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1.
In this paper we describe the Bayesian link between the cosmological mass function and the distribution of times at which isolated haloes of a given mass exist. By assuming that clumps of dark matter undergo monotonic growth on the time-scales of interest, this distribution of times is also the distribution of 'creation' times of the haloes. This monotonic growth is an inevitable aspect of gravitational instability. The spherical top-hat collapse model is used to estimate the rate at which clumps of dark matter collapse. This gives the prior for the creation time given no information about halo mass. Applying Bayes' theorem then allows any mass function to be converted into a distribution of times at which haloes of a given mass are created. This general result covers both Gaussian and non-Gaussian models. We also demonstrate how the mass function and the creation time distribution can be combined to give a joint density function, and discuss the relation between the time distribution of major merger events and the formula calculated. Finally, we determine the creation time of haloes within three N -body simulations, and compare the link between the mass function and creation rate with the analytic theory.  相似文献   

2.
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   

3.
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   

4.
Using high-resolution cosmological N -body simulations, we investigate the survival of dark matter satellites falling into larger haloes. Satellites preserve their identity for some time after merging. We compute their loss of mass, energy and angular momentum as they are dissolved by dynamical friction, tidal forces and collisions with other satellites. We also analyse the evolution of their internal structure. Satellites with less than a few per cent of the mass of the main halo may survive for several billion years, whereas larger satellites rapidly sink into the centre of the main halo potential well and lose their identity. Penetrating encounters between satellites are frequent and may lead to significant mass loss and disruption. Only a minor fraction of cluster mass (10–15 per cent on average) is bound to substructure at most redshifts of interest. We discuss the application of these results to the survival and extent of dark matter haloes associated with galaxies in clusters, and to their interactions. We find that a minor fraction of galaxy-size dark matter haloes are disrupted by redshift z  = 0. The fraction of satellites undergoing close encounters is similar to the observed fraction of interacting or merging galaxies in clusters at moderate redshift.  相似文献   

5.
We study the formation of tidal tails in pairs of merging disc galaxies with structural properties motivated by current theories of cold dark matter (CDM) cosmologies. In a recent study, Dubinski, Mihos & Hernquist showed that the formation of prominent tidal tails can be strongly suppressed by massive and extended dark haloes. For the large halo-to-disc mass ratio expected in CDM cosmologies their sequence of models failed to produce strong tails like those observed in many well-known pairs of interacting galaxies. In order to test whether this effect can constrain the viability of CDM cosmologies, we construct N ‐body models of disc galaxies with structural properties derived in analogy to the recent analytical work of Mo, Mao & White. With a series of self-consistent collisionless simulations of galaxy–galaxy mergers we demonstrate that even the discs of very massive dark haloes have no problems developing long tidal tails, provided the halo spin parameter is large enough. For our class of models, the halo-to-disc mass ratio is not a good indicator of the ability to produce tails. Instead, the relative size of disc and halo or, alternatively, the ratio of circular velocity to local escape speed at the half mass radius of the disc is a more useful criterion. This result holds in all CDM models. While tidal tails can provide useful information on the structure of galaxies, it thus appears unlikely that they are able to constrain the values of the cosmological parameters within these models.  相似文献   

6.
7.
The evolution of substructure embedded in non-dissipative dark haloes is studied through N -body simulations of isolated systems, both in and out of initial equilibrium, complementing cosmological simulations of the growth of structure. We determine by both analytic calculations and direct analysis of the N -body simulations the relative importance of various dynamical processes acting on the clumps, such as the removal of material by global tides, clump–clump heating, clump–clump merging and dynamical friction. The ratio of the internal clump velocity dispersion to that of the dark halo is an important parameter; as this ratio approaches a value of unity, heating by close encounters between clumps becomes less important, while the other dynamical processes continue to increase in importance. Our comparison between merging and disruption processes implies that spiral galaxies cannot be formed in a protosystem that contains a few large clumps, but can be formed through the accretion of many small clumps; elliptical galaxies form in a more clumpy environment than do spiral galaxies. Our results support the idea that the central cusp in the density profiles of dark haloes is the consequence of self-limiting merging of small, dense haloes. This implies that the collapse of a system of clumps/substructure is not sufficient to form a cD galaxy, with an extended envelope; plausibly, subsequent accretion of large galaxies is required. The post-collapse system is in general triaxial, with rounder systems resulting from fewer, but more massive, clumps. Persistent streams of material from disrupted clumps can be found in the outer regions of the final system, and at an overdensity of around 0.75, can cover 10 to 30 per cent of the sky.  相似文献   

8.
We examine the accretion and merger histories of central and satellite galaxies in a smoothed particle hydrodynamics (SPH) cosmological simulation that resolves galaxies down to  7 × 109 M  . Most friends-of-friends haloes in the simulation have a distinct central galaxy, typically 2–5 times more massive than the most massive satellite. As expected, satellites have systematically higher assembly redshifts than central galaxies of the same baryonic mass, and satellites in more massive haloes form earlier. However, contrary to the simplest expectations, satellite galaxies continue to accrete gas and convert it to stars; the gas accretion declines steadily over a period of 0.5–1 Gyr after the satellite halo merges with a larger parent halo. Satellites in a cluster mass halo eventually begin to lose baryonic mass. Typically, satellites in our simulation are 0.1–0.2 mag bluer than in models that assume no gas accretion on to satellites after a halo merger. Since   z = 1  , 27 per cent of central galaxies (above  3 × 1010 M  ) and 22 per cent of present-day satellite galaxies have merged with a smaller system above a 1:4 mass ratio; about half of the satellite mergers occurred after the galaxy became a satellite and half before. In effect, satellite galaxies can remain 'central' objects of halo substructures, with continuing accretion and mergers, making the transition in assembly histories and physical properties a gradual one. Implementing such a gradual transformation in semi-analytic models would improve their agreement with observed colour distributions of satellite galaxies in groups and with the observed colour dependence of galaxy clustering.  相似文献   

9.
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   

10.
We use a high-resolution ΛCDM numerical simulation to calculate the mass function of dark matter haloes down to the scale of dwarf galaxies, back to a redshift of 15, in a  50 h −1 Mpc  volume containing 80 million particles. Our low-redshift results allow us to probe low-σ density fluctuations significantly beyond the range of previous cosmological simulations. The Sheth & Tormen mass function provides an excellent match to all of our data except for redshifts of 10 and higher, where it overpredicts halo numbers increasingly with redshift, reaching roughly 50 per cent for the  1010–1011 M  haloes sampled at redshift 15. Our results confirm previous findings that the simulated halo mass function can be described solely by the variance of the mass distribution, and thus has no explicit redshift dependence. We provide an empirical fit to our data that corrects for the overprediction of extremely rare objects by the Sheth & Tormen mass function. This overprediction has implications for studies that use the number densities of similarly rare objects as cosmological probes. For example, the number density of high-redshift  ( z ≃ 6) QSOs  , which are thought to be hosted by haloes at 5σ peaks in the fluctuation field, are likely to be overpredicted by at least a factor of 50 per cent. We test the sensitivity of our results to force accuracy, starting redshift and halo-finding algorithm.  相似文献   

11.
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   

12.
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   

13.
The non‐linear dynamics of bending instability and vertical structure of a galactic stellar disc embedded into a spherical halo are studied with N‐body numerical modelling. Development of the bending instability in stellar galactic disc is considered as the main factor that increases the disc thickness. Correlation between the disc vertical scale height and the halo‐to‐disc mass ratio is predicted from the simulations. The method of assessment of the spherical‐to‐disc mass ratio for edge‐on spiral galaxies with a small bulge is considered. Modelling of eight edge‐on galaxies: NGC 891, NGC 4738, NGC 5170, UGC 6080, UGC 7321, UGC 8286, UGC 9422 and UGC 9556 is performed. Parameters of stellar discs, dark haloes and bulges are estimated. The lower limit of the dark‐to‐luminous mass ratio in our galaxies is of the order of one within the limits of their stellar discs. The dark haloes dominate by mass in the galaxies with very thin stellar discs (NGC 5170, UGC 7321 and UGC 8286) (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

14.
An analytical model is presented for the post-collapse equilibrium structure of virialized objects that condense out of a low-density cosmological background universe, either matter-dominated or flat with a cosmological constant. This generalizes the model we derived previously for an Einstein–de Sitter (EdS) universe. The model is based upon the assumption that cosmological haloes form from the collapse and virialization of 'top-hat' density perturbations, and are spherical, isotropic and isothermal. This leads to the prediction of a unique, non-singular, truncated isothermal sphere (TIS), a particular solution of the Lane–Emden equation (suitably modified when Λ≠0) . The size and virial temperature are unique functions of the mass and redshift of formation of the object for a given background universe. The central density is roughly proportional to the critical density of the universe at the epoch of collapse. This TIS model is in good agreement with observations of the internal structure of dark-matter-dominated haloes on scales ranging from dwarf galaxies to X-ray clusters. It also reproduces many of the average properties of haloes in simulations of the cold dark matter (CDM) model to good accuracy, suggesting that it is a useful analytical approximation for haloes that form from realistic initial conditions. Our TIS model matches the density profiles of haloes in CDM N -body simulations outside the innermost region, while avoiding the steep central cusp of the latter which is in apparent conflict with observations. The TIS model may also be relevant to non-standard CDM models, such as that for self-interacting dark matter, recently proposed to resolve this conflict.  相似文献   

15.
An inside–out model for the formation of haloes in a hierarchical clustering scenario is studied. The method combines the picture of the spherical infall model and a modification of the extended Press–Schechter theory. The mass accretion rate of a halo is defined to be the rate of its mass increase due to minor mergers. The accreted mass is deposited at the outer shells without changing the density profile of the halo inside its current virial radius. We applied the method to a flat Λ-cold dark matter universe. The resulting density profiles are compared with analytical models proposed in the literature, and a very good agreement is found. A trend is found of the inner density profile to become steeper for larger halo mass, which also results from recent N -body simulations. Additionally, present-day concentrations as well as their time evolution are derived and it is shown that they reproduce the results of large cosmological N -body simulations.  相似文献   

16.
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   

17.
We study the formation of galaxies in a Λ cold dark matter (ΛCDM) universe using high-resolution hydrodynamical simulations with a multiphase treatment of gas, cooling and feedback, focusing on the formation of discs. Our simulations follow eight isolated haloes similar in mass to the Milky Way and extracted from a large cosmological simulation without restriction on spin parameter or merger history. This allows us to investigate how the final properties of the simulated galaxies correlate with the formation histories of their haloes. We find that, at   z = 0  , none of our galaxies contains a disc with more than 20 per cent of its total stellar mass. Four of the eight galaxies nevertheless have well-formed disc components, three have dominant spheroids and very small discs, and one is a spheroidal galaxy with no disc at all. The   z = 0  spheroids are made of old stars, while discs are younger and formed from the inside-out. Neither the existence of a disc at   z = 0  nor the final disc-to-total mass ratio seems to depend on the spin parameter of the halo. Discs are formed in haloes with spin parameters as low as 0.01 and as high as 0.05; galaxies with little or no disc component span the same range in spin parameter. Except for one of the simulated galaxies, all have significant discs at   z ≳ 2  , regardless of their   z = 0  morphologies. Major mergers and instabilities which arise when accreting cold gas is misaligned with the stellar disc trigger a transfer of mass from the discs to the spheroids. In some cases, discs are destroyed, while in others, they survive or reform. This suggests that the survival probability of discs depends on the particular formation history of each galaxy. A realistic ΛCDM model will clearly require weaker star formation at high redshift and later disc assembly than occurs in our models.  相似文献   

18.
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   

19.
In the current ΛCDM cosmological scenario, N -body simulations provide us with a universal mass profile, and consequently a universal equilibrium circular velocity of the virialized objects, as galaxies. In this paper we obtain, by combining kinematical data of their inner regions with global observational properties, the universal rotation curve of disc galaxies and the corresponding mass distribution out to their virial radius. This curve extends the results of Paper I, concerning the inner luminous regions of Sb–Im spirals, out to the edge of the galaxy haloes.  相似文献   

20.
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   

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