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1.
In an earlier paper, we quantified the mean merger rate of dark matter haloes as a function of redshift z , descendant halo mass M 0, and progenitor halo mass ratio ξ using the Millennium simulation of the Λ cold dark matter cosmology. Here, we broaden that study and investigate the dependence of the merger rate of haloes on their surrounding environment. A number of local mass overdensity variables, both including and excluding the halo mass itself, are tested as measures of a halo's environment. The simple functional dependence on   z , M 0  , and ξ of the merger rate found in our earlier work, is largely preserved in different environments, but we find that the overall amplitude of the merger rate has a strong positive correlation with the environmental densities. For galaxy-mass haloes, we find mergers to occur ∼2.5 times more frequently in the densest regions than in voids at both   z = 0  and higher redshifts. Higher mass haloes show similar trends. We present a fitting form for this environmental dependence that is a function of both mass and local density and valid out to   z = 2  . The amplitude of the progenitor (or conditional) mass function shows a similar correlation with local overdensity, suggesting that the extended Press–Schechter model for halo growth needs to be modified to incorporate environmental effects.  相似文献   

2.
We generalize the Doroshkevich's celebrated formulae for the eigenvalues of the initial shear field associated with Gaussian statistics to the local non-Gaussian   fnl   model. This is possible because, to at least second order in   fnl   , distributions at fixed overdensity are unchanged from the case   fnl = 0  . We use this generalization to estimate the effect of   fnl ≠ 0  on the abundance of virialized haloes. Halo abundances are expected to be related to the probability that a certain quantity in the initial fluctuation field exceeds a threshold value, and we study two choices for this variable: it can either be the sum of the eigenvalues of the initial deformation tensor (the initial overdensity) or its smallest eigenvalue. The approach based on a critical overdensity yields results which are in excellent agreement with numerical measurements. We then use these same methods to develop approximations describing the sensitivity of void abundances on   fnl   . While a positive   fnl   produces more extremely massive haloes, it makes fewer extremely large voids. Its effect thus is qualitatively different from a simple rescaling of the normalization of the density fluctuation field σ8. Therefore, void abundances furnish complementary information to cluster abundances, and a joint comparison of both might provide interesting constraints on primordial non-Gaussianity.  相似文献   

3.
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   

4.
Using the Millennium N -body Simulation we explore how the shape and angular momentum of galaxy dark matter haloes surrounding the largest cosmological voids are oriented. We find that the major and intermediate axes of the haloes tend to lie parallel to the surface of the voids, whereas the minor axis points preferentially in the radial direction. We have quantified the strength of these alignments at different radial distances from the void centres. The effect of these orientations is still detected at distances as large as 2.2 R void from the void centre. Taking a subsample of haloes expected to contain disc-dominated galaxies at their centres we detect, at the 99.9 per cent confidence level, a signal that the angular momentum of those haloes tends to lie parallel to the surface of the voids. Contrary to the alignments of the inertia axes, this signal is only detected in shells at the void surface  (1 < R < 1.07  R void)  and disappears at larger distances. This signal, together with the similar alignment observed using real spiral galaxies, strongly supports the prediction of the Tidal Torque theory that both dark matter haloes and baryonic matter have acquired, conjointly, their angular momentum before the moment of turnaround.  相似文献   

5.
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   

6.
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   

7.
We investigate the conditions for the existence of an expanding virial shock in the gas falling within a spherical dark matter halo. The shock relies on pressure support by the shock-heated gas behind it. When the radiative cooling is efficient compared with the infall rate, the post-shock gas becomes unstable; it collapses inwards and cannot support the shock. We find for a monatomic gas that the shock is stable when the post-shock pressure and density obey     . When expressed in terms of the pre-shock gas properties at radius r it reads as  ρ r Λ( T )/ u 3 < 0.0126  , where ρ is the gas density, u is the infall velocity and Λ( T ) is the cooling function, with the post-shock temperature   T ∝ u 2  . This result is confirmed by hydrodynamical simulations, using an accurate spheri-symmetric Lagrangian code. When the stability analysis is applied in cosmology, we find that a virial shock does not develop in most haloes that form before   z ∼ 2  , and it never forms in haloes less massive than a few  1011 M⊙  . In such haloes, the infalling gas is not heated to the virial temperature until it hits the disc, thus avoiding the cooling-dominated quasi-static contraction phase. The direct collapse of the cold gas into the disc should have non-trivial effects on the star formation rate and on outflows. The soft X-ray produced by the shock-heated gas in the disc is expected to ionize the dense disc environment, and the subsequent recombination would result in a high flux of Lα emission. This may explain both the puzzling low flux of soft X-ray background and the Lα emitters observed at high redshift.  相似文献   

8.
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   

9.
We explore the dependence of the central logarithmic slope of dark matter halo density profiles α on the spectral index n of the linear matter power spectrum P ( k ) using cosmological N -body simulations of scale-free models [i.e. P ( k ) ∝ k n ]. These simulations are based on a set of clear, reproducible and physically motivated criteria that fix the appropriate starting and stopping times for runs, and allow one to compare haloes across models with different spectral indices and mass resolutions. For each of our simulations we identify samples of well-resolved haloes in dynamical equilibrium and we analyse their mass profiles. By parametrizing the mass profile using a 'generalized' Navarro, Frenk & White profile in which the central logarithmic slope α is allowed to vary while preserving the r −3 asymptotic form at large radii, we obtain preferred central slopes for haloes in each of our models. There is a strong correlation between α and n , such that α becomes shallower as n becomes steeper. However, if we normalize our mass profiles by r −2, the radius at which the logarithmic slope of the density profile is −2, we find that these differences are no longer present. This is apparent if we plot the maximum slope     as a function of r / r −2– we find that the profiles are similar for haloes forming in different n models. This reflects the importance of concentration, and reveals that the concentrations of haloes forming in steep- n cosmologies tend to be smaller than those of haloes forming in shallow- n cosmologies. We conclude that there is no evidence for convergence to a unique central asymptotic slope, at least on the scales that we can resolve.  相似文献   

10.
We argue that a universal density profile for dark matter haloes arises as a natural consequence of hierarchical structure formation: it is a fixed point in the process of repeated mergers. We present analytic and numerical arguments for the emergence of a particular form of the central cusp profile. At small radii, the density should vary as r −α, with α determined by the way in which the characteristic density of haloes scales with their mass. If small haloes are dense, then α is large. The mass–density relation can be related to the power spectrum of initial fluctuations, P ( k ), through 'formation time' arguments. Early structure formation leads to steep cusps. For P ( k ) ∼  k n we find α ≃ 3(3 +  n )/(5 +  n ). The universal profile is generated by tidal stripping of small haloes as they merge with larger objects.  相似文献   

11.
Voids are a dominant feature of the low-redshift galaxy distribution. Several recent surveys have found evidence for the existence of large-scale structure at high redshifts as well. We present analytic estimates of galaxy void sizes at redshifts   z ∼ 5–10  using the excursion set formalism. We find that recent narrow-band surveys at   z ∼ 5–6.5  should find voids with characteristic scales of roughly 20 comoving Mpc and maximum diameters approaching 40 Mpc. This is consistent with existing surveys, but a precise comparison is difficult because of the relatively small volumes probed so far. At   z ∼ 7–10  , we expect characteristic void scales of ∼14–20 comoving Mpc assuming that all galaxies within dark matter haloes more massive than  1010 M⊙  are observable. We find that these characteristic scales are similar to the sizes of empty regions resulting from purely random fluctuations in the galaxy counts. As a result, true large-scale structure will be difficult to observe at   z ∼ 7–10  , unless galaxies in haloes with masses  ≲109 M⊙  are visible. Galaxy surveys must be deep and only the largest voids will provide meaningful information. Our model provides a convenient picture for estimating the 'worst-case' effects of cosmic variance on high-redshift galaxy surveys with limited volumes.  相似文献   

12.
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   

13.
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   

14.
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   

15.
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   

16.
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   

17.
Motivated by recent observational studies of the environment of   z ∼ 6  QSOs, we have used the Millennium Run (MR) simulations to construct a very large  (∼4°× 4°)  mock redshift survey of star-forming galaxies at   z ∼ 6  . We use this simulated survey to study the relation between density enhancements in the distribution of i 775-dropouts and Lyα emitters, and their relation to the most massive haloes and protocluster regions at   z ∼ 6  . Our simulation predicts significant variations in surface density across the sky with some voids and filaments extending over scales of 1°, much larger than probed by current surveys. Approximately one-third of all   z ∼ 6  haloes hosting i -dropouts brighter than   z = 26.5  mag  (≈ M *UV, z =6)  become part of   z = 0  galaxy clusters. i -dropouts associated with protocluster regions are found in regions where the surface density is enhanced on scales ranging from a few to several tens of arcminutes on the sky. We analyse two structures of i -dropouts and Lyα emitters observed with the Subaru Telescope and show that these structures must be the seeds of massive clusters in formation. In striking contrast, six   z ∼ 6  QSO fields observed with Hubble Space Telescope show no significant enhancements in their i 775-dropout number counts. With the present data, we cannot rule out the QSOs being hosted by the most massive haloes. However, neither can we confirm this widely used assumption. We conclude by giving detailed recommendations for the interpretation and planning of observations by current and future ground- and space-based instruments that will shed new light on questions related to the large-scale structure at   z ∼ 6  .  相似文献   

18.
The time-scale for galaxies within merging dark matter haloes to merge with each other is an important ingredient in galaxy formation models. Accurate estimates of merging time-scales are required for predictions of astrophysical quantities such as black hole binary merger rates, the build-up of stellar mass in central galaxies and the statistical properties of satellite galaxies within dark matter haloes. In this paper, we study the merging time-scales of extended dark matter haloes using N -body simulations. We compare these results to standard estimates based on the Chandrasekhar theory of dynamical friction. We find that these standard predictions for merging time-scales, which are often used in semi-analytic galaxy formation models, are systematically shorter than those found in simulations. The discrepancy is approximately a factor of 1.7 for M sat/ M host≈ 0.1 and becomes larger for more disparate satellite-to-host mass ratios, reaching a factor of ∼3.3 for M sat/ M host≈ 0.01. Based on our simulations, we propose a new, easily implementable fitting formula that accurately predicts the time-scale for an extended satellite to sink from the virial radius of a host halo down to the halo's centre for a wide range of M sat/ M host and orbits. Including a central bulge in each galaxy changes the merging time-scale by ≲10 per cent. To highlight one concrete application of our results, we show that merging time-scales often used in the literature overestimate the growth of stellar mass by satellite accretion by ≈40 per cent, with the extra mass gained in low mass ratio mergers.  相似文献   

19.
Based on results from cold dark matter N -body simulations, we develop a dynamical model for the evolution of subhaloes within group-sized host haloes. Only subhaloes more massive than 5 × 108 M⊙ are considered, because they are massive enough to possibly host luminous galaxies. On their orbits within a growing host potential the subhaloes are subject to tidal stripping and dynamical friction. At the present time  ( z = 0)  , all model hosts have equal mass  ( M vir= 3.9 × 1013 M⊙)  but different concentrations associated with different formation times. We investigate the variation of subhalo (or satellite galaxy) velocity dispersion with host concentration and/or formation time. In agreement with the Jeans equation, the velocity dispersion of subhaloes increases with the host concentration. Between concentrations of ∼5 and ∼20, the subhalo velocity dispersions increase by a factor of ∼1.25. By applying a simplified tidal disruption criterion, that is, rejection of all subhaloes with a tidal truncation radius below 3  kpc at   z = 0  , the central velocity dispersion of the 'surviving' subhalo sample increases substantially for all concentrations. The enhanced central velocity dispersions in the surviving subhalo samples are caused by a lack of slow tangential motions. Additionally, we present a fitting formula for the anisotropy parameter which does not depend on concentration if the group-centric distances are scaled by r s, the characteristic radius of the Navarro, Frenk & White profile. Since the expected loss of subhaloes and galaxies due to tidal disruption increases the velocity dispersion of surviving galaxies, the observed galaxy velocity dispersion can substantially overestimate the virial mass.  相似文献   

20.
We present results from the first high-resolution hydrodynamical simulations of non-Gaussian cosmological models. We focus on the statistical properties of the transmitted Lyman-α flux in the high-redshift intergalactic medium. Imprints of non-Gaussianity are present and are larger at high redshifts. Differences larger than 20 per cent at   z > 3  in the flux probability distribution function for high-transmissivity regions (voids) are expected for values of the non-linearity parameter   f NL=±100  when compared to a standard Λ cold dark matter cosmology with   f NL= 0  . We also investigate the one-dimensional flux bispectrum: at the largest scales (corresponding to tens of Mpc), we expect deviations in the flux bispectrum up to 20 per cent at   z ∼ 4  (for   f NL=±100  ), significantly larger than deviations of ∼3 per cent in the flux power spectrum. We briefly discuss possible systematic errors that can contaminate the signal. Although challenging, a detection of non-Gaussianities in the interesting regime of scales and redshifts probed by the Lyman-α forest could be possible with future data sets.  相似文献   

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