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1.
Galaxies are believed to be in one-to-one correspondence with simulated dark matter subhaloes. We use high-resolution N -body simulations of cosmological volumes to calculate the statistical properties of subhalo (galaxy) major mergers at high redshift ( z = 0.6–5). We measure the evolution of the galaxy merger rate, finding that it is much shallower than the merger rate of dark matter host haloes at   z > 2.5  , but roughly parallels that of haloes at   z < 1.6  . We also track the detailed merger histories of individual galaxies and measure the likelihood of multiple mergers per halo or subhalo. We examine satellite merger statistics in detail: 15–35 per cent of all recently merged galaxies are satellites, and satellites are twice as likely as centrals to have had a recent major merger. Finally, we show how the differing evolution of the merger rates of haloes and galaxies leads to the evolution of the average satellite occupation per halo, noting that for a fixed halo mass, the satellite halo occupation peaks at   z ∼ 2.5  .  相似文献   

2.
We use high-quality optical rotation curves of nine low-luminosity disc galaxies to obtain the velocity profiles of the surrounding dark matter haloes. We find that they increase linearly with radius at least out to the edge of the stellar disc, implying that, over the entire stellar region, the density of the dark halo is about constant.
The properties of the mass structure of these haloes are similar to those found for a number of dwarf and low surface brightness galaxies, but provide a more substantial evidence of the discrepancy between the halo mass distribution predicted in the cold dark matter scenario and those actually detected around galaxies. We find that the density law proposed by Burkert reproduces the halo rotation curves, with halo central densities ( ρ 0∼1–4×10−24 g cm−3) and core radii ( r 0∼5–15 kpc) scaling as ρ 0∝ r 0−2/3.  相似文献   

3.
We use an extremely large volume  (2.4  h −3 Gpc3)  , high-resolution N -body simulation to measure the higher order clustering of dark matter haloes as a function of mass and internal structure. As a result of the large simulation volume and the use of a novel 'cross-moment' counts-in-cells technique which suppresses discreteness noise, we are able to measure the clustering of haloes corresponding to rarer peaks than was possible in previous studies; the rarest haloes for which we measure the variance are 100 times more clustered than the dark matter. We are able to extract, for the first time, halo bias parameters from linear up to fourth order. For all orders measured, we find that the bias parameters are a strong function of mass for haloes more massive than the characteristic mass   M *  . Currently, no theoretical model is able to reproduce this mass dependence closely. We find that the bias parameters also depend on the internal structure of the halo up to fourth order. For haloes more massive than   M *  , we find that the more concentrated haloes are more weakly clustered than the less concentrated ones. We see no dependence of clustering on concentration for haloes with masses   M < M *  ; this is contrary to the trend reported in the literature when segregating haloes by their formation time. Our results are insensitive to whether haloes are labelled by the total mass returned by the friends-of-friends group finder or by the mass of the most massive substructure. This implies that our conclusions are not an artefact of the particular choice of group finding algorithm. Our results will provide important input to theoretical models of galaxy clustering.  相似文献   

4.
We study the environmental dependence of the formation epoch of dark matter haloes in the Millennium Simulation: a ten billion particle N -body simulation of standard Lambda cold dark matter cosmology. A sensitive test of this dependence – the marked correlation function – reveals highly significant evidence that haloes of a given mass form earlier in denser regions. We define a marked cross-correlation function, which helps quantify how this effect depends upon the choice of the halo population used to define the environment. The mean halo formation redshift as a function of the local overdensity in dark matter is also well determined, and we see an especially clear dependence for galaxy-sized haloes. This contradicts one of the basic predictions of the excursion set model of structure formation, even though we see that this theory predicts other features of the distribution of halo formation epochs rather well. It also invalidates an assumption usually employed in the popular halo, or halo occupation distribution, models of galaxy clustering, namely that the distribution of halo properties is a function of halo mass but not of halo environment.  相似文献   

5.
One of the predictions of the standard cold dark matter model is that dark haloes have centrally divergent density profiles. An extensive body of rotation curve observations of dwarf and low surface brightness galaxies shows the dark haloes of those systems to be characterized by soft constant-density central cores. Several physical processes have been proposed to produce soft cores in dark haloes, each one with different scaling properties. With the aim of discriminating among them we have examined the rotation curves of dark-matter-dominated dwarf and low surface brightness galaxies and the inner mass profiles of two clusters of galaxies lacking a central cD galaxy and with evidence of soft cores in the centre. The core radii and central densities of these haloes scale in a well-defined manner with the depth of their potential wells, as measured through the maximum circular velocity. As a result of our analysis we identify self-interacting cold dark matter as a viable solution to the core problem, where a non-singular isothermal core is formed in the halo centre surrounded by a Navarro, Frenk & White profile in the outer parts. We show that this particular physical situation predicts core radii in agreement with observations. Furthermore, using the observed scalings, we derive an expression for the minimum cross-section ( σ ) which has an explicit dependence with the halo dispersion velocity ( v ). If m x is the mass of the dark matter particle: σ m x ≈4×10−25 (100 km s−1  v −1) cm2 GeV−1.  相似文献   

6.
A parametrized model of the mass distribution within the Milky Way is fitted to the available observational constraints. The most important single parameter is the ratio of the scalelength R d* of the stellar disc to R 0. The disc and bulge dominate v c( R ) at R ≲ R 0 only for R d,*/ R 0≲0.3. Since the only knowledge we have of the halo derives from studies like the present one, we allow it to contribute to the density at all radii. When allowed this freedom, however, the halo causes changes in assumptions relating to R  ≪  R 0 to affect profoundly the structure of the best-fitting model at R  ≫  R 0. For example, changing the disc slightly from an exponential surface-density profile significantly changes the form of v c( R ) at R  ≫  R 0, where the disc makes a negligible contribution to v c. Moreover, minor changes in the constraints can cause the halo to develop a deep hole at its centre that is not physically plausible. These problems call into question the proposition that flat rotation curves arise because galaxies have physically distinct haloes rather than outwards-increasing mass-to-light ratios.   The mass distribution of the Galaxy and the relative importance of its various components will remain very uncertain until more observational data can be used to constrain mass models. Data that constrain the Galactic force field at z ≳ R and at R  >  R 0 are especially important.  相似文献   

7.
We study the formation and evolution of voids in the dark matter distribution using various simulations of the popular Λ cold dark matter cosmogony. We identify voids by requiring them to be regions of space with a mean overdensity of −0.8 or less – roughly the equivalent of using a spherical overdensity group finder for haloes. Each of the simulations contains thousands of voids. The distribution of void sizes in the different simulations shows good agreement when differences in particle and grid resolution are accounted for. Voids very clearly correspond to minima in the smoothed initial density field. Apart from a very weak dependence on the mass resolution, the rescaled mass profiles of voids in the different simulations agree remarkably well. We find a universal void mass profile of the form  ρ(< r )/ρ( r eff) ∝ exp[( r / r eff)α]  , where r eff is the effective radius of a void and  α∼ 2  . The mass function of haloes in voids is steeper than that of haloes that populate denser regions. In addition, the abundances of void haloes seem to evolve somewhat more strongly between redshifts ∼1 and 0 than the global abundances of haloes.  相似文献   

8.
In the standard model of cosmic structure formation, dark matter haloes form by gravitational instability. The process is hierarchical: smaller systems collapse earlier, and later merge to form larger haloes. The galaxy clusters, hosted by the largest dark matter haloes, are at the top of this hierarchy and representing the largest as well as the last structures formed in the Universe, while the smaller and first haloes are those Earth-sized dark subhaloes that have been both predicted by theoretical considerations and found in numerical simulations, though there do not exist any observational hints of their existence. The probability that a halo of mass m at redshift z will be part of a larger halo of mass M at the present time can be described in the frame of the extended Press & Schecter theory making use of the progenitor (conditional) mass function. Using the progenitor mass function, we calculate analytically, at redshift zero, the distribution of subhaloes in mass, formation epoch and rarity of the peak of the density field at the formation epoch. That is done for a Milky Way size system, assuming both a spherical and an ellipsoidal collapse model. Our calculation assumes that small progenitors do not lose mass due to dynamical processes after entering the parent halo, and that they do not interact with other subhaloes. For a Λ cold dark matter power spectrum, we obtain a subhalo mass function  d n /d m   proportional to   m −α  with a model-independent  α∼ 2  . Assuming that the dark matter is a weakly interacting massive particle, the inferred distributions are used to test the feasibility of an indirect detection in the γ-ray energy band of such a population of subhaloes with a Gamma-ray Large Area Space Telescope like satellite.  相似文献   

9.
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   

10.
We study the merging history of dark matter haloes in N -body simulations and semi-analytical 'merger trees' based on the extended Press–Schechter (EPS) formalism. The main focus of our study is the joint distribution of progenitor number and mass as a function of redshift and parent halo mass. We begin by investigating the mean quantities predicted directly by the Press–Schechter (PS) and EPS formalism, such as the halo mass and conditional mass functions, and compare these predictions with the results of the simulations. The higher moments of this distribution are not predicted by the EPS formalism alone and must be obtained from the merger trees. We find that the Press–Schechter model deviates from the simulations at the level of 30–50 per cent on certain mass scales, and that the sense of the discrepancy changes as a function of redshift. We show that this discrepancy is reflected in the higher moments of the distribution of progenitor mass and number. We investigate some related statistics such as the accretion rate and the mass ratio of the largest two progenitors. For galaxy sized haloes ( M ∼1012 M⊙), we find that the merging history of haloes, as represented by these statistics, is well reproduced in the merger trees compared with the simulations. The agreement deteriorates for larger mass haloes. We conclude that merger trees based on the extended Press–Schechter formalism provide a reasonably reliable framework for semi-analytical models of galaxy formation.  相似文献   

11.
We use the Millennium Simulation (MS) to measure the cross-correlation between halo centres and mass (or equivalently the average density profiles of dark haloes) in a Lambda cold dark matter (ΛCDM) cosmology. We present results for radii in the range  10  h −1 kpc < r < 30  h −1 Mpc  and for halo masses in the range  4 × 1010 < M 200 < 4 × 1014  h −1 M⊙  . Both at   z = 0  and at   z = 0.76  these cross-correlations are surprisingly well fitted if the inner region is approximated by a density profile of NFW or Einasto form, the outer region by a biased version of the linear mass autocorrelation function, and the maximum of the two is adopted where they are comparable. We use a simulation of galaxy formation within the MS to explore how these results are reflected in cross-correlations between galaxies and mass. These are directly observable through galaxy–galaxy lensing. Here also we find that simple models can represent the simulation results remarkably well, typically to ≲10 per cent. Such models can be used to extend our results to other redshifts, to cosmologies with other parameters, and to other assumptions about how galaxies populate dark haloes. Our galaxy formation simulation already reproduces current galaxy–galaxy lensing data quite well. The characteristic features predicted in the galaxy–galaxy lensing signal should provide a strong test of the ΛCDM cosmology as well as a route to understanding how galaxies form within it.  相似文献   

12.
We study the mass assembly history (MAH) of dark matter haloes. We compare MAHs obtained using (i) merger trees constructed with the extended Press–Schechter (EPS) formalism, (ii) numerical simulations and (iii) the Lagrangian perturbation code pinocchio . We show that the pinocchio MAHs are in excellent agreement with those obtained using numerical simulations, while the EPS formalism predicts MAHs that occur too late. pinocchio , which is much less CPU intensive than N -body simulation, can be run on a simple personal computer, and does not require any labour intensive post-simulation analysis, therefore provides a unique and powerful tool to investigate the growth history of dark matter haloes. Using a suite of 55 pinocchio simulations, with 2563 particles each, we study the MAHs of 12 924 cold dark matter (CDM) haloes in a ΛCDM concordance cosmology. This is by far the largest set of haloes used for any such analysis. For each MAH we derive four different formation redshifts, which characterize different epochs during the assembly history of a dark matter halo. We show that haloes less massive than the characteristic non-linear mass scale establish their potential wells much before they acquire most of their mass. The time when a halo reaches its maximum virial velocity roughly divides its mass assembly into two phases, a fast-accretion phase which is dominated by major mergers, and a slow-accretion phase dominated by minor mergers. Each halo experiences about 3 ± 2 major mergers since its main progenitor had a mass equal to 1 per cent of the final halo mass. This major merger statistic is found to be virtually independent of halo mass. However, the average redshift at which these major mergers occur is strongly mass dependent, with more massive haloes experiencing their major mergers later.  相似文献   

13.
We study the distribution function (DF) of dark matter particles in haloes of mass range  1014–1015 M⊙  . In the numerical part of this work we measure the DF for a sample of relaxed haloes formed in the simulation of a standard Λ cold dark matter (ΛCDM) model. The DF is expressed as a function of energy E and the absolute value of the angular momentum L , a form suitable for comparison with theoretical models. By proper scaling we obtain the results that do not depend on the virial mass of the haloes. We demonstrate that the DF can be separated into energy and angular momentum components and propose a phenomenological model of the DF in the form     . This formulation involves three parameters describing the anisotropy profile in terms of its asymptotic values (β0 and  β∞  ) and the scale of transition between them ( L 0). The energy part   f E ( E )  is obtained via inversion of the integral for spatial density. We provide a straightforward numerical scheme for this procedure as well as a simple analytical approximation for a typical halo formed in the simulation. The DF model is extensively compared with the simulations: using the model parameters obtained from fitting the anisotropy profile, we recover the DF from the simulation as well as the profiles of the dispersion and kurtosis of radial and tangential velocities. Finally, we show that our DF model reproduces the power-law behaviour of phase-space density   Q =ρ( r )/σ3( r )  .  相似文献   

14.
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   

15.
We derive a simple semi-analytical approximation for lens equations with an arbitrary radially symmetric mass density ρ( r ), when   r /ξ0≪ 1  and ξ0 is the scalelength of the density profile. At the strong lensing regime, which is mostly constrained by the inner part of the mass density profile, we assume ρ∝ r α.
A dark matter (DM) haloes (GNFW model) are parametrized through a shape parameter α, a concentration parameter c 1 and the total mass M . We apply our semi-analytical model to show how the solutions of the axially symmetric lens equations are degenerated in respect to the parameters α and c 1.
In the case of an asymmetric dual image lens system, similar effective degeneracy is produced when the geometry of the lens is relaxed. Because it is impossible to determine the exact location of the source image, a family of solutions is acquired when the mass of the lens object and location of the observed images are fixed.
Our results indicate that the amount of degeneration is only weakly affected by the asymmetry in the lensing geometry set-up, e.g. the observational effective degeneracy is very close to the true physical degeneracy of the Einstein ring solutions. Basically with high-enough values for the concentration parameter, the degeneracy spawns the whole range for the shape parameter  α=[−2.0, −1.0]  .  相似文献   

16.
We investigate the figure rotation of dark matter haloes identified in Λ cold dark matter (CDM) simulations. We find that when strict criteria are used to select suitable haloes for study, five of the 222 haloes identified in our   z = 0  simulation output undergo coherent figure rotation over a  5 h −1 Gyr  period. We discuss the effects of varying the selection criteria and find that pattern speeds for a much larger fraction of the haloes can be measured when the criteria are relaxed. Pattern speeds measured over a  1 h −1 Gyr  period follow a lognormal distribution, centred at  Ωp= 0.2 h rad Gyr−1  with a maximum value of 0.94 h rad Gyr−1. Over a  5 h −1 Gyr  period, the average pattern speed of a halo is about  0.1 h rad Gyr−1  and the largest pattern speed found is  0.24 h rad Gyr−1  . Less than half of the selected haloes showed alignment between their figure rotation axis and minor axis, the exact fraction being somewhat dependent on how one defines a halo. While the pattern speeds observed are lower than those generally thought capable of causing spiral structure, we note that coherent figure rotation is found over very long periods and argue that further simulations would be required before strong conclusions about spiral structure in all galaxies could be drawn. We find no correlation between halo properties such as total mass and the pattern speed.  相似文献   

17.
Using a high-resolution cosmological N -body simulation, we identify the ejected population of subhaloes, which are haloes at redshift   z = 0  but were once contained in more massive 'host' haloes at high redshifts. The fraction of the ejected subhaloes in the total halo population of the same mass ranges from 9 to 4 per cent for halo masses from  ∼1011  to  ∼1012  h −1 M⊙  . Most of the ejected subhaloes are distributed within four times the virial radius of their hosts. These ejected subhaloes have distinct velocity distribution around their hosts in comparison to normal haloes. The number of subhaloes ejected from a host of given mass increases with the assembly redshift of the host. Ejected subhaloes in general reside in high-density regions, and have a much higher bias parameter than normal haloes of the same mass. They also have earlier assembly times, so that they contribute to the assembly bias of dark matter haloes seen in cosmological simulations. However, the assembly bias is not dominated by the ejected population, indicating that large-scale environmental effects on normal haloes are the main source for the assembly bias.  相似文献   

18.
We examine the properties of dark matter haloes within a rich galaxy cluster using a high-resolution simulation that captures the cosmological context of a cold dark matter universe. The mass and force resolution permit the resolution of 150 haloes with circular velocities larger than 80 km s−1 within the cluster virial radius of 2 Mpc (with Hubble constant H 0 = 50 km s−1 Mpc−1). This enables an unprecedented study of the statistical properties of a large sample of dark matter haloes evolving in a dense environment. The cumulative fraction of mass attached to these haloes varies from close to zero per cent at 200 kpc to 13 per cent at the virial radius. Even at this resolution the overmerging problem persists; haloes that pass within 100–200 kpc of the cluster centre are tidally disrupted. Additional substructure is lost at earlier epochs within the massive progenitor haloes. The median ratio of apocentric to pericentric radii is 6:1, so that the orbital distribution is close to isotropic, circular orbits are rare and radial orbits are common. The orbits of haloes are unbiased with respect to both position within the cluster and the orbits of the smooth dark matter background, and no velocity bias is detected. The tidal radii of surviving haloes are generally well-fitted using the simple analytic prediction applied to their orbital pericentres. Haloes within clusters have higher concentrations than those in the field. Within the cluster, halo density profiles can be modified by tidal forces and individual encounters with other haloes that cause significant mass loss —'galaxy harassment'. Mergers between haloes do not occur inside the cluster virial radius.  相似文献   

19.
We present the Millennium-II Simulation (MS-II), a very large N -body simulation of dark matter evolution in the concordance Λ cold dark matter (ΛCDM) cosmology. The MS-II assumes the same cosmological parameters and uses the same particle number and output data structure as the original Millennium Simulation (MS), but was carried out in a periodic cube one-fifth the size  (100  h −1 Mpc)  with five times better spatial resolution (a Plummer equivalent softening of  1.0  h −1 kpc  ) and with 125 times better mass resolution (a particle mass of  6.9 × 106  h −1 M⊙  ). By comparing results at MS and MS-II resolution, we demonstrate excellent convergence in dark matter statistics such as the halo mass function, the subhalo abundance distribution, the mass dependence of halo formation times, the linear and non-linear autocorrelations and power spectra, and halo assembly bias. Together, the two simulations provide precise results for such statistics over an unprecedented range of scales, from haloes similar to those hosting Local Group dwarf spheroidal galaxies to haloes corresponding to the richest galaxy clusters. The 'Milky Way' haloes of the Aquarius Project were selected from a lower resolution version of the MS-II and were then resimulated at much higher resolution. As a result, they are present in the MS-II along with thousands of other similar mass haloes. A comparison of their assembly histories in the MS-II and in resimulations of 1000 times better resolution shows detailed agreement over a factor of 100 in mass growth. We publicly release halo catalogues and assembly trees for the MS-II in the same format within the same archive as those already released for the MS.  相似文献   

20.
We confirm and extend the recent finding that the central surface density  μ0D≡ r 0ρ0  of galaxy dark matter haloes, where r 0 and  ρ0  are the halo core radius and central density, is nearly constant and independent of galaxy luminosity. Based on the co-added rotation curves (RCs) of ∼1000 spiral galaxies, the mass models of individual dwarf irregular and spiral galaxies of late and early types with high-quality RCs, and the galaxy–galaxy weak-lensing signals from a sample of spiral and elliptical galaxies, we find that  log μ0D= 2.15 ± 0.2  in units of  log(M⊙ pc−2)  . We also show that the observed kinematics of Local Group dwarf spheroidal galaxies are consistent with this value. Our results are obtained for galactic systems spanning over 14 mag, belonging to different Hubble types and whose mass profiles have been determined by several independent methods. In the same objects, the approximate constancy of  μ0D  is in sharp contrast to the systematical variations, by several orders of magnitude, of galaxy properties, including  ρ0  and central stellar surface density.  相似文献   

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