A new family of nonrelativistic, Newtonian, non-quantum equilibrium configurations describing galactic halos is introduced, by considering strange quark matter conglomerates with masses larger than about 8 GeV as new possible components of the dark matter. Originally introduced to explain the state of matter in neutron stars, such conglomerates may also form in the high-density and temperature conditions of the primordial Universe and then decouple from ordinary baryonic matter, providing the fundamental components of dark matter for the formation of pristine gravitational potential wells and the subsequent evolution of cosmic structures. The obtained results for halo mass and radius are consistent with the rotational velocity curve observed in the Galaxy. Additionally, the average density of such dark matter halos is similar to that derived for halos of dwarf spheroidal galaxies, which can therefore be interpreted as downscaled versions of larger dark matter distributions around Milky Way-sized galaxies and hint for a common origin of the two families of cosmic structures.
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.
The relation between properties of galaxies and dark matter halos they reside in can be valuable for structure formation and evolution. This paper focus on the baryonic-to-halo mass ratio (BHMR) and its evolution. We first review unique properties of self-gravitating collisionless dark matter flow (SG-CFD), followed by their application to derive BHMR. To maximize system entropy, the long-range interaction requires a broad size of halos to be formed. These halos facilitate inverse mass and energy cascade from small to large scales with a constant rate of energy cascade $\varepsilon_u$. In addi…
Halo-mediated mass and energy cascades are key to understand dark matter flow. Both cascades origin from the mass exchange between halo and out-of-halo sub-systems. Kinetic energy can be from the motion of halos and particle motion in halos. Similarly, potential energy can be due to the inter- and intra-halo interactions. Intra-halo virial equilibrium is established much faster than inter-halo. Change of energy of entire system comes from virilization in halos. At statistically steady state, continuous mass exchange is required to sustain growth of total halo mass $M_h\propto a^{1/2}$ and ener…
We study the Jeans mass-radius relation of Bose-Einstein condensate dark matter in Newtonian gravity. We show at a general level that it is similar to the mass-radius relation of Bose-Einstein condensate dark matter halos [P.H. Chavanis, Phys. Rev. D {\bf 84}, 043531 (2011)]. Bosons with a repulsive self-interaction generically evolve from the Thomas-Fermi regime to the noninteracting regime as the Universe expands. In the Thomas-Fermi regime, the Jeans radius remains approximately constant while the Jeans mass decreases. In the noninteracting regime, the Jeans radius increases while the Jeans…
Observational studies of nearby galaxies have demonstrated correlations between the mass of the central supermassive black holes (BHs) and properties of the host galaxies, notably the stellar bulge mass or central stellar velocity dispersion. Motivated by these correlations, the theoretical paradigm has emerged, in which BHs and bulges co-evolve. However, this picture was challenged by observational and theoretical studies, which hinted that the fundamental connection may be between BHs and dark matter halos, and not necessarily with their host galaxies. Based on a study of 3130 elliptical gal…
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…
Gravitational instability is a key process that may lead to fragmentation of gaseous structures (sheets, filaments, haloes) in astrophysics and cosmology. We introduce here a method to derive analytic expressions for the growth rate of gravitational instability in a plane stratified medium. We consider a pressure-confined, static, self-gravitating fluid of arbitrary polytropic exponent, with both free and rigid boundary conditions. The method we detail here can naturally be generalised to analyse the stability of more complex systems. Our analytical results are in excellent agreement with nume…
The field which binds a thermal fermionic cloud is defined as a Hartree integral upon its density. In turn, the density results from the field via a Thomas-Fermi occupation of the local phase space. This defines a complete theory of all properties and observables for the cloud. As an application to dark matter halos, comparisons with astronomic data on dwarf spheroidal galaxies are provided and discussed. Estimates of the elementary fermion mass are obtained, serving as a phase-space bound on fermionic dark matter.
Cosmological N-body simulations have revealed many empirical relationships of dark matter halos, yet the physical origin of these halo properties still remains unclear. On the other hand, the attempts to establish the statistical mechanics for self-gravitating systems have encountered many formal difficulties, and little progress has been made for about fifty years. The aim of this work is to strengthen the validity of the statistical-mechanical approach we have proposed previously to explain the dark matter halo properties. By introducing an effective pressure instead of the radial pressure t…
Previously, we showed that surface density profiles of the form of a power-law times a Sersic function satisfy the hydrostatic Jeans equations, a variety of observational constraints, and the condition of a minimal radial entropy profile in two-dimensional galaxy discs with fixed power-law, halo potentials. It was assumed that such density profiles are generated by star scattering by clumps, waves, or other inhomogeneities. Here we generalize these models to self-gravitating discs. The cylindrically symmetric Poisson equation imposes strong constraints. Scattering processes favor smoothness, s…
(abbreviated) The statistical mechanics of self-gravitating systems is a long-held puzzle. In this work, we employ a phenomenological entropy form of ideal gas, first proposed by White & Narayan, to revisit this issue. By calculating the first-order variation of the entropy, subject to the mass- and energy-conservation constraints, we obtain an entropy stationary equation. Incorporated with the Jeans equation, and by specifying some functional form for the anisotropy parameter beta, we numerically solve the two equations, and demonstrate that the velocity anisotropy parameter plays an importan…
Self-gravitating Bose-Einstein condensates (BEC) have been proposed in various astrophysical contexts, including Bose-stars and BEC dark matter halos. These systems are described by a combination of the Gross-Pitaevskii and Poisson equations (the GPP system). In the analysis of these hypothetical objects, the Thomas-Fermi (TF) approximation is widely used. This approximation is based on the assumption that in the presence of a large number of particles, the kinetic term in the Gross-Pitaevskii energy functional can be neglected, yet it is well known that this assumption is violated near the co…
This paper studies the scale and redshift variation of density and velocity distributions in self-gravitating collisionless dark matter flow by a halo-based non-projection approach. All particles are divided into halo and out-of-halo particles for redshift variation of distributions. Without projecting particle fields onto a structured grid, the scale variation is analyzed by identifying all particle pairs on different scales $r$. We demonstrate that: i) Delaunay tessellation can be used to reconstruct the density field. The density correlation, spectrum, and dispersion functions were obtained…
In this paper, we consider the problem of the evolution of the disk subsystem of galaxies in view of the halo. To this end, we have studied the dependence of the evolution of a non-linearly non-radially disk oscillating in its plane depending on the basic parameters of the dark matter halo numerically. The dark matter halo stabilizes the instabilities in the plane of the disk, but destabilizes its vertical oscillations. The global disk structure is dependent strongly on the mass and shape of the of dark matter halo. The evolutionary dependence of the oscillation process of a self-gravitating d…
Essay selected for Honorable mention 2014 by the Gravity Research Foundation. We study an isothermal system of semi-degenerate self-gravitating fermions in General Relativity (GR). The most general solutions present mass density profiles with a central degenerate compact core governed by quantum statistics followed by an extended plateau, and ending in a power law behaviour $r^{-2}$. By fixing the fermion mass $m$ in the keV regime, the different solutions depending on the free parameters of the model: the degeneracy and temperature parameters at the center, are systematically constructed alon…
We develop the kinetic theory of classical and quantum particles (fermions and bosons) in gravitational interaction. The kinetic theory of quantum particles may have applications in the context of dark matter. For simplicity, we consider an infinite and spatially homogeneous system (or make a local approximation) and neglect collective effects. This leads to the quantum Landau equation derived heuristically in [Chavanis, Physica A 332, 89 (2004)]. We establish its main properties: conservation laws, $H$-theorem, equilibrium state, relaxation time, quantum diffusion and friction coefficients, q…
Recent developments in computer hardware and software enable researchers to simulate the self-gravitating evolution of galaxies at a resolution comparable to the actual number of stars. Here we present the results of a series of such simulations. We performed $N$-body simulations of disk galaxies with between 100 and 500 million particles over a wide range of initial conditions. Our calculations include a live bulge, disk, and dark matter halo, each of which is represented by self-gravitating particles in the $N$-body code. The simulations are performed using the gravitational $N$-body tree-co…
Self-gravitating Newtonian systems consisting of a very large number of particles have generally defied attempts to describe them using statistical mechanics. This is paradoxical since many astronomical systems, or simulations thereof, appear to have universal, equilibrium structures for which no physical basis exist. A decade ago we showed that extremizing the number of microstates with a given energy per unit mass, under the constraints of conserved total energy and mass, leads to the maximum entropy state, $n(E) \propto \exp (-β(E-Φ_0))-1$, known as DARKexp. This differential energy distrib…
We completed the development of simulation code that is designed to study the behavior of a conjectured dark matter galactic halo that is in the form of a Bose-Einstein Condensate (BEC). The BEC is described by the Gross-Pitaevskii equation, which can be solved numerically using the Crank-Nicholson method. The gravitational potential, in turn, is described by Poisson's equation, that can be solved using the relaxation method. Our code combines these two methods to study the time evolution of a self-gravitating BEC. The inefficiency of the relaxation method is balanced by the fact that in subse…
The statistical mechanics of self-gravitating systems has not been well understood, and still remains an open question so far. In a previous study by Kang & He, we showed that the fluid approximation may give a clue to further investigate this problem. In fact, there are indeed many dynamical similarities between self-gravitating and fluid systems. Based on a fluid-like entropy, that work explained successfully the outer density profiles of dark matter halos, but there left some drawbacks with the calculation concerning extremizing process of the entropy. In the current paper, with the improve…
We construct a series of model galaxies in rotational equilibrium consisting of gas, stars, and a fixed dark matter (DM) halo and study how these equilibrium systems depend on the mass and form of the DM halo, gas temperature, non-thermal and rotation support against gravity, and also on the redshift of galaxy formation. For every model galaxy we find the minimum gas mass M_g^min required to achieve a state in which star formation (SF) is allowed according to contemporary SF criteria. The obtained M_g^min--M_DM relations are compared against the baryon-to-DM mass relation M_b--M_DM inferred fr…
Twenty three years ago, cosmological N-body simulations revealed quasi-universal NFW dark matter halos, whose physical origin is still unclear. This work tries to solve this issue by Landau-Ginzburg (LG) theory in equilibrium statistical mechanics. We replace the order parameter in LG theory by density and consider the dark matter halos as fluctuations from the equilibrium state of the background, which can be the main halos for the subhalos, or the homogeneous and isotropic Universe for the galaxy cluster halos. With the assumption that the fluctuations of Helmholtz free energy depend mainly …
The problem of modeling the distribution of dark matter in galaxies in terms of equilibrium configurations of collisionless self-gravitating quantum particles is considered. We first summarize the pioneering model of a Newtonian self-gravitating Fermi gas in thermodynamic equilibrium developed by Ruffini and Stella (1983), which is shown to be the generalization of the King model for fermions. We further review the extension of the former model developed by Gao, Merafina and Ruffini (1990), done for any degree of fermion degeneracy at the center ($θ_0$), within general relativity. Finally, we …
In a previous study, we formulated a framework of the entropy-based equilibrium statistical mechanics for self-gravitating systems. This theory is based on the Boltzmann-Gibbs entropy and includes the generalized virial equations as additional constraints. With the truncated distribution function to the lowest order, we derived a set of second-order equations for the equilibrium states of the system. In this work, the numerical solutions of these equations are investigated. It is found that there are three types of solutions for these equations. Both the isothermal and divergent solutions are …
We investigate the distribution of dark matter in galaxies by solving the equations of equilibrium of a self-gravitating system of massive fermions (`inos') at selected temperatures and degeneracy parameters within general relativity. Our most general solutions show, as a function of the radius, a segregation of three physical regimes: 1) an inner core of almost constant density governed by degenerate quantum statistics; 2) an intermediate region with a sharply decreasing density distribution followed by an extended plateau, implying quantum corrections; 3) an asymptotic, $ρ\propto r^{-2}$ cla…
We study quasi-stationary states (QSS) resulting from violent relaxation in the one-dimensional self-gravitating "sheet model", revisiting in particular the question of the adequacy of the theory of Lynden-Bell (LB) to describe them. For "waterbag" initial conditions characterized by a single phase space density, the prediction of this theory is, in this model, a function of only one parameter, which can conveniently be chosen to be the ratio of the energy to that in the degenerate limit. Studying a class of such initial conditions in which the shape of the initial waterbag is varied, we find …
Dark-matter halos grown in cosmological simulations appear to have central NFW-like density cusps with mean values of $d\logρ/d\log r \approx -1$, and some dispersion, which is generally parametrized by the varying index $α$ in the Einasto density profile fitting function. Non-universality in profile shapes is also seen in observed galaxy clusters and possibly dwarf galaxies. Here we show that non-universality, at any given mass scale, is an intrinsic property of DARKexp, a theoretically derived model for collisionless self-gravitating systems. We demonstrate that DARKexp - which has only one …
Low-energy, self-gravitating solutions of a scalar field coupled to gravity, described by the Schrodinger-Poisson system, are good candidates for realistic astrophysical structures, being particularly suited to describe dark matter halos. In this work we study the scenario in which one of these structures is gravitationally perturbed by a point-like mass. We analyse the effects that the body has on the distribution of the scalar field and how it backreacts on the body's motion. We show that an initially static, spherical structure can develop rotating non-spherical clumps, the amplitude and th…
We study the non-linear structure formation in cosmology accounting for the quantum nature of the dark matter (DM) particles in the initial conditions at decoupling, as well as in the relaxation and stability of the DM halos. Differently from cosmological N-body simulations, we use a thermodynamic approach for collisionless systems of self-gravitating fermions in General Relativity, in which the halos reach the steady state by maximizing a coarse-grained entropy. We show the ability of this approach to provide answers to crucial open problems in cosmology, among others: the mass and nature of …
The formation and stability of collisionless self-gravitating systems are long standing problems, which date back to the work of D. Lynden-Bell on violent relaxation and extends to the issue of virialization of dark matter (DM) halos. An important prediction of such a relaxation process is that spherical equilibrium states can be described by a Fermi-Dirac phase-space distribution, when the extremization of a coarse-grained entropy is reached. In the case of DM fermions, the most general solution develops a degenerate compact core surrounded by a diluted halo. As shown recently, the latter is …
We investigate the black hole (BH) scaling relation in galaxies using a model in which the galaxy halo and central BH are a self-gravitating sphere of dark matter (DM) with an isotropic, adiabatic equation of state. The equipotential where the escape velocity approaches the speed of light defines the horizon of the BH. We find that the BH mass ($m_\bullet$) depends on the DM entropy, when the effective thermal degrees of freedom ($F$) are specified. Relations between BH and galaxy properties arise naturally, with the BH mass and DM velocity dispersion following $m_\bullet\proptoσ^{F/2}$ (for g…
The halo-mediated inverse mass cascade is a key feature of the intermediate statistically steady state for self-gravitating collisionless dark matter flow (SG-CFD). A broad spectrum of halos and halo groups are necessary to form from inverse mass cascade for long-range interaction system to maximize its entropy. The limiting velocity ($\textbf X$), speed ($\textbf Z$), and energy ($\textbf E$) distributions of collisionless particles can be obtained analytically from a maximum entropy principle. Halo mass function, the distribution of total mass in halos, is a fundamental quantity for structur…
We study the vertical stellar distribution of the Milky Way thin disk in detail with particular focus on the outer disk. We treat the galactic disk as a gravitationally coupled, three-component system consisting of stars, atomic hydrogen gas, and molecular hydrogen gas in the gravitational field of the dark matter halo. The self-consistent vertical distribution for stars and gas in such a realistic system is obtained for radii between 4-22 kpc. The inclusion of an additional gravitating component constrains the vertical stellar distribution toward the mid-plane, so that the mid-plane density i…
It has long been known that no static, spherically symmetric, asymptotically flat Klein-Gordon scalar field configuration surrounding a nonrotating black hole can exist in general relativity. In a series of previous papers we proved that, at the effective level, this no-hair theorem can be circumvented by relaxing the staticity assumption: for appropriate model parameters there are quasi-bound scalar field configurations living on a fixed Schwarzschild background which, although not being strictly static, have a larger lifetime than the age of the universe. This situation arises when the mass …
In this paper we suggest the existence in the central regions of spiral galaxies of collisionless, scale-free, rigidly rotating, self-gravitating discs with spiral symmetry. Such discs must be truncated at a finite radius, and they must be stabilized and rendered self-similar by a suitable halo. The halo and the rotating disc share the self-similar class and must form together to arrive at the suggested state. We make comparisons with the well-known rigidly rotating, Kalnajs discs; one of which is axi-symmetric and finite while the other is infinite and decomposed into spiral modes. We find th…
Spherical systems with polytropic equations of state are of great interest in astrophysics. They are widely used to describe neutron stars, red giants, white dwarfs, brown dwarfs, main sequence stars, galactic halos, and globular clusters of diverse sizes. In this paper we construct analytically a family of self-gravitating spherical models in the post-Newtonian approximation of general relativity. These models present interesting cusps in their density profiles which are appropriate for the modeling of galaxies and dark matter halos. The systems described here are anisotropic in the sense tha…
Simulations of the clustering of cold dark matter yield dark-matter halos that have central density cusps, but observations of totally dark-matter dominated dwarf spheroidal galaxies imply that they do not have cuspy central density profiles. We use analytic calculations and numerical modelling to argue that whenever stars form, central density cusps are likely to be erased. Gas that accumulates in the potential well of an initially cuspy dark-matter halo settles into a disc. Eventually the surface density of the gas exceeds the threshold for fragmentation into self-gravitating clouds. The clo…
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 re-investigate the Fornax cusp-core problem using observational results on the spatial and mass distributions of globular clusters (GCs) in order to put constraints on the dark matter profile. We model Fornax using high-resolution N-body simulations with entirely live systems, i.e. self-gravitating systems composed of stars and dark matter, which account correctly for dynamical friction and tidal effects between Fornax and the globular clusters. We test two alternative hypotheses, which are a cored and a cuspy halo for Fornax by exploring a reasonable range of initial conditions on globular…
Inverse mass cascade is a key feature of the intermediate statistically steady state for self-gravitating collisionless dark matter flow (SG-CFD). This paper focus on effects of mass cascade on halo energy, momentum, dispersion, size, and density. Halo with fast mass accretion has an expanding core. Mass cascade forms a new layer of mass that deforms the original halo and induces nonzero radial flow (outwards in core and inwards in outer regions). The inward/outward flow leads to an extra length scale (scale radius) that is not present in isothermal profile. Halo concentration c=3.5 can be der…
The kinematics of stars and planetary nebulae in early type galaxies provide vital clues to the enigmatic physics of their dark matter halos. We fit published data for fourteen such galaxies using a spherical, self-gravitating model with two components: (1) a Sersic stellar profile fixed according to photometric parameters, and (2) a polytropic dark matter halo that conforms consistently to the shared gravitational potential. The polytropic equation of state can describe extended theories of dark matter involving self-interaction, non-extensive thermostatistics, or boson condensation (in a cla…
It is a well-known fact that the gravitational effect of dark matter in galaxies is only noticeable when the orbital accelerations drop below $a_0 \simeq 2\times 10^{-8}$ cm s$^{-1}$ (Milgrom's Law). This peculiarity of the dynamic behaviour of galaxies was initially ascribed to a modification of Newtonian dynamics (MOND theory) and, consequently, it was used as an argument to criticize the dark matter hypothesis. In our model, warm dark matter is composed by collisionless Vlasov particles with a primordial typical velocity $\simeq 330$ km s$^{-1}$ and, consequently, they evaporated from galac…
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…
Recently, we have shown that if the ISM is governed by super-sonic turbulent flows, the excursion-set formalism can be used to calculate the statistics of self-gravitating objects over a wide range of scales. On the largest self-gravitating scales ('first crossing'), these correspond to GMCs, and on the smallest non-fragmenting self-gravitating scales ('last crossing'), to protostellar cores. Here, we extend this formalism to rigorously calculate the auto and cross-correlation functions of cores (and by extension, young stars) as a function of spatial separation and mass, in analogy to the cos…
