We consider the possibility that dark matter halos are described by the Fermi-Dirac distribution at finite temperature. This is the case if dark matter is a self-gravitating quantum gas made of massive neutrinos at statistical equilibrium. This is also the case if dark matter can be treated as a self-gravitating collisionless gas experiencing Lynden-Bell's type of violent relaxation. In order to avoid the infinite mass problem and carry out a rigorous stability analysis, we consider the fermionic King model. In this paper, we study the non-degenerate limit leading to the classical King model. This model was initially introduced to describe globular clusters. We propose to apply it also to large dark matter halos where quantum effects are negligible. We determine the caloric curve and study the thermodynamical stability of the different configurations. Equilibrium states exist only above a critical energy $E_c$ in the microcanonical ensemble and only above a critical temperature $T_c$ in the canonical ensemble. For $E<E_c$, the system undergoes a gravothermal catastrophe and, for $T<T_c$, it undergoes an isothermal collapse. We compute the profiles of density, circular velocity, and velocity dispersion. We compare the prediction of the classical King model to the observations of large dark matter halos. Because of collisions and evaporation, the central density increases while the slope of the halo density profile decreases until an instability takes place. We show that large dark matter halos are relatively well-described by the King model at, or close to, the point of marginal microcanonical stability. At that point, the King model generates a density profile that can be approximated by the modified Hubble profile. This profile has a flat core and decreases as $r^{-3}$ at large distances, like the observational Burkert profile. Less steep halos are unstable.
We discuss the nature of phase transitions in the fermionic King model which describes tidally truncated quantum self-gravitating systems. This distribution function takes into account the escape of high energy particles and has a finite mass. On the other hand, the Pauli exclusion principle puts an upper bound on the phase space density of the system and stabilizes it against gravitational collapse. As a result, there exists a statistical equilibrium state for any accessible values of energy and temperature. We plot the caloric curves and investigate the nature of phase transitions as a funct…
We investigate the origin of galaxy bimodality by quantifying the relative role of intrinsic and environmental drivers to the cessation (or `quenching') of star formation in over half a million local Sloan Digital Sky Survey (SDSS) galaxies. Our sample contains a wide variety of galaxies at z=0.02-0.2, with stellar masses of 8 < log(M*/M_sun) < 12, spanning the entire morphological range from pure disks to spheroids, and over four orders of magnitude in local galaxy density and halo mass. We utilise published star formation rates and add to this recent GIM2D photometric and stellar mass bulge …
In this paper, we present internal surface brightness profiles, using images in the F606W and F814W filter bands observed with the Advanced Camera for Surveys on the {\it Hubble Space Telescope}, for ten globular clusters (GCs) in the outer halo of M31. Standard King models are fitted to the profiles to derive their structural and dynamical parameters. The results show that, in general, the properties of clusters in M31 and the Milky Way fall in the same regions of parameter spaces. The outer halo GCs of M31 have larger ellipticities than most of GCs in M31 and the Milky Way. Their large ellip…
A number of dwarf spheroidal (dSph) galaxies are known to contain a more extended, metal-poor population with a flattish velocity dispersion profile, and a more concentrated, metal-rich population with a velocity dispersion declining with radius. The two populations can be modelled with Michie-King distribution functions (DFs) in the isothermal and in the sharply truncated limits, respectively. We argue that the truncation of the metal-rich population can be traced back to the spatial distribution of the star forming gas. Suppose D is the exponent of the first non-constant term in the Taylor e…
Wave dark matter ($ψ$DM), which satisfies the Schrödinger-Poisson equation, has recently attracted substantial attention as a possible dark matter candidate. Numerical simulations have in the past provided a powerful tool to explore this new territory of possibility. Despite their successes to reveal several key features of $ψ$DM, further progress in simulations is limited, in that cosmological simulations so far can only address formation of halos below $\sim 2\times 10^{11} M_\odot$ and substantially more massive halos have become computationally very challenging to obtain. For this reason, …
We compare the DARKexp differential energy distribution, N(E) \propto \exp(ϕ_0-E)-1, obtained from statistical mechanical considerations, to the results of N-body simulations of dark matter halos. We first demonstrate that if DARKexp halos had anisotropic velocity distributions similar to those of N-body simulated halos, their density and energy distributions could not be distinguished from those of isotropic DARKexp halos. We next carry out the comparison in two ways, using (1) the actual energy distribution extracted from simulations, and (2) N-body fitting formula for the density distributi…
We present an equilibrium statistical mechanical theory of collisionless self-gravitational systems with isotropic velocity distributions. Compared to existing standard theories, we introduce two changes: (1) the number of possible microstates is computed in energy (orbit) space rather than phase space and (2) low occupation numbers are treated more appropriately than using Stirling's approximation. Combined, the two modifications predict that the relaxed parts of collisionless self-gravitating systems, such as dark-matter halos, have a differential energy distribution N(E) ~ [exp(phi_0 - E) -…
The density profiles of dark matter haloes are commonly described by fitting functions such as the NFW or Einasto models, but these approximations break down in the transition region where halos become dominated by newly accreting matter. Here we present a simple, accurate new fitting function that is inspired by the asymptotic shapes of the separate orbiting and infalling halo components. The orbiting term is described as a truncated Einasto profile, $ρ_{\rm orb} \propto \exp \left[-2/α (r / r_{\rm s})^α- 1/β (r / r_{\rm t})^β\right]$, with a five-parameter space of normalization, physically …
We propose a new method for generating equilibrium models of spherical systems of collisionless particles that are finite in extent, but whose central regions resemble dark matter halos from cosmological simulations. This method involves iteratively removing unbound particles from a Navarro-Frenk-White profile truncated sharply at some radius. The resulting models are extremely stable, and thus provide a good starting point for N-body simulations of isolated halos. We provide a code to generate such models for NFW and a variety of other common density profiles. We then develop an analytic appr…
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…
In this paper, we present the density, ρ, velocity dispersion, σ, and ρ/σ^3 profiles of isotropic systems which have the energy distribution, N(E)\propto[\exp(ϕ_0-E)-1], derived in Paper I. This distribution, dubbed DARKexp, is the most probable final state of a collisionless self-gravitating system, which is relaxed in terms of particle energies, but not necessarily in terms of angular momentum. We compare the DARKexp predictions with the results obtained using the extended secondary infall model (ESIM). The ESIM numerical scheme is optimally suited for the purpose because (1) it relaxes only…
It has been shown in previous work that DARKexp, which is a theoretically derived, maximum entropy, one shape parameter model for isotropic collisionless systems, provides very good fits to simulated and observed dark-matter halos. Specifically, it fits the energy distribution, N(E), and the density profiles, including the central cusp. Here, we extend DARKexp N(E) to include the distribution in angular momentum, L^2, for spherically symmetric systems. First, we argue, based on theoretical, semi-analytical, and simulation results, that while dark-matter halos are relaxed in energy, they are no…
We argued that the standard field scalar potential couldn't be widely used for getting the adequate galaxies' curve lines and determining the profiles of dark matter their halo. For discovering the global properties of scalar fields that can describe the observable characteristics of dark matter on the cosmological space and time scales, we propose the simplest form of central symmetric potential celestial - mechanical type, i.e. U(ϕ) = -μ/ϕ. It was shown that this potential allows get rather satisfactorily dark matter profiles and rotational curves lines for dwarf galaxies. The good agreement…
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 …
Direct detection of Weakly Interacting Massive Particle (WIMP) candidates of Dark Matter (DM) is studied within the context of a self-consistent truncated isothermal model of the finite-size dark halo of the Galaxy based on the "King model" of the phase space distribution function of collisionless DM particles. Our halo model takes into account the modifications of the phase-space structure of the halo due to the gravitational influence of the observed visible matter in a self-consistent manner. The parameters of the halo model are determined by a fit to a recently determined circular rotation…
Accurately simulating core-collapse self-interacting dark matter halos
Ludwig-Maximilians-Universität München（慕尼黑大学）；Excellence Cluster ORIGINS（ORIGINS卓越集群）；University of California, Riverside（加州大学河滨分校）；Max-Planck-Institut für Astrophysik（马克斯·普朗克天体物理学研究所）
We derive the main physical galaxy properties: mass, halo radius, phase space density and velocity dispersion from a semiclassical gravitational approach in which fermionic WDM is treated quantum mechanically. They turn out to be compatible with observations. Pauli Principle implies for the fermionic DM phase-space density Q(r) = rho(r)/sigma^3(r) the quantum bound Q(r) < K m^4/hbar^3, where m is the DM particle mass, sigma(r) is the DM velocity dispersion and K is a pure number of order one which we estimate. N-body galaxy simulations produce a divergent Q(r) at r = 0 violating this quantum b…
We present a theoretical analysis of some unexplored aspects of relaxed Bose-Einstein condensate dark matter (BECDM) haloes. This type of ultralight bosonic scalar field dark matter is a viable alternative to the standard cold dark matter (CDM) paradigm, as it makes the same large-scale predictions as CDM and potentially overcomes CDM's small-scale problems via a galaxy-scale de Broglie wavelength. We simulate BECDM halo formation through mergers, evolved under the Schrödinger-Poisson equations. The formed haloes consist of a soliton core supported against gravitational collapse by the quantum…
MIGHTEE: The dark matter haloes, duty cycle and mechanical feedback from radio-AGN up to $z \sim 2.5$
University of Oxford（牛津大学）；School of Physics and Astronomy, Institute for Astronomy, University of Edinburgh（爱丁堡大学天体物理与天文学院天体物理研究所）；Department of Physics and Astronomy, University of the Western Cape（西开普大学物理与天文系）
We study the empirical relation between an astronomical object's angular momentum $J$ and mass $M$, $J=βM^α$, the $J-M$ relation, using N-body simulations. In particular, we investigate the time evolution of the $J-M$ relation to study how the initial power spectrum and cosmological model affect this relation, and to test two popular models of its origin - mechanical equilibrium and tidal torque theory. We find that in the $Λ$CDM model, $α$ starts with a value of $\sim 1.5$ at high redshift $z$, increases monotonically, and finally reaches $5/3$ near $z=0$, whereas $β$ evolves linearly with ti…
Approximating the peculiar velocity distribution of dark matter halos with Tsallis statistics
Chinese Academy of Sciences South America Center for Astronomy, National Astronomical Observatories, CAS（中国科学院南美天文中心，国家天文台）；Key Laboratory for Computational Astrophysics, National Astronomical Observatories, Chinese Academy of Sciences（计算天体物理重点实验室，国家天文台，中国科学院）
A dark force can impact the cosmological history of dark matter (DM), both explaining observed cores in dwarf galaxies and setting the DM relic density through annihilation to dark force bosons. For GeV - TeV DM mass, DM self-scattering in dwarf galaxy halos exhibits quantum mechanical resonances, analogous to a Sommerfeld enhancement for annihilation. We show that a simple model of DM with a dark force can accommodate all astrophysical bounds on self-interactions in halos and explain the observed relic density, through a single coupling constant.
We show that ultra-light scalar dark matter (fuzzy dark matter) in galaxies has a quantum mechanical typical acceleration scale about $10^{-10}\,\mbox{ms}^{-2}$, which leads to the baryonic Tully-Fisher relation. Baryonic matter at central parts of galaxies acts as a boundary condition for dark matter wave equation and influences stellar rotation velocities in halos. Without any modification of gravity or mechanics this model also explains the radial acceleration relation and MOND-like behavior of gravitational acceleration found in galaxies having flat rotation curves. This analysis can be ex…
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…
