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1.
If a magnetic field is frozen into a plasma that undergoes spherical compression, then the magnetic field B varies with the plasma density ρ according to   B ∝ρ2/3  . In the gravitational collapse of cosmological density perturbations, however, quasi-spherical evolution is very unlikely. In anisotropic collapses the magnetic field can be a much steeper function of gas density than in the isotropic case. We investigate the distribution of amplifications in realistic gravitational collapses from Gaussian initial fluctuations using the Zel'dovich approximation. Representing our results using a relation of the form   B ∝ρα  , we show that the median value of α can be much larger than the value  α= 2/3  resulting from spherical collapse, even if there is no initial correlation between magnetic field and principal collapse directions. These analytic arguments go some way towards understanding the results of numerical simulations.  相似文献   

2.
This paper considers the phenomenon of deep core collapse in collisional stellar systems, with stars of equal mass. The collapse takes place on some multiple,  ξ−1  , of the central relaxation time, and produces a density profile in which  ρ∝ r −α  , where α is a constant. The parameters α and ξ have usually been determined from simplified models, such as gas and Fokker–Planck models, often with the simplification of isotropy. Here we determine the parameters directly from N -body simulations carried out using the newly completed GRAPE-6.  相似文献   

3.
Cosmological N -body simulations were performed to study the evolution of the phase-space density   Q =ρ/σ3  of dark matter haloes. No significant differences in the scale relations   Q ∝σ−2.1  or   Q ∝ M −0.82  are seen for the 'cold' or 'warm' dark matter models. The follow-up of individual haloes from   z = 10  up to the present time indicate the existence of two main evolutionary phases: an early and fast one  (10 > z > 6.5)  , in which Q decreases on the average by a factor of 40 as a consequence of the randomization of bulk motions, and a late and long one  (6.5 > z ≥ 0)  , in which Q decreases by a factor of 20 because of mixing induced by merger events. The study of these haloes has also evidenced that rapid and positive variations of the velocity dispersion, induced by merger episodes, are related to a fast decrease of the phase-space density Q .  相似文献   

4.
N -body simulations predict that cold dark matter (CDM) halo-assembly occurs in two phases: (i) a fast-accretion phase with a rapidly deepening potential well; and (ii) a slow-accretion phase characterized by a gentle addition of mass to the outer halo with little change in the inner potential well. We demonstrate, using one-dimensional simulations, that this two-phase accretion leads to CDM haloes of the Navarro, Frenk & White (NFW) form and provides physical insight into the properties of the mass-accretion history that influence the final profile. Assuming that the velocities of CDM particles are effectively isotropized by fluctuations in the gravitational potential during the fast-accretion phase, we show that gravitational collapse in this phase leads to an inner profile  ρ( r ) ∝ r −1  . Slow accretion on to an established potential well leads to an outer profile with  ρ( r ) ∝ r −3  . The concentration of a halo is determined by the fraction of mass that is accreted during the fast-accretion phase. Using an ensemble of realistic mass-accretion histories, we show that the model predictions of the dependence of halo concentration on halo formation time and, hence, the dependence of halo concentration on halo mass, and the distribution of halo concentrations all match those found in cosmological N -body simulations. Using a simple analytic model that captures much of the important physics, we show that the inner   r −1  profile of CDM haloes is a natural result of hierarchical mass assembly with an initial phase of rapid accretion.  相似文献   

5.
We examine the effects of cooling flows on the T X– L Bol relation for a sample of the most X-ray luminous ( L Bol > 1045 erg s−1) clusters of galaxies known. Using high-quality ASCA X-ray spectra and ROSAT images we explicitly account for the effects of cooling flows on the X-ray properties of the clusters and show that this reduces the previously noted dispersion in the T X– L Bol relationship. More importantly, the slope of the relationship is flattened from L Bol ∝  T 3X to approximately L Bol ∝  T 2X, in agreement with recent theoretical models which include the effects of shocks and pre-heating on the X-ray gas. We find no evidence for evolution in the T X– L Bol relation within z  ∼ 0.3. Our results demonstrate that the effects of cooling flows must be accounted for before cosmological parameters can be determined from X-ray observations of clusters. The results presented here should provide a reliable basis for modelling the T X– L Bol relation at high X-ray luminosities.  相似文献   

6.
We present velocity dispersion measurements for 69 faint early-type galaxies in the core of the Coma cluster, spanning  −22.0 ≲ MR ≲−17.5 mag  . We examine the   L –σ  relation for our sample and compare it to that of bright elliptical galaxies (Es) from the literature. The distribution of the the faint early-type galaxies in the   L –σ  plane follows the relation   L ∝σ2.01±0.36  , which is significantly shallower from   L ∝σ4  as defined for the bright Es. While increased rotational support for fainter early-type galaxies could account for some of the difference in slope, we show that it cannot explain it. We also investigate the colour–σ relation for our Coma galaxies. Using the scatter in this relation, we constrain the range of galaxy ages as a function of their formation epoch for different formation scenarios. Assuming a strong coordination in the formation epoch of faint early-type systems in Coma, we find that most had to be formed at least 6 Gyr ago and over a short 1-Gyr period.  相似文献   

7.
We perform a stability test of triaxial models in Modified Newtonian Dynamics (MOND) using N -body simulations. The triaxial models considered here have densities that vary with   r −1  in the centre and   r −4  at large radii. The total mass of the model varies from 108 to  1010 M⊙  , representing the mass scale of dwarfs to medium-mass elliptical galaxies, respectively, from deep MOND to quasi-Newtonian gravity. We build triaxial galaxy models using the Schwarzschild technique, and evolve the systems for 200 Keplerian dynamical times (at the typical length-scale of 1.0 kpc). We find that the systems are virial overheating, and in quasi-equilibrium with the relaxation taking approximately 5 Keplerian dynamical times (1.0 kpc). For all systems, the change of the inertial (kinetic) energy is less than 10 per cent (20 per cent) after relaxation. However, the central profile of the model is flattened during the relaxation and the (overall) axis ratios change by roughly 10 per cent within 200 Keplerian dynamical times (at 1.0 kpc) in our simulations. We further find that the systems are stable once they reach the equilibrium state.  相似文献   

8.
We demonstrate that the luminosity function of the recently detected population of actively star-forming galaxies at redshift z  = 3 and the B -band luminosity function of quasi-stellar objects (QSOs) at the same redshift can both be matched with the mass function of dark matter haloes predicted by standard variants of hierarchical cosmogonies for lifetimes of optically bright QSOs anywhere in the range 106 to 108 yr. There is a strong correlation between the lifetime and the required degree of non-linearity in the relation between black hole and halo mass. We suggest that the mass of supermassive black holes may be limited by the back-reaction of the emitted energy on the accretion flow in a self-gravitating disc. This would imply a relation of black hole to halo mass of the form M bh ∝  v 5halo ∝  M 5/3halo and a typical duration of the optically bright QSO phase of a few times 107 yr. The high integrated mass density of black holes inferred from recent black hole mass estimates in nearby galaxies may indicate that the overall efficiency of supermassive black holes for producing blue light is smaller than previously assumed. We discuss three possible accretion modes with low optical emission efficiency: (i) accretion at far above the Eddington rate, (ii) accretion obscured by dust, and (iii) accretion below the critical rate leading to an advection-dominated accretion flow lasting for a Hubble time. We further argue that accretion with low optical efficiency might be closely related to the origin of the hard X-ray background and that the ionizing background might be progressively dominated by stars rather than QSOs at higher redshift.  相似文献   

9.
We present a semi-analytic treatment of galactic winds within high-resolution, large-scale cosmological N -body simulations of a Λ cold dark matter (ΛCDM) universe. The evolution of winds is investigated by following the expansion of supernova-driven superbubbles around the several hundred thousand galaxies that form in an approximately spherical region of space with diameter 52  h −1 Mpc and mean density close to the mean density of the universe. We focus our attention on the impact of winds on the diffuse intergalactic medium. Initial conditions for mass loss at the base of winds are taken from Shu, Mo & Mao. Results are presented for the volume filling factor and the mass fraction of the intergalactic medium (IGM) affected by winds, and their dependence on the model parameters is carefully investigated. The mass-loading efficiency of bubbles is a key factor to determine the evolution of winds and their global impact on the IGM: the higher the mass loading, the later the IGM is enriched with metals. Galaxies with 109 < M ★ < 1010 M⊙ are responsible for most of the metals ejected into the IGM at   z = 3  , while galaxies with   M ★ < 109 M⊙   give a non-negligible contribution only at higher redshifts, when larger galaxies have not yet assembled. We find a higher mean IGM metallicity than Lyα forest observations suggest, and we argue that the discrepancy may be explained by the high temperatures of a large fraction of the metals in winds, which may not leave detectable imprints in absorption in the Lyα forest.  相似文献   

10.
Using N -body simulations with a large set of massless test particles, we compare the predictions of two theories of violent relaxation, the well-known Lynden-Bell theory and the more recent theory by Nakamura. We derive 'weakened' versions of both the theories in which we use the whole equilibrium coarse-grained distribution function     as a constraint instead of the total energy constraint. We use these weakened theories to construct expressions for the conditional probability   Ki (τ)  that a test particle initially at the phase-space coordinate τ would end-up in the i th macro-cell at equilibrium. We show that the logarithm of the ratio   Rij (τ) ≡ Ki (τ)/ Kj (τ)  is directly proportional to the initial phase-space density   f 0(τ)  for the Lynden-Bell theory and inversely proportional to   f 0(τ)  for the Nakamura theory. We then measure   Rij (τ)  using a set of N -body simulations of a system undergoing a gravitational collapse to check the validity of the two theories of violent relaxation. We find that both the theories are at odds with the numerical results, both qualitatively and quantitatively.  相似文献   

11.
Possible orbital histories of the Sgr dwarf galaxy are explored. A special-purpose N -body code is used to construct the first models of the Milky Way–Sgr dwarf system in which both the Milky Way and the Sgr dwarf are represented by full N -body systems and followed for a Hubble time. These models are used to calibrate a semi-analytic model of the Sgr dwarf's orbit that enables us to explore a wider parameter space than is accessible to the N -body models. We conclude that the extant data on the Sgr dwarf are compatible with a wide range of orbital histories. At one extreme the Sgr dwarf initially possesses ∼1011 M⊙ and starts from a Galactocentric distance R D(0)≳200 kpc. At the other extreme the Sgr dwarf starts with ∼109 M⊙ and R D(0)∼60 kpc, similar to its present apocentric distance. In all cases the Sgr dwarf is initially dark matter dominated and the current velocity dispersion of the Sgr dwarf's dark matter is tightly constrained to be 21±2 km s−1. This number is probably compatible with the smaller measured dispersion of the Sgr dwarf's stars because of (i) the dynamical difference between dark and luminous matter, and (ii) velocity anisotropy.  相似文献   

12.
We construct analytically stationary global configurations for both aligned and logarithmic spiral coplanar magnetohydrodynamics (MHD) perturbations in an axisymmetric background MHD disc with a power-law surface mass density  Σ0∝ r −α  , a coplanar azimuthal magnetic field   B 0∝ r −γ  , a consistent self-gravity and a power-law rotation curve   v 0∝ r −β  , where v 0 is the linear azimuthal gas rotation speed. The barotropic equation of state  Π∝Σ n   is adopted for both MHD background equilibrium and coplanar MHD perturbations where Π is the vertically integrated pressure and n is the barotropic index. For a scale-free background MHD equilibrium, a relation exists among  α, β, γ  and n such that only one parameter (e.g. β) is independent. For a linear axisymmetric stability analysis, we provide global criteria in various parameter regimes. For non-axisymmetric aligned and logarithmic spiral cases, two branches of perturbation modes (i.e. fast and slow MHD density waves) can be derived once β is specified. To complement the magnetized singular isothermal disc analysis of Lou, we extend the analysis to a wider range of  −1/4 < β < 1/2  . As an illustrative example, we discuss specifically the  β= 1/4  case when the background magnetic field is force-free. Angular momentum conservation for coplanar MHD perturbations and other relevant aspects of our approach are discussed.  相似文献   

13.
It is shown that the cuspy density distributions observed in the cores of elliptical galaxies can be realized by dissipationless gravitational collapse. The initial models consist of power-law density spheres such as ρ ∝ r −1 with anisotropic velocity dispersions. Collapse simulations are carried out by integrating the collisionless Boltzmann equation directly, on the assumption of spherical symmetry. From the results obtained, the extent of constant density cores, formed through violent relaxation, decreases as the velocity anisotropy increases radially, and practically disappears for extremely radially anisotropic models. As a result, the relaxed density distributions become more cuspy with increasing radial velocity anisotropy. It is thus concluded that the velocity anisotropy could be a key ingredient for the formation of density cusps in a dissipationless collapse picture. The velocity dispersions increase with radius in the cores according to the nearly power-law density distributions. The power-law index, n , of the density profiles, defined as ρ ∝ r − n , changes from n ≈2.1 at intermediate radii to a shallower power than n ≈2.1 toward the centre. This density bend can be explained from our postulated local phase-space constraint that the phase-space density accessible to the relaxed state is determined at each radius by the maximum phase-space density of the initial state.  相似文献   

14.
The algorithm ztrace of Monaco & Efstathiou is applied to the IRAS PSCz catalogue to reconstruct the initial conditions of our local Universe with a resolution down to ~5  h 1 Mpc. The one-point probability distribution function (PDF) of the reconstructed initial conditions is consistent with the assumptions that: (i) IRAS galaxies trace mass on scales of ~5  h 1 Mpc and (ii) the statistics of the primordial density fluctuations are Gaussian. We use simulated PSCz catalogues, constructed from N -body simulations with Gaussian initial conditions, to show that local non-linear bias can cause the recovered initial PDF (assuming no bias) to be non-Gaussian. However, for plausible bias models, the distortions of the recovered PDF would be difficult to detect using the volume finely sampled by the PSCz catalogue. So, for Gaussian initial conditions, a range of bias models remain compatible with our PSCz reconstruction results.  相似文献   

15.
We present intermediate-resolution spectroscopic data for a set of dwarf and giant galaxies in the Coma cluster, with  −20.6 < MR < −15.7.  The photometric and kinematic properties of the brighter galaxies can be cast in terms of parameters which present little scatter with respect to a set of scaling relations known as the fundamental plane. To determine the form of these fundamental scaling relations at lower luminosities, we have measured velocity dispersions for a sample comprising 69 galaxies on the border of the dwarf and giant regime. Combining these data with our photometric survey, we find a tight correlation of luminosity and velocity dispersion,   L ∝σ2.0  , substantially flatter than the Faber–Jackson relation characterizing giant elliptical galaxies. In addition, the variation of mass-to-light ( M / L ) ratio with velocity dispersion is quite weak in our dwarf sample:   M / L ∝σ0.2.  Our overall results are consistent with theoretical models invoking large-scale mass removal and subsequent structural readjustment, e.g. as a result of galactic winds.  相似文献   

16.
When an open system of classical point particles interacting by Newtonian gravity collapses and relaxes violently, an arbitrary amount of energy may, in principle, be carried away by particles which escape to infinity. We investigate here, using numerical simulations, how this released energy and other related quantities (notably the binding energy and size of the virialized structure) depend on the initial conditions, for the one-parameter family of starting configurations given by randomly distributing N cold particles in a spherical volume. Previous studies have established that the minimal size reached by the system scales approximately as   N 1/3  , a behaviour which follows trivially when the growth of perturbations (which regularize the singularity of the cold collapse in the   N  →∞  limit) is assumed to be unaffected by the boundaries. Our study shows that the energy ejected grows approximately in proportion to   N 1/3  , while the fraction of the initial mass ejected grows only very slowly with N , approximately logarithmically, in the range of N simulated. We examine in detail the mechanism of this mass and energy ejection, showing explicitly that it arises from the interplay of the growth of perturbations with the finite size of the system. A net lag of particles compared to their uniform spherical collapse trajectories develops first at the boundaries and then propagates into the volume during the collapse. Particles in the outer shells are then ejected as they scatter through the time-dependent potential of an already re-expanding central core. Using modified initial configurations, we explore the importance of fluctuations at different scales and discreteness (i.e. non-Vlasov) effects in the dynamics.  相似文献   

17.
We use cosmological Λ cold dark matter (CDM) numerical simulations to model the evolution of the substructure population in 16 dark matter haloes with resolutions of up to seven million particles within the virial radius. The combined substructure circular velocity distribution function (VDF) for hosts of 1011 to  1014 M⊙  at redshifts from zero to two or higher has a self-similar shape, is independent of host halo mass and redshift, and follows the relation  d n /d v = (1/8)( v cmax/ v cmax,host)−4  . Halo to halo variance in the VDF is a factor of roughly 2 to 4. At high redshifts, we find preliminary evidence for fewer large substructure haloes (subhaloes). Specific angular momenta are significantly lower for subhaloes nearer the host halo centre where tidal stripping is more effective. The radial distribution of subhaloes is marginally consistent with the mass profile for   r ≳ 0.3 r vir  , where the possibility of artificial numerical disruption of subhaloes can be most reliably excluded by our convergence study, although a subhalo distribution that is shallower than the mass profile is favoured. Subhalo masses but not circular velocities decrease towards the host centre. Subhalo velocity dispersions hint at a positive velocity bias at small radii. There is a weak bias towards more circular orbits at lower redshift, especially at small radii. We additionally model a cluster in several power-law cosmologies of   P ∝ kn   , and demonstrate that a steeper spectral index, n , results in significantly less substructure.  相似文献   

18.
We investigate the mean velocity dispersion and the velocity dispersion profile of stellar systems in modified Newtonian dynamics (MOND), using the N -body code n-mody , which is a particle-mesh-based code with a numerical MOND potential solver developed by Ciotti, Londrillo & Nipoti. We have calculated mean velocity dispersions for stellar systems following Plummer density distributions with masses in the range of 104 to  109 M⊙  and which are either isolated or immersed in an external field. Our integrations reproduce previous analytic estimates for stellar velocities in systems in the deep MOND regime  ( a i, a e≪ a 0)  , where the motion of stars is either dominated by internal accelerations  ( a i≫ a e)  or constant external accelerations  ( a e≫ a i)  . In addition, we derive for the first time analytic formulae for the line-of-sight velocity dispersion in the intermediate regime  ( a i∼ a e∼ a 0)  . This allows for a much-improved comparison of MOND with observed velocity dispersions of stellar systems. We finally derive the velocity dispersion of the globular cluster Pal 14 as one of the outer Milky Way halo globular clusters that have recently been proposed as a differentiator between Newtonian and MONDian dynamics.  相似文献   

19.
A new method is presented to obtain a non-parametric maximum likelihood estimate of the luminosity function and the selection function of a flux-limited redshift survey. The method parametrizes the selection function as a series of stepwise power laws and allows possible evolution of the luminosity function. We also propose a new technique to estimate the rate of evolution of the luminosity function. This is based on a minimization of the observed large-scale power with respect to the evolutionary model. We use an ensemble of mock surveys extracted from an N -body simulation to verify the power of this method. We apply our estimators to the 1.2-Jy survey of IRAS galaxies. We find a far-infrared luminosity function in good agreement with previously published results and evidence for rather strong evolution. If the comoving number density of IRAS galaxies is assumed to scale ∝ (1 +  z ) P , we estimate P  = 4.3 ± 1.4.  相似文献   

20.
We present J , H and K -band spectroscopy of Cygnus A, spanning 1.0–2.4 μm in the rest-frame and hence several rovibrational H2, H recombination and [Fe  ii ] emission lines. The lines are spatially extended by up to 6 kpc from the nucleus, but their distinct kinematics indicate that the three groups (H, H2 and [Fe  ii ]) are not wholly produced in the same gas. The broadest line, [Fe  ii ] λ 1.644, exhibits a non-Gaussian profile with a broad base (FWHM≃1040 km s−1), perhaps because of the interaction with the radio source. Extinctions to the line-emitting regions substantially exceed earlier measurements based on optical H recombination lines.
Hard X-rays from the quasar nucleus are likely to dominate the excitation of the H2 emission. The results of Maloney, Hollenbach & Tielens are thus used to infer the total mass of gas in H2 v=1–0 S(1)-emitting clouds as a function of radius, for gas densities of 103 and 105 cm−3, and stopping column densities N H=1022–1024 cm−2. Assuming azimuthal symmetry, at least 2.3×108 M⊙ of such material is present within 5 kpc of the nucleus, if the line-emitting clouds see an unobscured quasar spectrum. Alternatively, if the bulk of the X-ray absorption to the nucleus inferred by Ueno et al. actually arises in a circumnuclear torus, the implied gas mass rises to ∼1010 M⊙. The latter plausibly accounts for 109 yr of mass deposition from the cluster cooling flow, for which within this radius.  相似文献   

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