equations, with an anisotropic matter distribution, from a seed isotropic solution. The new solution is expressed in terms of integrals of an isotropic gravitational potential; and the integration can be completed exactly for particular isotropic seed metrics. A good feature of our approach is that the anisotropic solutions necessarily have an isotropic limit. We find two examples of anisotropic solutions which generalise the isothermal sphere and the Schwarzschild interior sphere. Both examples are expressed in closed form involving elementary functions only.Comment: 16 pages, to appear in Pramana - J. Phy

Anisotropic static solutions in modelling highly compact bodies

Einstein field equations for anisotropic spheres are solved and exact interior solutions obtained. This paper extends earlier treatments to include anisotropic models which accommodate a wider variety of physically viable energy densities. Two classes of solutions are possible. The first class contains the limiting case $\mu\propto r^{-2}$ for the energy density which arises in many astrophysical applications. In the second class the singularity at the center of the star is not present in the energy density. The models presented in this paper allow for increasing and decreasing profiles in the behavior of the energy density.Comment: 9 pages, to appear in Pramana - J. Phy

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 $t$ 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 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

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

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

Mechanisms of the Vertical Secular Heating of a Stellar Disk

We investigate the nonlinear growth stages of bending instability in stellar disks with exponential radial density profiles.We found that the unstable modes are global (the wavelengths are larger than the disk scale lengths) and that the instability saturation level is much higher than that following from a linear criterion. The instability saturation time scales are of the order of one billion years or more. For this reason, the bending instability can play an important role in the secular heating of a stellar disk in the $z$ direction. In an extensive series of numerical $N$-body simulations with a high spatial resolution, we were able to scan in detail the space of key parameters (the initial disk thickness $z_0$, the Toomre parameter $Q$, and the ratio of dark halo mass to disk mass $M_{\rm h} / M_{\rm d}$). We revealed three distinct mechanisms of disk heating in the $z$ direction: bending instability of the entire disk, bending instability of the bar, and heating on vertical inhomogeneities in the distribution of stellar matter.Comment: 22 pages including 8 figures. To be published in Astronomy Letters (v.29, 2003