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.
We examine the evolution of non-relativistic cold dark matter gravitationally coupled to baryons with modes deep inside the Hubble radius (sub-horizon regime) using akinetic theory approach within the realm of Newtonian theory. We obtain the general solution for the total density perturbation and we also show that a baryon perturbation catches up with the dark matter perturbation at late times, which in turn makes possible the formation of bound structures. We extend the linear perturbation analysis by considering the turn-around event, the collapse of matter, and its virialization process.
We study, using both theory and simulations, a system of self-gravitating sheets. A new statistical mechanics theory - free of any adjustable parameters - is derived to quantitatively predict the final stationary state achieved by this system after the process of collisionless relaxation is completed. The theory shows a very good agreement with the numerical simulations. The model sheds new light on the general mechanism of relaxation of self-gravitating systems and may help us to understand cold matter distribution in the Universe.
We study the vertical structure of polytropic, $P\propto ρ^Γ$, centrifugally-supported gaseous discs embedded in cold dark matter (CDM) halos. At fixed radius $R$, the shape of the vertical density profile depends only weakly on whether the disc is self-gravitating (SG) or not (NSG). The disc thickness, set by the midplane sound speed and circular velocity, $(c_s/V_c)R$, in the NSG case, and by the sound speed and surface density, $c_s^2/GΣ$, in SG discs, is smaller than either of these scales. SG discs are typically Toomre unstable, NSG discs are stable. Exponential discs in CDM halos with ro…
Massive stars shape the surrounding ISM by emitting ionizing photons and ejecting material through stellar winds. To study the impact of the momentum from the wind of a massive star on the surrounding neutral or ionized material, we implemented a new HEALPix-based momentum conserving wind scheme in the Smoothed Particle Hydrodynamics (SPH) code SEREN. A qualitative study of the impact of the feedback from an O7.5-like star on a self gravitating sphere shows that, on its own, the transfer of momentum from a wind onto cold surrounding gas has both a compressing and dispersing effect. It mostly a…
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 st…
We present hydrostatic equilibrium models of spherical, self-gravitating clouds of helium and molecular hydrogen, focusing on the cold, high-density regime where solid- or liquid-hydrogen can form. The resulting structures have masses from 0.1 Msun down to several x 1.e-8 Msun, and span a broad range of radii: 1.e-4 < R(AU) < 1.e7. Our models are fully convective, but all have a two-zone character with the majority of the mass in a small, condensate-free core, surrounded by a colder envelope where phase equilibrium obtains. Convection in the envelope is unusual in that it is driven by a mean-m…
We study analytically the collapse of an initially smooth, cold, self-gravitating collisionless system in one dimension. The system is described as a central "S" shape in phase-space surrounded by a nearly stationary halo acting locally like a harmonic background on the S. To resolve the dynamics of the S under its self-gravity and under the influence of the halo, we introduce a novel approach using post-collapse Lagrangian perturbation theory. This approach allows us to follow the evolution of the system between successive crossing times and to describe in an iterative way the interplay betwe…
We report results of a study of the Newtonian dynamics of N self-gravitating particles which start in a quasi-uniform spherical configuration, without initial velocities. These initial conditions would lead to a density singularity at the origin at a finite time when N \rightarrow \infty, but this singularity is regulated at any finite N (by the associated density fluctuations). While previous studies have focussed on the behaviour as a function of N of the minimal size reached during the contracting phase, we examine in particular the size and energy of the virialized halo which results. We f…
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 $τ_c$, 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 …
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. …
Initially far out-of-equilibrium self-gravitating systems form, through a collisionless relaxation dynamics, quasi-stationary states (QSS). These may arise from a bottom-up aggregation of structures or in a top-down frame; their quasi-equilibrium properties are well described by the Jeans equation and are not universal, i.e. they depend on initial conditions. To understand the origin of such dependence, we present results of numerical experiments of initially cold and spherical systems characterized by various choices of the spectrum of initial density fluctuations. The amplitude of such fluct…
We revisit the issue of relaxation to thermal equilibrium in the so-called "sheet model", i.e., particles in one dimension interacting by attractive forces independent of their separation. We show that this relaxation may be very clearly detected and characterized by following the evolution of order parameters defined by appropriately normalized moments of the phase space distribution which probe its entanglement in space and velocity coordinates. For a class of quasi-stationary states which result from the violent relaxation of rectangular waterbag initial conditions, characterized by their v…
The collapse of an isolated, uniform and spherical cloud of self-gravitating particles represents a paradigmatic example of a relaxation process leading to the formation of a quasi-stationary state in virial equilibrium. We consider several N-body simulations of such a system, with the initial velocity dispersion as a free parameter. We show that there is a clear difference between structures formed when the initial virial ratio is b_0 =2K_0/W_0 < b_0^c ~ -1/2 and b_0> b_0^c. These two sets of initial conditions give rise respectively to a mild and violent relaxation occurring in about the sam…
We simulate the evolution of one-dimensional gravitating collisionless systems from non- equilibrium initial conditions, similar to the conditions that lead to the formation of dark- matter halos in three dimensions. As in the case of 3D halo formation we find that initially cold, nearly homogeneous particle distributions collapse to approach a final equilibrium state with a universal density profile. At small radii, this attractor exhibits a power-law behavior in density, ρ(x) \propto |x|^(-γ_crit), γ_crit \simeq 0.47, slightly but significantly shallower than the value γ = 1/2 suggested prev…
The secular evolution of an infinitely thin tepid isolated galactic disc made of a finite number of particles is investigated using the inhomogeneous Balescu-Lenard equation expressed in terms of angle-action variables. The matrix method is implemented numerically in order to model the induced gravitational polarization. Special care is taken to account for the amplification of potential fluctuations of mutually resonant orbits and the unwinding of the induced swing amplified transients. Quantitative comparisons with ${N-}$body simulations yield consistent scalings with the number of particles…
The stability of radially anisotropic rotating stellar systems with a central density cusp
Consiglio Nazionale delle Ricerche, Istituto dei Sistemi Complessi（意大利国家研究委员会复杂系统研究所）；INFN – Sezione di Firenze（佛罗伦萨意大利国家核物理研究所）；INAF – Osservatorio Astrofisico di Arcetri（阿切特里天体物理观测台）；University of Edinburgh（爱丁堡大学）
The spiral structure of the Milky Way can be simulated by adopting percolation theory, where the active zones are produced by the evolution of many supernova (SN). Here we assume conversely that the percolative process is triggered by superbubbles (SB), the result of multiple SNs. A first thermal model takes into account a bursting phase which evolves in a medium with constant density, and a subsequent adiabatic expansion which evolves in a medium with decreasing density along the galactic height. A second cold model follows the evolution of an SB in an auto-gravitating medium in the framework…
An isolated, initially cold and ellipsoidal cloud of self-gravitating particles represents a relatively simple system to study the effects of the 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 particles energy change and thus determine the properties of the final energy distribution, particularly the appearance of two species of particles: bound and…
Prestellar cores are self-gravitating dense and cold structures within molecular clouds where future stars are born. They are expected, at the stage of transitioning to the protostellar phase, to harbor centrally concentrated dense (sub)structures that will seed the formation of a new star or the binary/multiple stellar systems. Characterizing this critical stage of evolution is key to our understanding of star formation. In this work, we report the detection of high density (sub)structures on the thousand-au scale in a sample of dense prestellar cores. Through our recent ALMA observations tow…
Filaments are key for star formation models. As part of the study carried out by the Herschel GCC Programme, here we study the filament properties presented in GCC.VII in context with theoretical models of filament formation and evolution. A conservative sample of filaments at a distance D<500pc was extracted with the Getfilaments algorithm. Their physical structure was quantified according to two main components: the central (Gaussian) region (core component), and the power-law like region dominating the filament column density profile at larger radii (wing component). The properties and beha…
(Abridged) Extensions of the standard model of particle physics predict very light bosons, ranging from about 10^{-5} eV for the QCD axion to 10^{-33} eV for ultra-light particles, which could be the cold dark matter (CDM) in the Universe. If so, their phase-space density must be high enough to form a Bose-Einstein condensate (BEC). The fluid-like nature of BEC-CDM dynamics differs from that of standard collisionless CDM (sCDM), so observations of galactic haloes may distinguish them. sCDM has problems with galaxy observations on small scales, which BEC-CDM may overcome for a large range of pa…
This chapter reviews the nature of turbulence in the Galactic interstellar medium (ISM) and its connections to the star formation (SF) process. The ISM is turbulent, magnetized, self-gravitating, and is subject to heating and cooling processes that control its thermodynamic behavior. The turbulence in the warm and hot ionized components of the ISM appears to be trans- or subsonic, and thus to behave nearly incompressibly. However, the neutral warm and cold components are highly compressible, as a consequence of both thermal instability in the atomic gas and of moderately-to-strongly supersonic…
Self-gravitating astronomical objects often show a central plateau in the density profile (core) whose physical origin is hotly debated. Cores are theoretically expected in N-body systems of maximum entropy, however, they are not present in the canonical N-body numerical simulations of cold dark matter (CDM). Our work shows that despite this apparent contradiction between theory and numerical simulations, they are fully consistent. Simply put, cores are characteristic of systems in thermodynamic equilibrium, but thermalizing collisions are purposely suppressed in CDM simulations. When collisio…
We present numerical experiments aimed to study the correlation between the magnetic field strength, $B$, and the density, $n$, in the cold atomic interstellar medium (CNM). We analyze 24 magneto-hydrodynamic models with different initial magnetic field intensities ($B_0=$0.4, 2.1, 4.2, and 8.3 $μ$G) and/or mean densities (2, 3, and 4 cm$^{-3}$), in the presence of driven and decaying turbulence, with and without self-gravity, in a cubic computational domain with 100 pc by side. Our main findings are: i) For forced simulations, which reproduce the main observed physical conditions of the CNM i…
