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1.
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   

2.
The formation of galaxy clusters in hierarchically clustering universes is investigated by means of high-resolution N -body simulations. The simulations are performed using a newly developed multimass scheme which combines a PM code with a high-resolution N -body code. Numerical effects resulting from time-stepping and gravitational softening are investigated, as well as the influence of the simulation box size and of the assumed boundary conditions. Special emphasis is laid on the formation process and the influence of various cosmological parameters. Cosmogonies with massive neutrinos are also considered. Differences between clusters in the same cosmological model seem to dominate over differences caused by differing background cosmogony. The cosmological model can alter the time evolution of cluster collapse, but the merging pattern remains fairly similar, e.g. the number of mergers and the mass ratio of mergers. The gross properties of a halo, such as its size and total angular momentum, also evolve in a similar manner for all cosmogonies, and can be described using analytical models. It is shown that the density distribution of a halo shows a characteristic radial dependence which follows a power law with a slope of =1 at small radii and =3 at large radii, independent of the background cosmogony or the considered redshift. The shape of the density profiles follows the generic form proposed by Navarro et al. for all hierarchically clustering scenarios, and retains very little information about the formation process or the cosmological model. Only the central matter concentration of a halo is correlated with the formation time and therefore the corresponding cosmogony. We emphasize the role of non-radial motions of the halo particles in the evolution of the density profile.  相似文献   

3.
A modified version of the extended Press–Schechter model for the growth of dark-matter haloes was introduced in two previous papers, with the aim of explaining the mass–density relation shown by haloes in high-resolution cosmological simulations. In this model, major mergers are well separated from accretion, thereby allowing a natural definition of halo formation and destruction. This makes it possible to derive analytic expressions for halo formation and destruction rates, the mass accretion rate and the probability distribution functions of halo formation times and progenitor masses. The stochastic merger histories of haloes can be readily derived and easily incorporated into semi-analytical models of galaxy formation, thus avoiding the usual problems encountered in the construction of Monte Carlo merger trees from the original extended Press–Schechter formalism. Here we show that the predictions of the modified Press–Schechter model are in good agreement with the results of N -body simulations for several scale-free cosmologies.  相似文献   

4.
We explore a possible origin for the puzzling anti-correlation between the formation epoch of galactic dark-matter haloes and their environment density. This correlation has been revealed from cosmological N -body simulations and is in conflict with the extended Press–Schechter model of halo clustering. Using similar simulations, we first quantify the straightforward association of an early formation epoch with a reduced mass-growth rate at late times. We then find that a primary driver of suppressed growth, by accretion and mergers, is tidal effects dominated by a neighbouring massive halo. The tidal effects range from a slowdown of the assembly of haloes due to the shear along the large-scale filaments that feed the massive halo to actual mass loss in haloes that pass through the massive halo. Using the restricted three-body problem, we show that haloes are prone to tidal mass loss within 1.5 virial radii of a larger halo. Our results suggest that the dependence of the formation epoch on environment density is a secondary effect induced by the enhanced density of haloes in filaments near massive haloes where the tides are strong. Our measures of assembly rate are particularly correlated with the tidal field at high redshifts   z ∼ 1  .  相似文献   

5.
We present a general recipe for constructing N -body realizations of galaxies comprising near spherical and disc components. First, an exact spherical distribution function for the spheroids (halo and bulge) is determined, such that it is in equilibrium with the gravitational monopole of the disc components. Second, an N -body realization of this model is adapted to the full disc potential by growing the latter adiabatically from its monopole. Finally, the disc is sampled with particles drawn from an appropriate distribution function, avoiding local-Maxwellian approximations. We performed test simulations and find that the halo and bulge radial density profile very closely match their target model, while they become slightly oblate due to the added disc gravity. Our findings suggest that vertical thickening of the initially thin disc is caused predominantly by spiral and bar instabilities, which also result in a radial re-distribution of matter, rather than scattering off interloping massive halo particles.  相似文献   

6.
We use the extended Press–Schechter formalism to investigate the rate at which cold dark matter haloes accrete mass. We discuss the shortcomings of previous methods that have been used to compute the mass accretion histories of dark matter haloes, and present an improved method based on the N -branch merger tree algorithm of Somerville & Kolatt. We show that this method no longer suffers from inconsistencies in halo formation times, and compare its predictions with high-resolution N -body simulations. Although the overall agreement is reasonable, there are slight inconsistencies which are most easily interpreted as a reflection of ellipsoidal collapse (as opposed to spherical collapse assumed in the Press–Schechter formalism). We show that the average mass accretion histories follow a simple, universal profile, and we present a simple recipe for computing the two scale-parameters which is applicable to a wide range of halo masses and cosmologies. Together with the universal profiles for the density and angular momentum distributions of cold dark matter haloes, these universal mass accretion histories provide a simple but accurate framework for modelling the structure and formation of dark matter haloes. In particular, they can be used as a backbone for modelling various aspects of galaxy formation where one is not interested in the detailed effects of merging. As an example we use the universal mass accretion history to compute the rate at which dark matter haloes accrete mass, which we compare with the cosmic star formation history of the Universe.  相似文献   

7.
We explain in simple terms how the build-up of dark haloes by merging compact satellites, as in the cold dark matter (CDM) cosmology, inevitably leads to an inner cusp of density profile  ρ∝ r −α  with  α≳ 1  , as seen in cosmological N -body simulations. A flatter halo core with  α < 1  exerts on the satellites tidal compression in all directions, which prevents the deposit of stripped satellite material in the core region. This makes the satellite orbits decay from the radius where  α∼ 1  to the halo centre with no local tidal mass transfer, and thus causes a rapid steepening of the inner profile to  α > 1  . These tidal effects, the resultant steepening of the profile to a cusp, and the stability of this cusp to tandem mergers with compact satellites are demonstrated using N -body simulations. The transition at  α∼ 1  is then addressed using toy models in the limiting cases of impulse and adiabatic approximations and using tidal radii for satellites on radial and circular orbits. In an associated paper, we address the subsequent slow convergence from either side to an asymptotic stable cusp with  α≳ 1  . Our analysis thus implies that an inner cusp is enforced when small haloes are typically more compact than larger haloes, as in the CDM scenario, such that enough satellite material makes it intact into the inner halo and is deposited there. We conclude that a necessary condition for maintaining a flat core, as indicated by observations, is that the inner regions of the CDM satellite haloes be puffed up by about 50 per cent such that when they merge into a larger halo they would be disrupted outside the halo core. This puffing up could be due to baryonic feedback processes in small haloes, which may be stimulated by the tidal compression in the halo cores.  相似文献   

8.
We perform collisionless N -body simulations of 1:1 galaxy mergers, using models which include a galaxy halo, disc and bulge, focusing on the behaviour of the halo component. The galaxy models are constructed without recourse to a Maxwellian approximation. We investigate the effect of varying the galaxies' orientation, their mutual orbit and the initial velocity anisotropy or cusp strength of the haloes upon the remnant halo density profiles and shape, as well as on the kinematics. We observe that the halo density profile (determined as a spherical average, an approximation we find appropriate) is exceptionally robust in mergers, and that the velocity anisotropy of our remnant haloes is nearly independent of the orbits or initial anisotropy of the haloes. The remnants follow the halo anisotropy – local density slope (β–γ) relation suggested by Hansen & Moore in the inner parts of the halo, but β is systematically lower than this relation predicts in the outer parts. Remnant halo axis ratios are strongly dependent on the initial parameters of the haloes and on their orbits. We also find that the remnant haloes are significantly less spherical than those described in studies of simulations which include gas cooling.  相似文献   

9.
We present N -body simulations of galaxy groups embedded in a common halo of matter. We study the influence of the different initial conditions upon the evolution of the group and show that denser configurations evolve faster, as expected. We then concentrate on the influence of the initial radial density profile of the common halo and of the galaxy distribution. We select two kinds of density distributions, a singular profile (modelled by a Hernquist distribution) and a profile with a flat core (modelled by a Plummer sphere). In all cases we witness the formation of a central massive object owing to mergings of individual galaxies and to accretion of stripped material, but both its formation history and its properties depend heavily on the initial distribution. In Hernquist models the formation is caused by a 'burst' of mergings in the inner parts, owing to the large initial concentration of galaxies in the centre. The merging rate is much slower in the initial phases of the evolution of a Plummer distribution, where the contribution of accretion to the formation of the central object is much more important. The central objects formed within Plummer distributions have projected density profiles which are not in agreement with the radial profiles of observed brightest cluster members, unless the percentage of mass in the common halo is small. In contrast, the central object formed in initially cusped models has projected radial profiles in very good agreement with those of brightest cluster members, sometimes also showing luminosity excess over the r 1/4 law in the outer parts, as is observed in cD galaxies.  相似文献   

10.
We investigate the properties of satellite galaxies formed in N -body/SPH simulations of galaxy formation in the ΛCDM cosmology. The simulations include the main physical effects thought to be important in galaxy formation and, in several cases, produce realistic spiral discs. In total, a sample of nine galaxies of luminosity comparable to the Milky Way was obtained. At magnitudes brighter than the resolution limit,   MV =−12  , the luminosity function of the satellite galaxies in the simulations is in excellent agreement with data for the Local Group. The radial number density profile of the model satellites, as well as their gas fractions also match observations very well. In agreement with previous N -body studies, we find that the satellites tend to be distributed in highly flattened configurations whose major axis is aligned with the major axis of the (generally triaxial) dark halo. In two out of three systems with sufficiently large satellite populations, the satellite system is nearly perpendicular to the plane of the galactic disc, a configuration analogous to that observed in the Milk Way. The discs themselves are perpendicular to the minor axis of their host haloes in the inner parts, and the correlation between the orientation of the galaxy and the shape of the halo persists even out to the virial radius. However, in one case the disc's minor axis ends up, at the virial radius, perpendicular to the minor axis of the halo. The angular momenta of the galaxies and their host halo tend to be well aligned.  相似文献   

11.
We derive analytic merger rates for dark matter haloes within the framework of the extended Press–Schechter (EPS) formalism. These rates become self-consistent within EPS once we realize that the typical merger in the limit of a small time-step involves more than two progenitors, contrary to the assumption of binary mergers adopted in earlier studies. We present a general method for computing merger rates that span the range of solutions permitted by the EPS conditional mass function, and focus on a specific solution that attempts to match the merger rates in N -body simulations. The corrected EPS merger rates are more accurate than the earlier estimates of Lacey & Cole by ∼20 per cent for major mergers and by up to a factor of ∼3 for minor mergers of mass ratio 1:104. Based on the revised merger rates, we provide a new algorithm for constructing Monte Carlo EPS merger trees, which could be useful in semi-analytic modelling. We provide analytic expressions and plot numerical results for several quantities that are very useful in studies of galaxy formation. This includes (i) the rate of mergers of a given mass ratio per given final halo, (ii) the fraction of mass added by mergers to a halo and (iii) the rate of mergers per given main progenitor. The creation and destruction rates of haloes serve for a self-consistency check. Our method for computing merger rates can be applied to conditional mass functions beyond EPS, such as those obtained by the ellipsoidal collapse model or extracted from N -body simulations.  相似文献   

12.
We model the acquisition of spin by dark-matter haloes in semi-analytic merger trees. We explore two different algorithms: one in which halo spin is acquired from the orbital angular momentum of merging satellites, and another in which halo spin is gained via tidal torquing on shells of material while still in the linear regime. We find that both scenarios produce the characteristic spin distribution of haloes found in N -body simulations, namely, a log-normal distribution with mean ≈ 0.04 and standard deviation ≈ 0.5 in the log. A perfect match requires fine-tuning of two free parameters. Both algorithms also reproduce the general insensitivity of the spin distribution to halo mass, redshift and cosmology seen in N -body simulations. The spin distribution can be made strictly constant by physically motivated scalings of the free parameters. In addition, both schemes predict that haloes that have had recent major mergers have systematically larger spin values. These algorithms can be implemented within semi-analytic models of galaxy formation based on merger trees. They yield detailed predictions of galaxy properties that strongly depend on angular momentum (such as size and surface brightness) as a function of merger history and environment.  相似文献   

13.
I study the evolution of halo density profiles as a function of time in the SCDM and ΛCDM cosmologies. Following Del Popolo, I calculate the concentration parameter c = r v / a and study its time evolution. For a given halo mass, I find that c ( z ) ∝ 1/(1+ z ) in both the ΛCDM and SCDM cosmology, in agreement with the analytic model of Bullock et al. and N -body simulations. In both models, a ( z ) is roughly constant. The present model predicts a stronger evolution of c ( z ) with respect to the Navarro, Frenk & White model. Finally I show some consequences of the results on galaxy modelling.  相似文献   

14.
The merging history of dark matter haloes is computed with the Merging Cell Model proposed by Rodrigues & Thomas. While originally discussed in the case of scale-free power spectra, it is developed and tested here in the framework of the cold dark matter cosmology. The halo mass function, the mass distribution of progenitors and child haloes, as well as the probability distribution of formation times, have been computed and compared with the available analytic predictions. The halo autocorrelation function has also been obtained (a first for a semi-analytic merging tree), and tested against analytic formulae. An overall good agreement is found between results of the model, and the predictions derived from the Press & Schechter theory and its extensions. More severe discrepancies appear when formulae that better describe N -body simulations are used for comparison. In many instances, the model can be a useful tool for following the hierarchical growth of structures. In particular, it is suitable for addressing the issue of the formation and evolution of galaxy clusters, as well as the population of Lyman-break galaxies at high redshift, and their clustering properties.  相似文献   

15.
Accepted 1998 January 26. Received 1998 January 26; in original form 1997 August 13This paper presents a stochastic approach to the clustering evolution of dark matter haloes in the Universe. Haloes, identified by a Press–Schechter-type algorithm in Lagrangian space, are described in terms of 'counting fields', acting as non-linear operators on the underlying Gaussian density fluctuations. By ensemble-averaging these counting fields, the standard Press–Schechter mass function as well as analytic expressions for the halo correlation function and corresponding bias factors of linear theory are obtained, extending the recent results by Mo & White. The non-linear evolution of our halo population is then followed by solving the continuity equation, under the sole hypothesis that haloes move by the action of gravity. This leads to an exact and general formula for the bias field of dark matter haloes, defined as the local ratio between their number density contrast and the mass density fluctuation. Besides being a function of position and 'observation' redshift, this random field depends upon the mass and formation epoch of the objects and is both non-linear and non-local. The latter features are expected to leave a detectable imprint on the spatial clustering of galaxies, as described, for instance, by statistics like the bispectrum and the skewness. Our algorithm may have several interesting applications, among which is the possibility of generating mock halo catalogues from low-resolution N -body simulations.  相似文献   

16.
We discuss the morphology, photometry and kinematics of the bars which have formed in three N -body simulations. These have initially the same disc and the same halo-to-disc mass ratio, but their haloes have very different central concentrations. The third model includes a bulge. The bar in the model with the centrally concentrated halo (model MH) is much stronger, longer and thinner than the bar in the model with the less centrally concentrated halo (model MD). Its shape, when viewed side-on, evolves from boxy to peanut and then to 'X'-shaped, as opposed to that of model MD, which stays boxy. The projected density profiles obtained from cuts along the bar major axis, for both the face-on and the edge-on views, show a flat part, as opposed to those of model MD which are falling rapidly. A Fourier analysis of the face-on density distribution of model MH shows very large  m=2  , 4, 6 and 8 components. Contrary to this, for model MD the components  m=6  and 8 are negligible. The velocity field of model MH shows strong deviations from axial symmetry, and in particular has wavy isovelocities near the end of the bar when viewed along the bar minor axis. When viewed edge-on, it shows cylindrical rotation, which the MD model does not. The properties of the bar of the model with a bulge and a non-centrally concentrated halo (MDB) are intermediate between those of the bars of the other two models. All three models exhibit a lot of inflow of the disc material during their evolution, so that by the end of the simulations the disc dominates over the halo in the inner parts, even for model MH, for which the halo and disc contributions were initially comparable in that region.  相似文献   

17.
We present predictions for the line-of-sight velocity dispersion profiles of dwarf spheroidal galaxies and compare them to observations in the case of the Fornax dwarf. The predictions are made in the framework of standard dynamical theory of spherical systems with different velocity distributions. The stars are assumed to be distributed according to Sérsic laws with parameters fitted to observations. We compare predictions obtained assuming the presence of dark matter haloes (with density profiles adopted from N -body simulations) with those resulting from Modified Newtonian Dynamics (MOND). If the anisotropy of velocity distribution is treated as a free parameter, observational data for Fornax are reproduced equally well by models with dark matter and with MOND. If stellar mass-to-light ratio of 1 M⊙/L⊙ is assumed, the required mass of the dark halo is     , two orders of magnitude larger than the mass in stars. The derived MOND acceleration scale is     . In both cases a certain amount of tangential anisotropy in the velocity distribution is needed to reproduce the shape of the velocity dispersion profile in Fornax.  相似文献   

18.
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19.
The stochasticity in the distribution of dark haloes in the cosmic density field is reflected in the distribution function   P V ( N h| δ m)  , which gives the probability of finding N h haloes in a volume V with mass density contrast δ m. We study the properties of this function using high-resolution N -body simulations, and find that   P V ( N h| δ m)  is significantly non-Poisson. The ratio between the variance and the mean goes from ∼1 (Poisson) at  1+ δ m≪1  to <1 (sub-Poisson) at  1+ δ m∼1  to >1 (super-Poisson) at  1+ δ m≫1  . The mean bias relation is found to be well described by halo bias models based on the Press–Schechter formalism. The sub-Poisson variance can be explained as a result of halo exclusion, while the super-Poisson variance at high δ m may be explained as a result of halo clustering. A simple phenomenological model is proposed to describe the behaviour of the variance as a function of δ m. Galaxy distribution in the cosmic density field predicted by semi-analytic models of galaxy formation shows similar stochastic behaviour. We discuss the implications of the stochasticity in halo bias to the modelling of higher order moments of dark haloes and of galaxies.  相似文献   

20.
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