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1.
2.
Pierre-Henri Chavanis 《Monthly notices of the Royal Astronomical Society》1998,300(4):981-991
We have suggested in a previous article that the coarse-grained evolution of a collisionless stellar system could be viewed as a diffusion process in velocity space compensated by an appropriate friction. Using a quasi-linear theory, we calculate the diffusion coefficient associated with this evolution. This provides a new self-consistent relaxation equation for f , the locally averaged distribution function. This equation bears some resemblance to the conventional Fokker–Planck equation of collisional systems but the friction term is non-linear in f (accounting for degeneracy effects) and the relaxation time is much smaller (in agreement with the concept of 'violent relaxation'). Under the condition that the diffusion current vanishes identically at equilibrium, we recover Lynden-Bell's distribution function; but if we allow stars to escape from the system at a constant rate, we can derive a truncated model which coincides with Lynden-Bell's solution in the core but provides a depletion of high-energy stars in the halo. This distribution function has a finite mass and is the generalization of the Michie–King model to the case of (possibly degenerate) collisionless stellar systems. 相似文献
3.
In his theory of violent relaxation, Lynden-Bell gave a rigorous derivation of the equilibrium distribution, but only a qualitative discussion of the manner in which equilibrium is attained Here we present a fully explicit dynamical theory of collisionless relaxation towards Lynden-Bel equilibrium.The analysis proceeds from the coarse-graining in phase space of the collisionless Boltzmann equation the mesh size being determined by the precision of the observational data. The theoretical developmen leads to a kinetic equation generalizing that obtained by Kadomtsev and Pogutse in the rather differen context of homogeneous plasma turbulence. The collision integral differs from the classical Fokker Planck type essentially by the appearance of products of three distribution functions. It drives th systems towards the Lynden-Bell equilibrium state, on a time-scale which is inversely proportional to th coarse-graining mesh and, in the non-degenerate limit, to the fine-grained phase density. Owing to th various approximations introduced, the theory does not, however, describe the violent relaxation proces itself, but rather its late quiescent phases. 相似文献
4.
We study how the internal structure of dark halos is affected if cold dark matter particles are assumed to have a large cross section for elastic collisions. We identify a cluster halo in a large cosmological N-body simulation and resimulate its formation with progressively increasing resolution. We compare the structure found in the two cases in which dark matter is treated as collisionless or as a fluid. For the collisionless case, the overall ellipticity of the cluster, the central density cusp, and the amount of surviving substructure are all similar to those found in earlier high-resolution simulations. Collisional dark matter results in a cluster that is more nearly spherical at all radii, has a steeper central density cusp, and has less-but still substantial-surviving substructure. As in the collisionless case, these results for a "fluid" cluster halo are expected to carry over approximately to smaller mass systems. The observed rotation curves of dwarf galaxies then argue that self-interacting dark matter can only be viable if intermediate cross sections produce structure that does not lie between the extremes we have simulated. 相似文献
5.
L. P. Osipkov 《Astrophysics》2000,43(3):351-358
Equations obtained in Part I of this investigation are solved and describe the gross dynamics of axisymmetric, collisionless
gravitating systems for small departures from the equilibrium position. The solution obtained describes a superposition of
oscillations with two eigenfrequencies. Against the background of periodic contractions and expansions, the system’s flattening
varies with a period half as long.
Translated from Astrofizika, Vol. 43, No. 3, pp. 483-492, July–September, 2000. 相似文献
6.
The CrossScale mission will advance our understanding of fundamental plasma processes in collisionless plasmas. It will exploit the excellent natural plasma laboratory provided by the Earth’s magnetosphere and the near-Earth solar wind and, in particular, carry out multi-scale studies that will strongly complement plasma studies in ground-based laboratories. Previous studies of collisionless plasmas in space environments across the solar system have shown the ubiquitous nature of suprathermal particles and that these particles exhibit a power-law energy spectrum. In this paper we discuss the great significance of these suprathermal particles for CrossScale studies. We show that the presence of these particles is a natural consequence of the collisionless regime as they can propagate across the heliosphere with little spectral change and are not thermalised by collisions. They are a key indicator of the non-equilibrium nature of collisionless plasmas and an important source of free energy that can drive plasma processes. We discuss how these suprathermal particles influence the overall properties of the plasma. In particular, the energy distribution of particles follows a Kappa, rather than Maxwellian, distribution and thus the plasma does not have a single thermodynamic temperature. We also discuss the importance of the suprathermal tail as a tool to diagnose the processes responsible for particle energisation in collisionless plasmas. Such energisation is a common feature in collisionless plasmas, especially in terms of the primary science targets for CrossScale: reconnection, shocks and turbulence. Finally we also touch on the value of using CrossScale studies to provide ground truth measurements for a number of astrophysical techniques that exploit the effects of energetic electrons in the distant universe. Throughout the paper, we stress that suprathermal (30 keV-1 MeV) measurements are essential to fully characterise particle distributions. We show that such measurements will benefit greatly from the improved spatial and temporal resolution (compared to Cluster) that is proposed for the HEP instrument on CrossScale. 相似文献
7.
Paul Goudfrooij Diane Gilmore Markus Kissler-Patig † Claudia Maraston 《Monthly notices of the Royal Astronomical Society》2006,369(2):697-704
We compare the conclusions reached using the coarse-graining technique employed by Henriksen for a one degree of freedom (per particle) collisionless system to those presented in a paper by Binney based on an exact one degree of freedom model. We find agreement in detail, but in addition we show that the isolated 1D system is self-similar and therefore unrelaxed. Fine graining of this system recovers much less prominent wave-like structure than in a spherically symmetric isotropic 3D system. The rate of central flattening is also reduced in the 1D system. We take this to be evidence that relaxation of collisionless systems proceeds ultimately by way of short wavelength Landau damping. N -body systems, both real and simulated, can be trapped in an incompletely relaxed state because of a break in the cascade of energy to small scales. This may be due to the rapid dissipation of the small-scale oscillations in an isolated system to the existence of conserved quantities such as angular momentum, or to the failure in simulations to resolve sub-Jeans length scales. Such a partially relaxed state appears to be the Navarro, Frenk and White (NFW) state and is to be expected especially in young systems. The NFW core is shown to be isolated. In non-isolated systems, continuing coarse-grained relaxation should be towards a density core in solid body rotation. 相似文献
8.
S. Goldstein 《Astrophysics and Space Science》1971,13(2):387-396
The stability of a constant density, self-gravitating system is investigated.The system considered is one-dimensional, collisionless and described by the sheet model.The equilibrium distribution functionF(E), E being the energy, is such that the system has constant density in real space over a finite region.An analytical treatment as well as computer experiment show stability for symmetric disturbances. 相似文献
9.
A full particle simulation study is carried out on a perpendicular collisionless shock with a relatively low Alfven Mach number (MA = 5). Recent self-consistent hybrid and full particle simulations have demonstrated ion kinetics are essential for the non-stationarity of perpendicular collisionless shocks, which means that physical processes due to ion kinetics modify the shock jump condition for fluid plasmas. This is a cross-scale coupling between fluid dynamics and ion kinetics. On the other hand, it is not easy to study cross-scale coupling of electron kinetics with ion kinetics or fluid dynamics, because it is a heavy task to conduct large-scale full particle simulations of collisionless shocks. In the present study, we have performed a two-dimensional (2D) electromagnetic full particle simulation with a “shock-rest-frame model”. The simulation domain is taken to be larger than the ion inertial length in order to include full kinetics of both electrons and ions. The present simulation result has confirmed the transition of shock structures from the cyclic self-reformation to the quasi-stationary shock front. During the transition, electrons and ions are thermalized in the direction parallel to the shock magnetic field. Ions are thermalized by low-frequency electromagnetic waves (or rippled structures) excited by strong ion temperature anisotropy at the shock foot, while electrons are thermalized by high-frequency electromagnetic waves (or whistler mode waves) excited by electron temperature anisotropy at the shock overshoot. Ion acoustic waves are also excited at the shock overshoot where the electron parallel temperature becomes higher than the ion parallel temperature. We expect that ion acoustic waves are responsible for parallel diffusion of both electrons and ions, and that a cross-scale coupling between an ion-scale mesoscopic instability and an electron-scale microscopic instability is important for structures and dynamics of a collisionless perpendicular shock. 相似文献
10.
We show that the spin period of the white dwarf in the magnetic cataclysmic variable (CV) EX Hydrae represents an equilibrium state in which the corotation radius is comparable with the distance from the white dwarf to the inner Lagrange point. We also show that a continuum of spin equilibria exists at which P spin is significantly longer than ∼0.1 P orb . Most systems occupying these equilibrium states should have orbital periods below the CV period gap, as observed. 相似文献
11.
We determine the mass profile of a synthetic cluster built from the combination of 59 nearby clusters observed in the ESO
Nearby Abell Cluster Survey (ENACS). We use ellipticals and S0s as tracers of the cluster potential, and solve the Jeans equation
assuming isotropic orbits. Such an assumption is justified by the analysis of the shape of the velocity distribution of ellipticals
and S0s. We find that the cluster mass profile is consistent with the Navarro, Frenk and White(NFW) model. We use this cluster
mass profile to search for equilibrium solutions for the other cluster galaxy populations: very bright ellipticals (M
R
≤–22+5 log h),early-type spirals (Sa-Sb), and late-type spirals and irregulars (Sbc-Ir), together with emission-line galaxies. We find
equilibrium solutions for both the early- and the late-spirals, but not for the very bright ellipticals. The dynamics of very
bright ellipticals is probably affected by dissipative processes which invalidate the use of the collisionless Jeans equation.
The equilibrium solution found for the early-spirals implies them to move on nearly-isotropic orbits. Late-spirals are instead
found to be on mildly radial orbits, with the radial anisotropy increasing outwards. We discuss the implications of these
results for the evolutionary histories of the different populations of cluster galaxies.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
12.
We present a general scheme for constructing Monte Carlo realizations of equilibrium, collisionless galaxy models with known distribution function (DF) f 0 . Our method uses importance sampling to find the sampling DF f s that minimizes the mean-square formal errors in a given set of projections of the DF f 0 . The result is a multimass N -body realization of the galaxy model in which 'interesting' regions of phase space are densely populated by lots of low-mass particles, increasing the effective N there, and less interesting regions by fewer, higher mass particles.
As a simple application, we consider the case of minimizing the shot noise in estimates of the acceleration field for an N -body model of a spherical Hernquist model. Models constructed using our scheme easily yield a factor of ∼100 reduction in the variance at the central acceleration field when compared to a traditional equal-mass model with the same number of particles. When evolving both models with a real N -body code, the diffusion coefficients in our model are reduced by a similar factor. Therefore, for certain types of problems, our scheme is a practical method for reducing the two-body relaxation effects, thereby bringing the N -body simulations closer to the collisionless ideal. 相似文献
As a simple application, we consider the case of minimizing the shot noise in estimates of the acceleration field for an N -body model of a spherical Hernquist model. Models constructed using our scheme easily yield a factor of ∼100 reduction in the variance at the central acceleration field when compared to a traditional equal-mass model with the same number of particles. When evolving both models with a real N -body code, the diffusion coefficients in our model are reduced by a similar factor. Therefore, for certain types of problems, our scheme is a practical method for reducing the two-body relaxation effects, thereby bringing the N -body simulations closer to the collisionless ideal. 相似文献
13.
E. V. Polyachenko V. L. Polyachenko I. G. Shukhman 《Monthly notices of the Royal Astronomical Society》2007,379(2):573-596
We study spherical and disc clusters in a near-Keplerian potential of galactic centres or massive black holes. In such a potential orbit precession is commonly retrograde, that is, the direction of the orbit precession is opposite to the orbital motion. It is assumed that stellar systems consist of nearly-radial orbits. We show that if there is a loss-cone at low angular momentum (e.g. due to consumption of stars by a black hole), an instability similar to loss-cone instability in plasma may occur. The gravitational loss-cone instability is expected to enhance black hole feeding rates. For spherical systems, the instability is possible for the number of spherical harmonics l ≥ 3 . If there is some amount of counter-rotating stars in flattened systems, they generally exhibit the instability independent of azimuthal number m . The results are compared with those obtained recently by Tremaine for distribution functions monotonically increasing with angular momentum.
The analysis is based on simple characteristic equations describing small perturbations in a disc or a sphere of stellar orbits highly elongated in radius. These characteristic equations are derived from the linearized Vlasov equations (combining the collisionless Boltzmann kinetic equation and the Poisson equation), using the action-angle variables. We use two techniques for analysing the characteristic equations: the first one is based on preliminary finding of neutral modes, and the second one employs a counterpart of the plasma Penrose–Nyquist criterion for disc and spherical gravitational systems. 相似文献
The analysis is based on simple characteristic equations describing small perturbations in a disc or a sphere of stellar orbits highly elongated in radius. These characteristic equations are derived from the linearized Vlasov equations (combining the collisionless Boltzmann kinetic equation and the Poisson equation), using the action-angle variables. We use two techniques for analysing the characteristic equations: the first one is based on preliminary finding of neutral modes, and the second one employs a counterpart of the plasma Penrose–Nyquist criterion for disc and spherical gravitational systems. 相似文献
14.
Satoru Ikeuchi 《Astrophysics and Space Science》1986,118(1-2):509-514
As a model of the Lyman absorbing systems of quasar lights, the gravitational equilibrium of a baryon clump within an extended dark matter composed of collisionless particles is examined. There exists the critical mass below the clump is stable. It is highly probable that these baryon clumps may be the Lyman absorbers.Paper presented at the IAU Third Asian-Pacific Regional Meeting, held in Kyoto, Japan, between 30 September–6 October, 1984. 相似文献
15.
Du Jiulin 《Astrophysics and Space Science》2007,312(1-2):47-55
By a natural nonextensive generalization of the conservation of energy in the q-kinetic theory, we study the nonextensivity and the power-law distributions for the many-body systems with the self-gravitating
long-range interactions. It is shown that the power-law distributions describe the long-range nature of the interactions and
the non-local correlations within the self-gravitating system with the inhomogeneous velocity dispersion. A relation is established
between the nonextensive parameter q≠1 and the measurable quantities of the self-gravitating system: the velocity dispersion and the mass density. Correspondingly,
the nonextensive parameter q can be uniquely determined from the microscopic dynamical equation and thus the physical interpretation of q different from unity can be clearly presented. We derive a nonlinear differential equation for the radial density dependence
of the self-gravitating system with the inhomogeneous velocity dispersion, which can correctly describe the density distribution
for the dark matter in the above physical situation. We also apply this q-kinetic approach to analyze the nonextensivity of self-gravitating collisionless systems and self-gravitating gaseous dynamical
systems, giving the power-law distributions the clear physical meaning.
相似文献
16.
S. Sridhar 《Journal of Astrophysics and Astronomy》1987,8(3):257-262
Recent work on the violent relaxation of collisionless stellar systems has been based on the notion of a wide class of entropy
functions. A theorem concerning entropy increase has been proved. We draw attention to some underlying assumptions that have
been ignored in the applications of this theorem to stellar dynamical problems. Once these are taken into account, the use
of this theorem is at best heuristic. We present a simple counter-example. 相似文献
17.
We analyze the R-and K s-band photometric profiles for two independent samples of edge-on galaxies. The thickness of old stellar disks is shown to be related to the relative masses of the spherical and disk components of galaxies. The radial-to-vertical scale length ratio for galactic disks increases (the disks become thinner) with increasing total mass-to-light ratio of the galaxies, which reflects the relative contribution of the dark halo to the total mass, and with decreasing central deprojected disk brightness (density). Our results are in good agreement with numerical models of collisionless disks that evolved to a marginally stable equilibrium state. This suggests that, in most galaxies, the vertical stellar-velocity dispersion, on which the equilibrium-disk thickness depends, is close to a minimum value that ensures disk stability. The thinnest edge-on disks appear to be low-brightness galaxies in which the dark-halo mass far exceeds the stellar-disk mass. 相似文献
18.
We present a hybrid technique of N -body simulation to deal with collisionless stellar systems having an inhomogeneous global structure. We combine a treecode and a self-consistent field code such that each of the codes models a different component of the system being investigated. The treecode is suited to treatment of dynamically cold or clumpy components, which may undergo significant evolution within a dynamically hot system. The hot system is appropriately evolved by the self-consistent field code. This combined code is particularly suited to a number of problems in galactic dynamics. Applications of the code to these problems are briefly discussed. 相似文献
19.
G. Q. Luo 《Astrophysics and Space Science》1996,235(1):9-15
This is an extension study of the grand canonical approach of the equation of state to the equilibrium calculation for radiative opacities. We discuss the construction of atomic configurations from the ion stages and excitation states of atoms. The atomic configuration is essentially important to the grand canonical approach, and also useful to the radiative opacity calculation. We present the complete formalism for the calculation of atomic configuration probabilities and population fractions. We show that the grand canonical approach provides a shortcut in the computation of thermodynamic equilibrium. We mainly discuss its use in two cases for the equilibrium calculation. 相似文献
20.
Kyoung W. Min 《Astrophysics and Space Science》1988,145(1):167-169
Linear dispersion relations are solved numerically for collisionless self-gravitating systems. The results are compared to those of hydrodynamic approach. Both theories yield similar dispersion relations, with predictions of instability when the system is cold enough. In a collisionless system, however, the perturbation is found to die away without oscillations when the system is stable. A mixed system of hot-component particles and cold-component particles is also studied. The stability of such system is dominated by the temperature of the cold particles. Again, the oscillatory behaviour is not found in this case, regardless of the stability of the system. 相似文献