Long-Range Correlations in Self-Gravitating N-Body Systems

Observed self-gravitating systems reveal often fragmented non-equilibrium structures that feature characteristic long-range correlations. However, models accounting for non-linear structure growth are not always consistent with observations and a better understanding of self-gravitating $N$-body systems appears necessary. Because unstable gravitating systems are sensitive to non-gravitational perturbations we study the effect of different dissipative factors as well as different small and large scale boundary conditions on idealized $N$-body systems. We find, in the interval of negative specific heat, equilibrium properties differing from theoretical predictions made for gravo-thermal systems, substantiating the importance of microscopic physics and the lack of consistent theoretical tools to describe self-gravitating gas. Also, in the interval of negative specific heat, yet outside of equilibrium, unforced systems fragment and establish transient long-range correlations. The strength of these correlations depends on the degree of granularity, suggesting to make the resolution of mass and force coherent. Finally, persistent correlations appear in model systems subject to an energy flow.Comment: 20 pages, 21 figures. Accepted for publication in A&

Substellar fragmentation in self-gravitating fluids with a major phase transition

The existence of substellar cold H2 globules in planetary nebulae and the mere existence of comets suggest that the physics of cold interstellar gas might be much richer than usually envisioned. We study the case of a cold gaseous medium in ISM conditions which is subject to a gas-liquid/solid phase transition. First the equilibrium of general non-ideal fluids is studied using the virial theorem and linear stability analysis. Then the non-linear dynamics is studied by using simulations to characterize the expected formation of solid bodies analogous to comets. The simulations are run with a state of the art molecular dynamics code (LAMMPS). The long-range gravitational forces can be taken into account with short-range molecular forces with finite limited computational resources by using super-molecules, provided the right scaling is followed. The concept of super-molecule is tested with simulations, allowing us to correctly satisfy the Jeans instability criterion for one-phase fluids. The simulations show that fluids presenting a phase transition are gravitationally unstable as well, independent of the strength of the gravitational potential, producing two distinct kinds of sub-stellar bodies, those dominated by gravity ("planetoids") and those dominated by molecular attractive force ("comets"). Observations, formal analysis and computer simulations suggest the possibility of the formation of substellar H2 clumps in cold molecular clouds due to the combination of phase transition and gravity. Fluids presenting a phase transition are gravitationally unstable, independent of the strength of the gravitational potential. Arbitrarily small H2 clumps may form even at relatively high temperatures up to 400 - 600K, according to virial analysis. The combination of phase transition and gravity may be relevant for a wider range of astrophysical situations, such as proto-planetary disks.Comment: 24 pages, 44 figures. accepted for publication in A&

Solid H2 in the interstellar medium

Condensation of H 2 in the interstellar medium (ISM) has long been seen as a possibility, either by deposition on dust grains or thanks to a phase transition combined with self-gravity. H 2 condensation might explain the observed low efficiency of star formation and might help to hide baryons in spiral galaxies. Our aim is to quantify the solid fraction of H 2 in the ISM due to a phase transition including self-gravity for different densities and temperatures in order to use the results in more complex simulations of the ISM as subgrid physics. We used molecular dynamics simulations of fluids at different temperatures and densities to study the formation of solids. Once the simulations reached a steady state, we calculated the solid mass fraction, energy increase, and timescales. By determining the power laws measured over several orders of magnitude, we extrapolated to lower densities the higher density fluids that can be simulated with current computers. The solid fraction and energy increase of fluids in a phase transition are above 0.1 and do not follow a power law. Fluids out of a phase transition are still forming a small amount of solids due to chance encounters of molecules. The solid mass fraction and energy increase of these fluids are linearly dependent on density and can easily be extrapolated. The timescale is below one second, the condensation can be considered instantaneous. The presence of solid H 2 grains has important dynamic implications on the ISM as they may be the building blocks for larger solid bodies when gravity is included. We provide the solid mass fraction, energy increase, and timescales for high density fluids and extrapolation laws for lower densities.Comment: accepted for publication in A&

Bifurcation at Complex Instability

The properties of motion close to the transition of a stable family of periodic orbits to complex instability is investigated with two symplectic 4D mappings, natural extensions of the standard mapping. As for the other types of instabilities new families of periodic orbits may bifurcate at the transition; but, more generally, families of {\sl isolated invariant curves} bifurcate, similar to but distinct from a Hopf bifurcation. The evolution of the stable invariant curves and their bifurcations are described.Comment: 5 pages, self-unpacking uuencoded compressed Postscript, Contribution at the NATO ASI Conference on "Hamiltonian Systems with Three or More Degrees of Freedom, Barcelona, Spain, June 19-30, 199