首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献，搜索用时 15 毫秒
1.
We present a simple and intuitive approximation for solving the perturbation theory (PT) of small cosmic fluctuations. We consider only the spherically symmetric or monopole contribution to the PT integrals, which yields the exact result for tree-graphs (i.e. at leading order). We find that the non-linear evolution in Lagrangian space is then given by a simple local transformation over the initial conditions, although it is not local in Euler space. This transformation is found to be described by the spherical collapse (SC) dynamics, as it is the exact solution in the shearless (and therefore local) approximation in Lagrangian space. Taking advantage of this property, it is straightforward to derive the one-point cumulants, ξJ, for both the unsmoothed and smoothed density fields to arbitrary order in the perturbative regime. To leading-order this reproduces, and provides us with a simple explanation for, the exact results obtained by Bernardeau. We then show that the SC model leads to accurate estimates for the next corrective terms when compared with the results derived in the exact perturbation theory making use of the loop calculations. The agreement is within a few per cent for the hierarchical ratios S J  = ξ J /ξ J −12. We compare our analytic results with N -body simulations, which turn out to be in very good agreement up to scales where σ ≈ 1. A similar treatment is presented to estimate higher order corrections in the Zel'dovich approximation. These results represent a powerful and readily usable tool to produce analytical predictions that describe the gravitational clustering of large-scale structure in the weakly non-linear regime.  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.
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   

4.
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   

5.
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   

6.
We study the distribution function (DF) of dark matter particles in haloes of mass range  1014–1015 M⊙  . In the numerical part of this work we measure the DF for a sample of relaxed haloes formed in the simulation of a standard Λ cold dark matter (ΛCDM) model. The DF is expressed as a function of energy E and the absolute value of the angular momentum L , a form suitable for comparison with theoretical models. By proper scaling we obtain the results that do not depend on the virial mass of the haloes. We demonstrate that the DF can be separated into energy and angular momentum components and propose a phenomenological model of the DF in the form     . This formulation involves three parameters describing the anisotropy profile in terms of its asymptotic values (β0 and  β∞  ) and the scale of transition between them ( L 0). The energy part   f E ( E )  is obtained via inversion of the integral for spatial density. We provide a straightforward numerical scheme for this procedure as well as a simple analytical approximation for a typical halo formed in the simulation. The DF model is extensively compared with the simulations: using the model parameters obtained from fitting the anisotropy profile, we recover the DF from the simulation as well as the profiles of the dispersion and kurtosis of radial and tangential velocities. Finally, we show that our DF model reproduces the power-law behaviour of phase-space density   Q =ρ( r )/σ3( r )  .  相似文献   

7.
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   

8.
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   

9.
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   

10.
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   

11.
The stability of Trojan type orbits around Neptune is studied. As the first part of our investigation, we present in this paper a global view of the stability of Trojans on inclined orbits. Using the frequency analysis method based on the fast Fourier transform technique, we construct high-resolution dynamical maps on the plane of initial semimajor axis a 0 versus inclination i 0. These maps show three most stable regions, with i 0 in the range of  (0°, 12°), (22°, 36°)  and  (51°, 59°),  respectively, where the Trojans are most probably expected to be found. The similarity between the maps for the leading and trailing triangular Lagrange points L 4 and L 5 confirms the dynamical symmetry between these two points. By computing the power spectrum and the proper frequencies of the Trojan motion, we figure out the mechanisms that trigger chaos in the motion. The Kozai resonance found at high inclination varies the eccentricity and inclination of orbits, while the  ν8  secular resonance around   i 0∼ 44°  pumps up the eccentricity. Both mechanisms lead to eccentric orbits and encounters with Uranus that introduce strong perturbation and drive the objects away from the Trojan like orbits. This explains the clearance of Trojan at high inclination  (>60°)  and an unstable gap around  44°  on the dynamical map. An empirical theory is derived from the numerical results, with which the main secular resonances are located on the initial plane of  ( a 0, i 0)  . The fine structures in the dynamical maps can be explained by these secular resonances.  相似文献   

12.
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   

13.
We generalize the Doroshkevich's celebrated formulae for the eigenvalues of the initial shear field associated with Gaussian statistics to the local non-Gaussian   fnl   model. This is possible because, to at least second order in   fnl   , distributions at fixed overdensity are unchanged from the case   fnl = 0  . We use this generalization to estimate the effect of   fnl ≠ 0  on the abundance of virialized haloes. Halo abundances are expected to be related to the probability that a certain quantity in the initial fluctuation field exceeds a threshold value, and we study two choices for this variable: it can either be the sum of the eigenvalues of the initial deformation tensor (the initial overdensity) or its smallest eigenvalue. The approach based on a critical overdensity yields results which are in excellent agreement with numerical measurements. We then use these same methods to develop approximations describing the sensitivity of void abundances on   fnl   . While a positive   fnl   produces more extremely massive haloes, it makes fewer extremely large voids. Its effect thus is qualitatively different from a simple rescaling of the normalization of the density fluctuation field σ8. Therefore, void abundances furnish complementary information to cluster abundances, and a joint comparison of both might provide interesting constraints on primordial non-Gaussianity.  相似文献   

14.
The cumulant correlators, C pq , are statistical quantities that generalize the better-known S p parameters; the former are obtained from the two-point probability distribution function of the density fluctuations while the latter describe only the one-point distribution. If galaxy clustering develops from Gaussian initial fluctuations and a small-angle approximation is adopted, standard perturbative methods suggest a particular hierarchical relationship of the C pq for projected clustering data, such as that obtained from the Automatic Plate Measuring (APM) survey. We establish the usefulness of the two-point cumulants for describing hierarchical clustering by comparing such calculations against available measurements from projected catalogues, finding very good agreement. We extend the idea of cumulant correlators to multipoint generalized cumulant correlators (related to the higher-order correlation functions). We extend previous studies in the highly non-linear regime to express the generalized cumulant correlators in terms of the underlying 'tree amplitudes' of hierarchical scaling models. Such considerations lead to a technique for determining these hierarchical amplitudes, to arbitrary order, from galaxy catalogues and numerical simulations. Knowledge of these amplitudes yields important clues about the phenomenology of gravitational clustering. For instance, we show that a three-point cumulant correlator can be used to separate the tree amplitudes up to sixth order. We also combine the particular hierarchical Ansatz of Bernardeau & Schaeffer with extended and hyper-extended perturbation theory to infer values of the tree amplitudes in the highly non-linear regime.  相似文献   

15.
  相似文献   

16.
In this paper, we present a new method to estimate, for each turbulent layer labelled i , the horizontal wind speed   v ( h i )  , the standard deviation of the horizontal wind speed fluctuations  σ v ( hi )  and the integrated value of   C 2 n   over the thickness  Δ hi   of the turbulent layer   C 2 n ( hi )Δ hi   , where   hi   is the altitude of the turbulent layer. These parameters are extracted from single star scintillation spatiotemporal cross-correlation functions of atmospheric speckles obtained within the generalized mode. This method is based on the simulated annealing algorithm to find the optimal solution required to solve the problem. Astrophysics parameters for adaptive optics are also calculated using   C 2 n ( hi )  and   v ( hi )  values. The results of other techniques support this new method.  相似文献   

17.
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   

18.
We estimate the two- and three-dimensional power spectra, P 2( K ) and P 3( k ), of the galaxy distribution by applying a maximum likelihood estimator to pixel maps of the APM Galaxy Survey. The analysis provides optimal estimates of the power spectra and of their covariance matrices if the fluctuations are assumed to be Gaussian. Our estimates of P 2( K ) and P 3( k ) are in good agreement with previous work, but we find that the errors at low wavenumbers have been underestimated in some earlier studies. If the galaxy power spectrum is assumed to have the same shape as the mass power spectrum, then the APM maximum likelihood P 3( k ) estimates at k ≤0.19  h  Mpc−1 constrain the amplitude and shape parameter of a scale-invariant CDM model to lie within the 2 σ ranges 0.74≤( σ 8)g≤1.28 and 0.06≤Γ≤0.46 . Using the Galactic extinction estimates of Schlegel, Finkbeiner & Davis, we show that Galactic obscuration has a negligible effect on galaxy clustering over most of the area of the APM Galaxy Survey.  相似文献   

19.
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   

20.
Using N -body simulations with a large set of massless test particles, we compare the predictions of two theories of violent relaxation, the well-known Lynden-Bell theory and the more recent theory by Nakamura. We derive 'weakened' versions of both the theories in which we use the whole equilibrium coarse-grained distribution function     as a constraint instead of the total energy constraint. We use these weakened theories to construct expressions for the conditional probability   Ki (τ)  that a test particle initially at the phase-space coordinate τ would end-up in the i th macro-cell at equilibrium. We show that the logarithm of the ratio   Rij (τ) ≡ Ki (τ)/ Kj (τ)  is directly proportional to the initial phase-space density   f 0(τ)  for the Lynden-Bell theory and inversely proportional to   f 0(τ)  for the Nakamura theory. We then measure   Rij (τ)  using a set of N -body simulations of a system undergoing a gravitational collapse to check the validity of the two theories of violent relaxation. We find that both the theories are at odds with the numerical results, both qualitatively and quantitatively.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号