We study the collapse of an isolated, initially cold, irregular (but almost spherical) and (slightly) inhomogeneous cloud of self-gravitating particles. The cloud is driven towards a virialized quasi-equilibrium state by a fast relaxation mechanism, occurring in a typical time τc, whose signature is a large change in the particle energy distribution. Post-collapse particles are divided into two main species: bound and free, the latter being ejected from the system. Because of the initial system’s anisotropy, the time varying gravitational field breaks spherical symmetry so that the ejected mass can carry away angular momentum and the bound system can gain a non-zero angular momentum. In addition, while strongly bound particles form a compact core, weakly bound ones may form, in a time scale of the order of τc, several satellite sub-structures. These satellites have a finite lifetime that can be longer than τc and generally form a flattened distribution. Their origin and their abundance are related to the amplitude and nature of initial density fluctuations and to the initial cloud deviations from spherical symmetry, which are both amplified during the collapse phase. Satellites show a time dependent virial ratio that can be different from the equilibrium value b≈−1: although they are bound to the main virialized object, they are not necessarily virially relaxed.

# Category Archives: Highlights on physics papers

# Stable clustering and the resolution of dissipationless cosmological N-body simulations

# Gravitational structure via violent relaxation

Talk given at the workshop

# The secular evolution of self-gravitating systems over cosmic ages

Abstract.

*Isolated, initially cold and spherically symmetric self-gravitating systems may give rise to a virial equilibrium state which is far from spherically symmetric, and typically triaxial, and with no-zero angular momentum. We discuss the main features of the dynamical mechanism that gives rise to such a quasi-stationary configuration stressing the potential interest from an observational point of view.*

# The secular evolution of self-gravitating systems over cosmic ages

I will participate to the meeting

# The secular evolution of self-gravitating systems over cosmic ages

These are the title and abstract of my talk:

**Gravitational structure formation via violent relaxation**

*Isolated, initially cold and spherically symmetric self-gravitating systems may give rise to a virial equilibrium state which is far from spherically symmetric, and typically triaxial, and with no-zero angular momentum. We discuss the main features of the dynamical mechanism that gives rise to such a quasi-stationary configuration stressing the potential interest from an observational point of view.*

# On the origin of the angular momentum of galaxies

The **angular momentum** is a conserved quantity and the usual theoretical interpretation of the origin of the angular momentum of galaxies is that this is originated by from tidal interactions of the galaxy with its neighborhoods. We propose in this paper (in print in **Astronomy and Astrophysics**) a new mechanism for its origin based that can be efficient also for the case of an isolated object (or for an object with small tidal interactions). The **new mechanism** works as follows : during the violent relaxation of an isolated self-gravitating system a significant fraction of its mass may be ejected. If the time varying gravitational field also breaks spherical symmetry this mass can potentially carry angular momentum. Thus starting initial configurations with zero angular momentum can in principle lead to a bound virialized system with non-zero angular momentum even though the overall angular momentum is conserved. A simple picture of this mechanism is illustrated in the following figure. The astrophysical and cosmological implications of such a fundamental physical process will be subject of a forthcoming work.

(For more details see http://lanl.arxiv.org/abs/1505.03371 now in press in Astronomy and Astrophysics)

# Angular momentum generation in cold gravitational collapse

During the violent relaxation of a self-gravitating system a significant fraction of its mass may be ejected. If the time varying gravitational field also breaks spherical symmetry this mass can potentially carry angular momentum. Thus starting initial configurations with zero angular momentum can in principle lead to a bound virialized system with non-zero angular momentum. We explore here, using numerical simulations, how much angular momentum can be generated in a virialized structure in this way, starting from configurations of cold particles which are very close to spherically symmetric. For initial configurations in which spherical symmetry is broken only by the Poissonian fluctuations associated with the finite particle number N, with N in range 1000 to 100000, we find that the relaxed structures have standard “spin” parameters λ∼0,001 and decreasing slowly with N. For slightly ellipsoidal initial conditions, in which the finite-N fluctuations break the residual reflection symmetries, we observe values λ∼0,01 i.e. of the same order of magnitude as those reported for elliptical galaxies and dark matter halos in cosmological simulations. The net angular momentum vector is typically aligned close to normal to the major semi-axis of the triaxial relaxed structure, and also with that of the ejected mass. This simple mechanism may provide an alternative, or complement, to “tidal torque theory” for understanding the origin of angular momentum in astrophysical structures.

# On the generation of triaxiality in the collapse of cold spherical self-gravitating systems

Initially cold and spherically symmetric self-gravitating systems may give rise to a virial equilibrium state which is far from spherically symmetric, and typically triaxial. We focus here on how the degree of symmetry breaking in the final state depends on the initial density profile. We note that the most asymmetric structures result when, during the collapse phase, there is a strong injection of energy preferentially into the particles which are localized initially in the outer shells. These particles are still collapsing when the others, initially located in the inner part, are already re-expanding; the motion of particles in a time varying potential allow them to gain kinetic energy — in some cases enough to be ejected from the system. We show that this mechanism of energy gain amplifies the initial small deviations from perfect spherical symmetry due to finite N fluctuations. This amplification is more efficient when the initial density profile depends on radius, because particles have a greater spread of fall times compared to a uniform density profile, for which very close to symmetric final states are obtained}. These effects lead to a distinctive correlation of the orientation of the final structure with the distribution of ejected mass, and also with the initial (very small) angular fluctuations.

# Violent relaxation of ellipsoidal clouds

David Benhaiem and Francesco Sylos Labini

An isolated, initially cold and ellipsoidal cloud of self-gravitating particles represents a relatively simple system in which to study the effects of deviations from spherical symmetry in the mechanism of violent relaxation. Initial deviations from spherical symmetry are shown to play a dynamical role that is equivalent to that of density fluctuations in the case of an initially spherical cloud. Indeed, these deviations control the amount of particle-energy change and thus determine the properties of the final energy distribution, particularly the appearance of two species of particles: bound and free. Ejection of mass and energy from the system, together with the formation of a density profile decaying as ρ(*r*) ∼ *r*^{−4} and a Keplerian radial velocity dispersion profile, are prominent features similar to those observed after the violent relaxation of spherical clouds. In addition, we find that ejected particles are characterized by highly non-spherical shapes, the features of which can be traced in the initial deviations from spherical symmetry that are amplified during the dynamical evolution: particles can indeed form anisotropic configurations, like bars and/or discs, even though the initial cloud was very close to spherical.

# The Scientific Competitiveness of Nations

Andrea Gabrielli, Francesco Sylos Labini

**Published: December 10, 2014 DOI: 10.1371/journal.pone.0113470**

**“Diversification thus represents the key element that correlates with scientific and technological competitiveness.”**

# The Scientific Competitivness of Nations

by Giulio Cimini, Andrea Gabrielli and Francesco Sylos Labini,

**PLOS one i in the press **

We use citation data of scientific articles produced by individual nations in different scientific domains to determine the structure and efficiency of national research systems. We characterize the scientific fitness of each nation−that is, the competitiveness of its research system−and the complexity of each scientific domain by means of a non-linear iterative algorithm able to assess quantitatively the advantage of scientific diversification. We find that technological leading nations, beyond having the largest production of scientific papers and the largest number of citations, do not specialize in a few scientific domains. Rather, they diversify as much as possible their research system. On the other side, less developed nations are competitive only in scientific domains where also many other nations are present. Diversification thus represents the key element that correlates with scientific and technological competitiveness. A remarkable implication of this structure of the scientific competition is that the scientific domains playing the role of “markers” of national scientific competitiveness are those not necessarily of high technological requirements, but rather addressing the most “sophisticated” needs of the society.