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1.
In Paper I of this series, we introduced the spherical collapse (SC) approximation in Lagrangian space as a way of estimating the cumulants ξ J of density fluctuations in cosmological perturbation theory (PT). Within this approximation, the dynamics is decoupled from the statistics of the initial conditions, so we are able to present here the cumulants for generic non-Gaussian initial conditions, which can be estimated to arbitrary order including the smoothing effects. The SC model turns out to recover the exact leading-order non-linear contributions up to terms involving non-local integrals of the J -point functions. We argue that for the hierarchical ratios S J , these non-local terms are subdominant and tend to compensate each other. The resulting predictions show a non-trivial time evolution that can be used to discriminate between models of structure formation. We compare these analytic results with non-Gaussian N -body simulations, which turn out to be in very good agreement up to scales where σ ≲ 1.  相似文献   

2.
Cosmological perturbation theory (PT) is a useful tool to study the cumulants of the density and velocity fields in the large-scale structure of the Universe. In Papers I and II of this series we saw that the spherical collapse (SC) model provides the exact solution to PT at tree-level and gives a good approximation to the loop corrections (next-to-leading orders), indicating negligible tidal effects. Here, we derive predictions for the (smoothed) cumulants of the velocity divergence field θ ≡ ▽ ⊙  v for an irrotational fluid in the SC model. By comparing these with the exact analytic results of Scoccimarro &38; Frieman, it is shown that, at least for the unsmoothed case, the loop corrections to the cumulants of θ are dominated by tidal effects. However, most of the tidal contribution seems to cancel out when computing the hierarchical ratios, T J  = 〈θ J 〉 / 〈θ2〉  J −1. We also extend the work presented in Papers I and II to give predictions for the cumulants of the density and velocity divergence fields in non-flat spaces. In particular, we show the equivalence between the spherically symmetric solution to the equations of motion in the SC model (given in terms of the density) and that of the Lagrangian PT approach (given in terms of the displacement field). It is shown that the Ω dependence is very weak for both cosmic fields even at one loop (a 10 per cent effect at most), except for the overall factor f (Ω) that couples to the velocity divergence.  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.
We use the spherical collapse (SC) approximation to derive expressions for the smoothed redshift-space probability distribution function (PDF), as well as the p -order hierarchical amplitudes S p , in both real and redshift space. We compare our results with numerical simulations, focusing on the     standard CDM model, where redshift distortions are strongest. We find good agreement between the SC predictions and the numerical PDF in real space even for     , where σ L is the linearly evolved rms fluctuation on the smoothing scale. In redshift space, reasonable agreement is possible only for     . Numerical simulations also yield a simple empirical relation between the real-space PDF and the redshift-space PDF: we find that for     , the redshift-space PDF, [ P δ ( z )], is, to a good approximation, a simple rescaling of the real-space PDF, P [ δ ], i.e.,     where σ and σ ( z ) are the real-space and redshift-space rms fluctuations, respectively. This result applies well beyond the validity of linear perturbation theory, and it is a good fit for both the standard CDM model and the ΛCDM model. It breaks down for SCDM at     , but provides a good fit to the ΛCDM models for σ L as large as 0.8.  相似文献   

5.
We consider a situation where the density and peculiar velocities in real space are linear, and we calculate ξ s , the two-point correlation function in redshift space, incorporating all non-linear effects which arise as a consequence of the map from real to redshift space. Our result is non-perturbative and it includes the effects of possible multi-streaming in redshift space. We find that the deviations from the predictions of the linear redshift distortion analysis increase for the higher spherical harmonics of ξ s . While the deviations are insignificant for the monopole ξ 0, the hexadecapole ξ 4 exhibits large deviations from the linear predictions. For a COBE normalized     ,     cold dark matter (CDM) power spectrum, our results for ξ 4 deviate from the linear predictions by a factor of two on the scale of ∼10  h −1 Mpc. The deviations from the linear predictions depend separately on f (Ω) and b . This holds the possibility of removing the degeneracy that exists between these two parameters in the linear analysis of redshift surveys which yields only     .
We also show that the commonly used phenomenological model, where the non-linear redshift two-point correlation function is calculated by convolving the linear redshift correlation function with an isotropic pair velocity distribution function, is a limiting case of our result.  相似文献   

6.
This paper presents a comparison of the predictions for the two- and three-point correlation functions of density fluctuations, ξ and ζ , in gravitational perturbation theory (PT) against large cold dark matter (CDM) simulations. This comparison is made possible for the first time on large weakly non-linear scales (>10  h −1 Mpc) thanks to the development of a new algorithm for estimating correlation functions for millions of points in only a few minutes. Previous studies in the literature comparing the PT predictions of the three-point statistics with simulations have focused mostly on Fourier space, angular space or smoothed fields. Results in configuration space, such as those presented here, were limited to small scales where leading-order PT gives a poor approximation. Here we also propose and apply a method for separating the first-order and subsequent contributions to PT by combining different output times from the evolved simulations. We find that in all cases there is a regime where simulations do reproduce the leading-order (tree-level) predictions of PT for the reduced three-point function   Q 3∼ ζ / ξ 2  . For steeply decreasing correlations (such as the standard CDM model) deviations from the tree-level results are important even at relatively large scales, ≃20 Mpc  h −1. On larger scales ξ goes to zero and the results are dominated by sampling errors. In more realistic models (such as the ΛCDM cosmology) deviations from the leading-order PT become important at smaller scales   r ≃10 Mpc  h -1  , although this depends on the particular three-point configuration. We characterize the range of validity of this agreement and show the behaviour of the next-order (one-loop) corrections.  相似文献   

7.
This is the second paper of a series where we study the clustering of luminous red galaxies (LRG) in the recent spectroscopic Sloan Digital Sky Survey (SDSS) data release, DR6, which has 75 000 LRG covering over  1 Gpc3  h −3  for  0.15 < z < 0.47  . Here, we focus on modelling redshift-space distortions in  ξ(σ, π)  , the two-point correlation in separate line-of-sight and perpendicular directions, at small scales and in the line-of-sight. We show that a simple Kaiser model for the anisotropic two-point correlation function in redshift space, convolved with a distribution of random peculiar velocities with an exponential form, can describe well the correlation of LRG on all scales. We show that to describe with accuracy the so-called 'fingers-of-God' (FOG) elongations in the radial direction, it is necessary to model the scale dependence of both bias b and the pairwise rms peculiar velocity σ12 with the distance. We show how both quantities can be inferred from the  ξ(σ, π)  data. From   r ≃ 10 Mpc  h −1  to   r ≃ 1 Mpc  h −1  , both the bias and σ12 are shown to increase by a factor of 2: from   b = 2  to 4 and from  σ12= 400  to  800 km s−1  . The latter is in good agreement, within a 5 per cent accuracy in the recovered velocities, with direct velocity measurements in dark matter simulations with  Ωm= 0.25  and  σ8= 0.85  .  相似文献   

8.
Cold collapse of a cluster composed of small identical clumps, each of which is in virial equilibrium, is considered. Since the clumps have no relative motion with respect to each other initially, the cluster collapses under its own gravity. At the first collapse of the cluster, most of the clumps are destroyed, but some survive. In order to find the condition for the clumps to survive, we made a systematic study in two-parameter space: the number of the clumps N c and the size of the clump r v . We obtained the condition N c ≫ 1 and n k  ≥ 1, where n k is related to r v and the initial radius of the cluster R ini through the relation R ini/ r v  = 2 N ( n k +5)/6c. A simple analytical argument supports the numerical result. This n k corresponds to the index of the power spectrum of the density fluctuation in the cosmological hierarchical clustering, and thus our result may suggest that in the systems smaller than 2/Ω h 2)Mpc, the first violent collapse is strong enough to sweep away all the substructures that exist before the collapse.  相似文献   

9.
We present the results of a spectroscopic multisite campaign for the β Cephei star 12 (DD) Lacertae. Our study is based on more than thousand high-resolution high S/N spectra gathered with eight different telescopes in a time span of 11 months. In addition, we make use of numerous archival spectroscopic measurements. We confirm 10 independent frequencies recently discovered from photometry, as well as harmonics and combination frequencies. In particular, the slowly pulsating B-stars (SPB)-like g -mode with frequency 0.3428 d−1 reported before is detected in our spectroscopy. We identify the four main modes as  (ℓ1, m 1) = (1, 1), (ℓ2, m 2) = (0, 0), (ℓ3, m 3) = (1, 0)  and  (ℓ4, m 4) = (2, 1)  for   f 1= 5.178 964 d−1, f 2= 5.334 224 d−1, f 3= 5.066 316 d−1  and   f 4= 5.490 133 d−1  , respectively. Our seismic modelling shows that f 2 is likely the radial first overtone and that the core overshooting parameter  αov  is lower than 0.4 local pressure scale heights.  相似文献   

10.
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   

11.
We present a correlation function analysis for the catalogue of photometric redshifts obtained from the Hubble Deep Field image by Fernandez-Soto, Lanzetta & Yahil. By dividing the catalogue into redshift bins of width Δ z =0.4 we measured the angular correlation function w ( θ ) as a function of redshift up to z ∼4.8. From these measurements we derive the trend of the correlation length r 0. We find that r 0( z ) is roughly constant with look-back time up to z ≃2, and then increases to higher values at z ≳2.4. We estimate the values of r 0, assuming ξ ( r , z )=[ r r 0( z )]− γ , γ =1.8 and various geometries. For Ω0=1 we find r 0( z =3)≃7.00±4.87  h −1 Mpc, in good agreement with the values obtained from analysis of the Lyman break galaxies.  相似文献   

12.
correlator of the galaxy density field Q 21 is examined from the point of view of biasing. It is shown that, to leading order, it depends on two biasing parameters b b 2, and on q 21, the underlying cumulant correlator of the mass. As the skewness Q 3 has analogous properties, the slope of the correlation function −γ, Q 3 and Q 21 uniquely determine the bias parameter on a particular scale to be b  = γ/6( Q 21 −  Q 3), when working in the context of gravitational instability with Gaussian initial conditions. Thus on large scales, easily accessible with the future Sloan Digital Sky Survey and the 2 Degree Field Survey, it will be possible to extract b b 2 from simple counts-in-cells measurements. Moreover, the higher order cumulants, Q N , successively determine the higher order biasing parameters. From these it is possible to predict higher order cumulant correlators as well. Comparison of the predictions with the measurements will provide internal consistency checks on the validity of the assumptions in the theory, most notably perturbation theory of the growth of fluctuations by gravity and Gaussian initial conditions. Since the method is insensitive Ω, it can be successfully combined with results from velocity fields, which determine Ω0.6/b, to measure the total density parameter in the Universe.  相似文献   

13.
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   

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 non-linear scaling relations (NSRs) to investigate the effects arising from the existence of negative correlations on the evolution of gravitational clustering in an expanding universe. It turns out that such anticorrelated regions have important dynamical effects on all scales. In particular, the mere existence of negative values for the linear two-point correlation function ξ¯ L over some range of scales starting from l = L 0 implies that the non-linear correlation function is bounded from above at all scales x < L 0 . This also results in the relation ξ¯   ∝  x −3 , at these scales, at late times, independent of the original form of the correlation function. Current observations do not rule out the existence of negative ξ¯ for 200  h −1 Mpc≲ ξ¯ ≲1000  h −1 Mpc; the present work may thus have relevance for the real Universe. The only assumption made in the analysis is the existence of NSR; the results are independent of the form of the NSR as well as of the stable clustering hypothesis.  相似文献   

16.
Theoretical electron density sensitive line ratios   R 1– R 6  of Si  x soft X-ray emission lines are presented. We found that these line ratios are sensitive to electron density n e, and the ratio R 1 is insensitive to electron temperature T e. For reliable determination of the electron density of laboratory and astrophysical plasmas, atomic data, such as electron impact excitation rates, are very important. Our results reveal that the discrepancy of the line ratios from different atomic data calculated with the distorted wave (DW) approximation and the R-matrix method is up to 19 per cent at   n e= 2 × 108 cm−3  . We applied the theoretical intensity ratio R 1 to the Low Energy Transmission Grating Spectrometer (LETGS) spectrum of the solar-like star Procyon. By comparing the observed value (1.29) with the theoretical calculation, the derived electron density n e is  2.6 × 108 cm−3  , which is consistent with that derived from  (C  v < 8.3 × 108 cm−3)  . When the temperature structure of the Procyon corona is taken into account, the derived electron density increases from   n e= 2.6 × 108  to  2.8 × 108 cm−3  .  相似文献   

17.
Using the ray-bundle method for calculating gravitational lens magnifications, we outline a method by which the magnification probability may be determined specifically in the weak lensing limit for cosmological models obtained from N -body simulations.
16 different models are investigated, which are variations on three broad classes of cold dark matter model: the standard model with  (Ω0, λ 0)=(1.0,0.0)  , the open model with  (Ω0, λ 0)=(0.3,0.0)  and the lambda model, which is a flat model with a cosmological constant  (Ω0, λ 0)=(0.3,0.7)  .
The effects of varying the Hubble parameter, H 0, the power spectrum shape parameter, Γ, and the cluster mass normalization, σ 8, are studied. It is shown that there is no signature of these parameters in the weak lensing magnification distributions. The magnification probability distributions are also shown to be independent of the numerical parameters such as the lens mass and simulation box size in the N -body simulations.  相似文献   

18.
We show how the continuity equation can be used to determine pattern speeds in the Milky Way Galaxy (MWG). This method, first discussed by Tremaine & Weinberg in the context of external galaxies, requires projected positions, ( l , b ), and line-of-sight velocities for a spatially complete sample of relaxed tracers. If the local standard of rest (LSR) has a zero velocity in the radial direction ( u LSR), then the quantity that is measured is  Δ V ≡Ωp R 0- V LSR  , where Ωp is the pattern speed of the non-axisymmetric feature, R 0 is the distance of the Sun from the Galactic centre and V LSR is the tangential motion of the LSR, including the circular velocity. We use simple models to assess the reliability of the method for measuring a single, constant pattern speed of either a bar or spiral in the inner MWG. We then apply the method to the OH/IR stars in the ATCA/VLA OH 1612-MHz survey of Sevenster et al., finding  Δ V =252±41 km s-1,  if   u LSR=0  . Assuming further that   R 0=8 kpc  and   V LSR=220 km s-1,  this gives  Ωp=59±5 km s-1 kpc-1  with a possible systematic error of perhaps 10 km s−1 kpc−1. The non-axisymmetric feature for which we measure this pattern speed must be in the disc of the MWG.  相似文献   

19.
It has been found that the near-infrared flux variations of Seyfert galaxies satisfy relations of the form   Fi ≈α i j +β i j Fj   , where Fi , Fj are the fluxes in filters i and j ; and  α i , j , β i , j   are constants. These relations have been used to estimate the constant contributions of the non-variable underlying galaxies. The paper attempts a formal treatment of the estimation procedure, allowing for the possible presence of a third component, namely non-variable hot dust. In an analysis of a sample of 38 Seyfert galaxies, inclusion of the hot dust component improves the model fit in approximately half the cases. All derived dust temperatures are below 300 K, in the range 540–860 K or above 1300 K. A noteworthy feature is the estimation of confidence intervals for the component contributions: this is achieved by bootstrapping. It is also pointed out that the model implies that such data could be fruitfully analysed in terms of principal components.  相似文献   

20.
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