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1.
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2.
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   

3.
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4.
We investigate the mean velocity dispersion and the velocity dispersion profile of stellar systems in modified Newtonian dynamics (MOND), using the N -body code n-mody , which is a particle-mesh-based code with a numerical MOND potential solver developed by Ciotti, Londrillo & Nipoti. We have calculated mean velocity dispersions for stellar systems following Plummer density distributions with masses in the range of 104 to  109 M⊙  and which are either isolated or immersed in an external field. Our integrations reproduce previous analytic estimates for stellar velocities in systems in the deep MOND regime  ( a i, a e≪ a 0)  , where the motion of stars is either dominated by internal accelerations  ( a i≫ a e)  or constant external accelerations  ( a e≫ a i)  . In addition, we derive for the first time analytic formulae for the line-of-sight velocity dispersion in the intermediate regime  ( a i∼ a e∼ a 0)  . This allows for a much-improved comparison of MOND with observed velocity dispersions of stellar systems. We finally derive the velocity dispersion of the globular cluster Pal 14 as one of the outer Milky Way halo globular clusters that have recently been proposed as a differentiator between Newtonian and MONDian dynamics.  相似文献   

5.
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   

6.
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   

7.
We have studied the effects of gas density inhomogeneities on the escape of ionizing Lyman continuum (Lyc) photons from Milky Way type galaxies via 3D numerical simulations using the Monte Carlo radiative transfer code crash . To this aim a comparison between a smooth Gaussian distribution (GDD) and an inhomogeneous, fractal one (FDD) has been made with realistic assumptions for the ionizing stellar sources based on available data in the solar neighbourhood. In both cases the escape fraction f esc increases with ionization rate  ˙ γ   (although for the FDD with a flatter slope) and they become equal at  ˙ γ =2×1050 s-1  where   f esc=0.11  . FDD allows escape fractions of the same order also at lower  ˙ γ ,  when Lyc photon escape is sharply suppressed by GDD. Values of the escape fraction as high as 0.6 can be reached (GDD) for  ˙ γ ≈9×1050 s-1  , corresponding to a star formation rate (SFR) of roughly 2 M⊙ yr−1; at this ionizing luminosity the FDD is less transparent  ( f esc≈0.28)  . If high-redshift galaxies have gas column densities similar to local ones, and are characterized by such high SFRs and by a predominantly smooth (i.e. turbulence-free) interstellar medium, our results suggest that they should considerably contribute to – and possibly dominate – the cosmic UV background.  相似文献   

8.
A comparison between published field galaxy stellar mass functions (GSMFs) shows that the cosmic stellar mass density is in the range 4–8 per cent of the baryon density (assuming  Ωb= 0.045  ). There remain significant sources of uncertainty for the dust correction and underlying stellar mass-to-light ratio even assuming a reasonable universal stellar initial mass function. We determine the   z < 0.05  GSMF using the New York University Value-Added Galaxy Catalog sample of 49 968 galaxies derived from the Sloan Digital Sky Survey and various estimates of stellar mass. The GSMF shows clear evidence for a low-mass upturn and is fitted with a double Schechter function that has  α2≃−1.6  . At masses below  ∼108.5 M⊙  , the GSMF may be significantly incomplete because of missing low-surface-brightness galaxies. One interpretation of the stellar mass–metallicity relation is that it is primarily caused by a lower fraction of available baryons converted to stars in low-mass galaxies. Using this principle, we determine a simple relationship between baryonic mass and stellar mass and present an 'implied baryonic mass function'. This function has a faint-end slope,  α2≃−1.9  . Thus, we find evidence that the slope of the low-mass end of the galaxy mass function could plausibly be as steep as the halo mass function. We illustrate the relationship between halo baryonic mass function → galaxy baryonic mass function → GSMF. This demonstrates the requirement for peak galaxy formation efficiency at baryonic masses  ∼1011 M⊙  corresponding to a minimum in feedback effects. The baryonic-infall efficiency may have levelled off at lower masses.  相似文献   

9.
The evolution of the abundance of galaxy clusters depends sensitively on the value of the cosmological density parameter, Ω0. Recent ASCA data are used to quantify this evolution as measured by the cluster X-ray temperature function. A χ2 minimization fit to the cumulative temperature function, as well as a maximum-likelihood estimate (which requires additional assumptions about cluster luminosities), leads to the estimate Ω0 ≈ 0.45 ± 0.25 (1σ statistical error). Various systematic uncertainties are considered, none of which significantly enhances the probability that Ω0 = 1. These conclusions hold for models with or without a cosmological constant, i.e., with Λ0 = 0 or Λ0 = 1 − Ω0. The statistical uncertainties are at least as large as any of the individual systematic errors that have been considered here, suggesting that additional temperature measurements of distant clusters will allow an improvement in this estimate. An alternative method that uses the highest redshift clusters to place an upper limit on Ω0 is also presented and tentatively applied, with the result that Ω0  1 can be ruled out at the 98 per cent confidence level. Whilst this method does not require a well-defined statistical sample of distant clusters, there are still modelling uncertainties that preclude a firmer conclusion at this time.  相似文献   

10.
Collisionless stellar systems are driven towards equilibrium by mixing of phase-space elements. I show that the excess-mass function     [where     is the coarse-grained distribution function] always decreases on mixing . D ( f ) gives the excess mass from values of     . This novel form of the mixing theorem extends the maximum phase-space density argument to all values of f . The excess-mass function can be computed from N -body simulations and is additive: the excess mass of a combination of non-overlapping systems is the sum of their individual D ( f ). I propose a novel interpretation for the coarse-grained distribution function, which avoids conceptual problems with the mixing theorem.
As an example application, I show that for self-gravitating cusps (  ρ∝ r −γ  as   r → 0  ) the excess mass   D ∝ f −2(3−γ)/(6−γ)  as   f →∞  , i.e. steeper cusps are less mixed than shallower ones, independent of the shape of surfaces of constant density or details of the distribution function (e.g. anisotropy). This property, together with the additivity of D ( f ) and the mixing theorem, implies that a merger remnant cannot have a cusp steeper than the steepest of its progenitors. Furthermore, I argue that the cusp of the remnant should not be shallower either, implying that the steepest cusp always survives.  相似文献   

11.
We study the polarization properties of relativistic reconfinement shocks with chaotic magnetic fields. Using our hydrodynamical model of their structure, we calculate synthetic polarization maps, longitudinal polarization profiles and discuss the spatially averaged polarization degree as a function of jet half-opening angle  Θ j   , jet Lorentz factor  Γ j   and observer inclination angle to the jet axis  θobs  . We find that for  θobs≲Θ j   the wave electric vectors are parallel in the vicinity of the structure ends and perpendicular in between, while for  θobs > Θ j   the polarization can only be perpendicular. The spatially averaged polarization degree does not exceed 30 per cent. Parallel average polarization, with polarization degrees lower than 10 per cent, has been found for  θobs < Θ j   under the condition  Γ j Θ j > 1  . As earlier works predicted the parallel polarization from relativistic conical shocks, we explain our results by discussing conical shocks with divergent upstream flow.  相似文献   

12.
We calculate the coefficient of bulk viscosity by considering the non-leptonic weak interactions in the cores of hybrid stars with both hyperons and quarks. We first determine the dependence of the production rate of neutrons on the reaction rate of quarks in the non-leptonic processes, that is,  Γ n = K s Γ s +ΓΛ+ 2ΓΣ−  . The conversion rate,   K s   , in our scenario is a complicated function of baryon number density. We also consider the medium effect of quark matter on bulk viscosity. Using these results, we estimate the limiting rotation of the hybrid stars, which may suppress the r-mode instability more effectively. Hybrid stars should be the candidates for the extremely rapid rotators.  相似文献   

13.
We investigate the large-scale clustering of radio sources in the FIRST 1.4-GHz survey by analysing the distribution function ( counts in cells ). We select a reliable sample from the the FIRST catalogue, paying particular attention to the problem of how to define single radio sources from the multiple components listed. We also consider the incompleteness of the catalogue. We estimate the angular two-point correlation function w (θ), the variance Ψ2 and skewness Ψ3 of the distribution for the various subsamples chosen on different criteria. Both w (θ) and Ψ2 show power-law behaviour with an amplitude corresponding to a spatial correlation length of r 0 ∼ 10  h −1Mpc. We detect significant skewness in the distribution, the first such detection in radio surveys. This skewness is found to be related to the variance through Ψ3 =  S 3(Ψ2)α, with α = 1.9 ± 0.1, consistent with the non-linear gravitational growth of perturbations from primordial Gaussian initial conditions. We show that the amplitude of variance and the skewness are consistent with realistic models of galaxy clustering.  相似文献   

14.
We investigate the influence of the ionization of helium on the low-degree acoustic oscillation frequencies in model solar-type stars. The signature in the oscillation frequencies characterizing the ionization-induced depression of the first adiabatic exponent γ is a superposition of two decaying periodic functions of frequency ν, with 'frequencies' that are approximately twice the acoustic depths of the centres of the He  i and He  ii ionization regions. That variation is probably best exhibited in the second frequency difference  Δ2ν n ,  l ≡ν n −1,  l − 2ν n ,  l +ν n +1,  l   . We show how an analytic approximation to the variation of γ leads to a simple representation of this oscillatory contribution to Δ2ν which can be used to characterize the γ variation, our intention being to use it as a seismic diagnostic of the helium abundance of the star. We emphasize that the objective is to characterize γ, not merely to find a formula for Δ2ν that reproduces the data.  相似文献   

15.
We use three-integral models to infer the distribution function (DF) of the boxy E3–E4 galaxy NGC 1600 from surface brightness and line-profile data on the minor and major axes. We assume axisymmetry and that the mass-to-light ratio is constant in the central ∼1 R e. Stars in the resulting gravitational potential move mainly on regular orbits. We use an approximate third integral K from perturbation theory and write the DF as a sum of basis functions in the three integrals E , L z and K . We then fit the projected moments of these basis functions to the kinematic observables and deprojected density, using a non-parametric algorithm. The deduced dynamical structure is radially anisotropic, with σ θ σ r ≈ σ φ σ r ≈0.7 on the major axis. Both on the minor axis and near the centre the velocity distribution is more isotropic; thus the model is flattened by equatorial radial orbits. The kinematic data are fitted without the need for a central black hole; the central mass determined previously from ground-based data therefore overestimates the actual black-hole mass. The mass-to-light ratio of the stars is M L V =6  h 50. The anisotropy structure of NGC 1600 with a radially anisotropic main body and more nearly isotropic centre is similar to that found recently in NGC 1399, 2434, 3379 and 6703, suggesting that this pattern may be common amongst massive elliptical galaxies. We discuss a possible merger origin of NGC 1600 in the light of these results.  相似文献   

16.
We consider a differentially rotating, 2D stellar disc perturbed by two steady-state spiral density waves moving at different pattern speeds. Our investigation is based on direct numerical integration of initially circular test-particle orbits. We examine a range of spiral strengths and spiral speeds and show that stars in this time-dependent gravitational field can be heated (their random motions increased). This is particularly noticeable in the simultaneous propagation of a two-armed spiral density wave near the corotation resonance (CR), and a weak four-armed one near the inner and outer 4:1 Lindblad resonances. In simulations with two spiral waves moving at different pattern speeds, we find: (i) the variance of the radial velocity,  σ2 R   , exceeds the sum of the variances measured from simulations with each individual pattern; (ii)  σ2 R   can grow with time throughout the entire simulation; (iii)  σ2 R   is increased over a wider range of radii compared to that seen with one spiral pattern; and (iv) particles diffuse radially in real space, whereas they do not when only one spiral density wave is present. Near the CR with the stronger, two-armed pattern, test-particles are observed to migrate radially. These effects take place at or near resonances of both spirals, so we interpret them as the result of stochastic motions. This provides a possible new mechanism for increasing the stellar velocity dispersion in galactic discs. If multiple spiral patterns are present in the Galaxy, we predict that there should be large variations in the stellar velocity dispersion as a function of radius.  相似文献   

17.
It is shown that the cuspy density distributions observed in the cores of elliptical galaxies can be realized by dissipationless gravitational collapse. The initial models consist of power-law density spheres such as ρ ∝ r −1 with anisotropic velocity dispersions. Collapse simulations are carried out by integrating the collisionless Boltzmann equation directly, on the assumption of spherical symmetry. From the results obtained, the extent of constant density cores, formed through violent relaxation, decreases as the velocity anisotropy increases radially, and practically disappears for extremely radially anisotropic models. As a result, the relaxed density distributions become more cuspy with increasing radial velocity anisotropy. It is thus concluded that the velocity anisotropy could be a key ingredient for the formation of density cusps in a dissipationless collapse picture. The velocity dispersions increase with radius in the cores according to the nearly power-law density distributions. The power-law index, n , of the density profiles, defined as ρ ∝ r − n , changes from n ≈2.1 at intermediate radii to a shallower power than n ≈2.1 toward the centre. This density bend can be explained from our postulated local phase-space constraint that the phase-space density accessible to the relaxed state is determined at each radius by the maximum phase-space density of the initial state.  相似文献   

18.
When the total angular momentum of a binary system   J tot= J orb+ J spin  is at a certain critical (minimum) value, a tidal instability occurs which eventually forces the stars to merge into a single, rapidly rotating object. The instability occurs when   J orb= 3 J spin  , which in the case of contact binaries corresponds to a minimum mass ratio   q min≈  0.071–0.078. The minimum mass ratio is obtained under the assumption that stellar radii are fixed and independent. This is not the case with contact binaries where, according to the Roche model, we have   R 2= R 2( R 1, a , q )  . By finding a new criterion for contact binaries, which arises from  d J tot= 0  , and assuming   k 21≠ k 22  for the component's dimensionless gyration radii, a theoretical lower limit   q min= 0.094–0.109  for overcontact degree   f = 0–1  is obtained.  相似文献   

19.
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   

20.
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   

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