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1.
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   

2.
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   

3.
This paper presents the properties of a family of scale-free triaxial haloes. We adduce arguments to suggest that the velocity ellipsoids of such models are aligned in conical coordinates. We provide an algorithm to find the set of conically aligned velocity second moments that support a given density against the gravity field of the halo. The case of the logarithmic ellipsoidal model – the simplest triaxial generalization of the familiar isothermal sphere – is examined in detail. The velocity dispersions required to hold up the self-consistent model are analytic. The velocity distribution of the dark matter can be approximated as a triaxial Gaussian with semiaxes equal to the velocity dispersions.
There are roughly 20 experiments worldwide that are searching for evidence of scarce interactions between weakly interacting massive-particle dark matter (WIMP) and detector nuclei. The annual modulation signal, caused by the Earth's rotation around the Sun, is a crucial discriminant between WIMP events and the background. The greatest rate is in June, the least in December. We compute the differential detection rate for energy deposited by the rare WIMP–nucleus interactions in our logarithmic ellipsoidal halo models. Triaxiality and velocity anisotropy change the total rate by up to ∼40 per cent, and have a substantial effect on the amplitude of the annual modulation signal. The overall rate is greatest, but the amplitude of the modulation is weakest, in our radially anisotropic halo models. Even the sign of the signal can be changed. Restricting attention to low energy events, the models predict that the maximum rate occurs in December, and not in June.  相似文献   

4.
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   

5.
We investigate the correlation between the supermassive black holes (SMBHs) mass ( M bh) and the stellar velocity dispersion  (σ*)  in two types of host galaxies: the early-type bulges (disc galaxies with classical bulges or elliptical galaxies) and pseudo-bulges. In the form  log ( M bh/M⊙) =α+β log (σ*/200 km s−1)  , the best-fitting results for the 39 early-type bulges are the slope  β= 4.06 ± 0.28  and the normalization  α= 8.28 ± 0.05  ; the best-fitting results for the nine pseudo-bulges are  β= 4.5 ± 1.3  and  α= 7.50 ± 0.18  . Both relations have intrinsic scatter in  log  M bh  of ≲0.27 dex. The   M bh–σ*  relation for pseudo-bulges is different from the relation in the early-type bulges over the 3σ significance level. The contrasting relations indicate the formation and growth histories of SMBHs depend on their host type. The discrepancy between the slope of the   M bh–σ*  relations using different definition of velocity dispersion vanishes in our sample, a uniform slope will constrain the coevolution theories of the SMBHs and their host galaxies more effectively. We also find the slope for the 'core' elliptical galaxies at the high-mass range of the relation appears steeper  (β≃ 5–6)  , which may be the imprint of their origin of dissipationless mergers.  相似文献   

6.
The kinematics of satellite galaxies reflect the masses of the extended dark matter haloes in which they orbit, and thus shed light on the mass–luminosity relation (MLR) of their corresponding central galaxies. In this paper, we select a large sample of centrals and satellites from the Sloan Digital Sky Survey and measure the kinematics (velocity dispersions) of the satellite galaxies as a function of the r -band luminosity of the central galaxies. Using the analytical framework presented in More, van den Bosch & Cacciato, we use these data to infer both the mean and the scatter of the MLR of central galaxies, carefully taking account of selection effects and biases introduced by the stacking procedure. As expected, brighter centrals on average reside in more massive haloes. In addition, we find that the scatter in halo masses for centrals of a given luminosity,  σlog  M   , also increases with increasing luminosity. As we demonstrate, this is consistent with  σlog  L   , which reflects the scatter in the conditional probability function   P ( L c| M )  , being independent of halo mass. Our analysis of the satellite kinematics yields  σlog  L = 0.16  ±  0.04  , in excellent agreement with constraints from clustering and group catalogues, and with predictions from a semi-analytical model of galaxy formation. We thus conclude that the amount of stochasticity in galaxy formation, which is characterized by  σlog  L   , is well constrained, independent of halo mass and in a good agreement with current models of galaxy formation.  相似文献   

7.
We use cosmological Λ cold dark matter (CDM) numerical simulations to model the evolution of the substructure population in 16 dark matter haloes with resolutions of up to seven million particles within the virial radius. The combined substructure circular velocity distribution function (VDF) for hosts of 1011 to  1014 M⊙  at redshifts from zero to two or higher has a self-similar shape, is independent of host halo mass and redshift, and follows the relation  d n /d v = (1/8)( v cmax/ v cmax,host)−4  . Halo to halo variance in the VDF is a factor of roughly 2 to 4. At high redshifts, we find preliminary evidence for fewer large substructure haloes (subhaloes). Specific angular momenta are significantly lower for subhaloes nearer the host halo centre where tidal stripping is more effective. The radial distribution of subhaloes is marginally consistent with the mass profile for   r ≳ 0.3 r vir  , where the possibility of artificial numerical disruption of subhaloes can be most reliably excluded by our convergence study, although a subhalo distribution that is shallower than the mass profile is favoured. Subhalo masses but not circular velocities decrease towards the host centre. Subhalo velocity dispersions hint at a positive velocity bias at small radii. There is a weak bias towards more circular orbits at lower redshift, especially at small radii. We additionally model a cluster in several power-law cosmologies of   P ∝ kn   , and demonstrate that a steeper spectral index, n , results in significantly less substructure.  相似文献   

8.
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   

9.
We reassess the hypothesis that Lyman-break galaxies (LBGs) at redshifts   z ∼ 3  mark the centres of the most massive dark matter haloes at that epoch. First we reanalyse the kinematic measurements of Pettini et al. and Erb et al. of the rest-frame optical emission lines of LBGs. We compare the distribution of the ratio of the rotation velocity to the central line width, against the expected distribution for galaxies with random inclination angles, modelled as singular isothermal spheres. The model fits the data well. On this basis we argue that the central line width provides a predictor of the circular velocity at a radius of several kpc. Assembling a larger sample of LBGs with measured line widths, we compare these results against the theoretical ΛCDM rotation curves of Mo, Mao & White, under the hypothesis that LBGs mark the centres of the most massive dark matter haloes. We find that the circular velocities are overpredicted by a substantial factor, which we estimate conservatively as  1.8 ± 0.4  . This indicates that the model is probably incorrect. The model of LBGs as relatively low-mass starburst systems, of Somerville, Primack & Faber, provides a good fit to the data.  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.
We calculate the cooling times at constant density for haloes with virial temperatures from 100 K to  1×105 K  that originate from a 3 σ fluctuation of a CDM power spectrum in three different cosmologies. Our intention is to determine the first objects that can cool to low temperatures, but not to follow their dynamical evolution. We identify two generations of haloes: those with low virial temperatures,   T vir≲9000 K  that remain largely neutral, and those with larger virial temperatures that become ionized. The lower temperature, lower mass haloes are the first to cool to 75 per cent of their virial temperature. The precise temperature and mass of the first objects are dependent upon the molecular hydrogen (H2) cooling function and the cosmological model. The higher mass haloes collapse later but, in this paradigm, cool much more efficiently once they have done so, first via electronic transitions and then via molecular cooling: in fact, a greater residual ionization once the haloes cool below 9000 K results in an enhanced H2 production and hence a higher cooling rate at low temperatures than for the lower mass haloes, so that within our constant-density model it is the former that are the first to cool to really low temperatures. We discuss the possible significance of this result in the context of CDM models in which the shallow slope of the initial fluctuation spectrum on small scales leads to a wide range of halo masses (of differing overdensities) collapsing over a small redshift interval. This 'crosstalk' is sufficiently important that both high- and low-mass haloes collapse during the lifetimes of the massive stars which may be formed at these epochs. Further investigation is thus required to determine which generation of haloes plays the dominant role in early structure formation.  相似文献   

12.
We present new Planetary Nebula Spectrograph observations of the ordinary elliptical galaxy NGC 4494, resulting in positions and velocities of 255 planetary nebulae out to seven effective radii (25 kpc). We also present new wide-field surface photometry from MMT/Megacam, and long-slit stellar kinematics from VLT/FORS2. The spatial and kinematical distributions of the planetary nebulae agree with the field stars in the region of overlap. The mean rotation is relatively low, with a possible kinematic axis twist outside  1 R e  . The velocity dispersion profile declines with radius, though not very steeply, down to  ∼70 km s−1  at the last data point.
We have constructed spherical dynamical models of the system, including Jeans analyses with multi-component Λ cold dark matter (CDM) motivated galaxies as well as logarithmic potentials. These models include special attention to orbital anisotropy, which we constrain using fourth-order velocity moments. Given several different sets of modelling methods and assumptions, we find consistent results for the mass profile within the radial range constrained by the data. Some dark matter (DM) is required by the data; our best-fitting solution has a radially anisotropic stellar halo, a plausible stellar mass-to-light ratio and a DM halo with an unexpectedly low central density. We find that this result does not substantially change with a flattened axisymmetric model.
Taken together with other results for galaxy halo masses, we find suggestions for a puzzling pattern wherein most intermediate-luminosity galaxies have very low concentration haloes, while some high-mass ellipticals have very high concentrations. We discuss some possible implications of these results for DM and galaxy formation.  相似文献   

13.
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   

14.
We analyse a   z < 0.1  galaxy sample from the Sloan Digital Sky Survey focusing on the variation in the galaxy colour bimodality with stellar mass     and projected neighbour density Σ, and on measurements of the galaxy stellar mass functions. The characteristic mass increases with environmental density from about  1010.6  to     (Kroupa initial mass function,   H 0= 70  ) for Σ in the range  0.1–10 Mpc−2  . The galaxy population naturally divides into a red and blue sequence with the locus of the sequences in colour–mass and colour–concentration indices not varying strongly with environment. The fraction of galaxies on the red sequence is determined in bins of 0.2 in  log Σ  and     bins). The red fraction   f r   generally increases continuously in both Σ and     such that there is a unified relation:     . Two simple functions are proposed which provide good fits to the data. These data are compared with analogous quantities in semi-analytical models based on the Millennium N -body simulation: the Bower et al. and Croton et al. models that incorporate active galactic nucleus feedback. Both models predict a strong dependence of the red fraction on stellar mass and environment that is qualitatively similar to the observations. However, a quantitative comparison shows that the Bower et al. model is a significantly better match; this appears to be due to the different treatment of feedback in central galaxies.  相似文献   

15.
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   

16.
This is the second in a series of papers dedicated to unveiling the mass structure and orbital content of a sample of flattened early-type galaxies in the Coma cluster. The ability of our orbit libraries to reconstruct internal stellar motions and the mass composition of a typical elliptical in the sample is investigated by means of Monte Carlo simulations of isotropic rotator models. The simulations allow a determination of the optimal amount of regularization needed in the orbit superpositions. It is shown that under realistic observational conditions and with the appropriate regularization, internal velocity moments can be reconstructed to an accuracy of ≈15 per cent; the same accuracy can be achieved for the circular velocity and dark matter fraction. In contrast, the flattening of the halo remains unconstrained. Regularized orbit superpositions are applied to a first galaxy in our sample, NGC 4807, for which stellar kinematical observations extend to  3  r eff  . The galaxy seems dark-matter dominated outside   r > 2  r eff  . Logarithmic dark matter potentials are consistent with the data, as well as NFW profiles, mimicking logarithmic potentials over the observationally sampled radial range. In both cases, the derived stellar mass-to-light ratio ϒ agrees well with independently obtained mass-to-light ratios from stellar population analysis. The achieved accuracy is  Δϒ≈ 0.5  . Kinematically, NGC 4807 is characterized by mild radial anisotropy outside   r > 0.5  r eff  , becoming isotropic towards the centre. Our orbit models hint at either a distinct stellar component or weak triaxiality in the outer parts of the galaxy.  相似文献   

17.
We present an improved strong-lensing analysis of Cl0024+1654  ( z = 0.39)  using deep Hubble Space Telescope ( HST )/Advanced Camera for Surveys (ACS)/NIC3 images, based on 33 multiply-lensed images of 11 background galaxies. These are found with a model that assumes mass approximately traces light, with a low-order expansion to allow for flexibility on large scales. The model is constrained initially by the well-known five-image system  ( z = 1.675)  and refined as new multiply-lensed systems are identified using the model. Photometric redshifts of these new systems are then used to constrain better the mass profile by adopting the standard cosmological relation between redshift and lensing distance. Our model requires only six free parameters to describe well all positional and redshift data. The resulting inner mass profile has a slope of  d log  M /d log  r ≃−0.55  , consistent with new weak-lensing measurements where the data overlap, at   r ≃ 200 kpc/ h 70  . The combined profile is well fitted by a high-concentration Navarro, Frenk & White (NFW) mass profile,   C vir∼ 8.6 ± 1.6  , similar to other well-studied clusters, but larger than predicted with standard Λ cold dark matter (ΛCDM). A well-defined radial critical curve is generated by the model and is clearly observed at   r ≃ 12  arcsec, outlined by elongated images pointing towards the centre of mass. The relative fluxes of the multiply-lensed images are found to agree well with the modelled magnifications, providing an independent consistency check.  相似文献   

18.
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   

19.
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   

20.
We present deep wide-field (16.4×16.4 arcmin2) Washington CT 1 CCD surface photometry of the giant elliptical galaxy NGC 4472, the brightest member of the Virgo cluster. Our data cover a wider and deeper field than any previous CCD photometry. A single King model does not give a good fit to the surface brightness profiles of NGC 4472, but they can be fitted approximately using two King models: with the separate models representing the inner and outer regions . Surface brightness profiles for the outer region can also be fitted approximately by a de Vaucouleurs law. There is clearly a negative colour gradient within 3 arcmin of NGC 4472, in the sense that the colour gets bluer with increasing radius. The slope of the colour gradient for this region is derived to be Δ μ ( C − T 1)=−0.08 mag arcsec−2 for Δ log  r =1, which corresponds to a metallicity gradient of Δ[Fe/H]=−0.2 dex. However, the surface colour becomes gradually redder with increasing radius beyond 3 arcmin. A comparison of the structural parameters of NGC 4472 in C and T 1 images has shown that there is little difference in the shapes of ellipses observed using isochromes or isophotes. In addition, photometric and structural parameters of NGC 4472 have been determined.  相似文献   

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