*We describe how a simple class of out of equilibrium, rotating and asymmetrical mass distributions evolve under their self-gravity to produce a quasi-planar spiral structure surrounding a virialized core, qualitatively resembling a spiral galaxy. The spiral structure is transient, but can survive tens of dynamical times, and further reproduces qualitatively noted features of spiral galaxies as the predominance of trailing two-armed spirals and large pitch angles. As our models are highly idealized, a detailed comparison with observations is not appropriate, but generic features of the velocity distributions can be identified to be potential observational signatures of such a mechanism. Indeed, the mechanism leads generically to a characteristic transition from predominantly rotational motion, in a region outside the core, to radial ballistic motion in the outermost parts. Such radial motions are excluded in our Galaxy up to 15 kpc, but could be detected at larger scales in the future by GAIA. We explore the apparent motions seen by external observers of the velocity distributions of our toy galaxies, and find that it is difficult to distinguish them from those of a rotating disc with sub-dominant radial motions at levels typically inferred from observations. These simple models illustrate the possibility that the observed apparent motions of spiral galaxies might be explained by non-trivial non-stationary mass and velocity distributions without invoking a dark matter halo or modification of Newtonian gravity. In this scenario the observed phenomenological relation between the centripetal and gravitational acceleration of the visible baryonic mass could have a simple explanation.*

# Category Archives: Highlights on physics papers

# Particle number dependence in the non-linear evolution of N-body self-gravitating systems

**Title**: Particle number dependence in the non-linear evolution of N-body

self-gravitating systems

**Authors**: David Benhaiem, Michael Joyce, Francesco Sylos Labini and Tirawut

Worrakitpoonpon

**Categories**: astro-ph.CO

**Comments**: 8 pages, 5 figures; to appear in MNRAS

**License**: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

https://arxiv.org/abs/1709.06657

Simulations of purely self-gravitating N-body systems are often used in

astrophysics and cosmology to study the collisionless limit of such systems.

Their results for macroscopic quantities should then converge well for

sufficiently large N. Using a study of the evolution from a simple space of

spherical initial conditions – including a region characterised by so-called

“radial orbit instability” – we illustrate that the values of N at which such

convergence is obtained can vary enormously. In the family of initial

conditions we study, good convergence can be obtained up to a few dynamical

times with N $ \sim 10^3$ – just large enough to suppress two body relaxation –

for certain initial conditions, while in other cases such convergence is not

attained at this time even in our largest simulations with N $\sim 10^5$. The

qualitative difference is due to the stability properties of fluctuations

introduced by the N-body discretisation, of which the initial amplitude depends

on N. We discuss briefly why the crucial role which such fluctuations can

potentially play in the evolution of the N-body system could, in particular,

constitute a serious problem in cosmological simulations of dark matter.

# Dynamics of self-gravitating systems

It was a long time that I wanted to fix the webpages about my research activity. Now I have done a first rough step in the organization of them… more is to come. This is the main one while the sub-pages are the following:

# Formation of satellites from cold collapse

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.

# 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.