Towards breaking the  -bias degeneracy in density--velocity comparisons

Chodorowski, Michal

doi:10.1046/j.1365-8711.1999.02710.x

Cited by 5 publications

(6 citation statements)

References 49 publications

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“…see Eqs. (128)(129)]. Similar results hold for higher-order N-point correlation functions ξ N [508], and imply that ξ N /ξ…”

Section: Stable Clusteringsupporting

confidence: 62%

“…see Eqs. (128)(129)]. Similar results hold for higher-order N-point correlation functions ξ N [508], and imply that ξ N /ξ N −1 2 as a function of physical separation become independent of time in the highly non-linear regime (1 ≪ ξ 2 ≪ .…”

Section: Stable Clusteringmentioning

confidence: 53%

“…54, APM measurements are somewhat below the PT predictions or N-body results at θ > ∼ 1 degrees [48], indicating possibly a slight bias for APM galaxies. But note that this difference is not very significant given the errors and the fact that there is a strong covariance and a significant 128 These errors should be considered more realistic than those given in the fifth and sixth entry in Table 16, which were derived by combining results at different angular scales assuming they are uncorrelated [249]. These errorbars also correspond roughly to a 2-σ confidence in a single all-sky map: they are twice as large as the ones in Fig.47.…”

Section: Three-point Statistics and Higher Ordermentioning

confidence: 95%

“…In particular a detailed analysis of the curvature in the δ − θ relation (through a 2 or r 2 ) would provide a way to break the degeneracy between biasing parameters (Sect. 7.1) and Ω m [128,56] 52 . Moreover, these results can be extended to take into account redshift distortion effects (Sect.…”

Section: The Velocity-density Relationmentioning

confidence: 96%

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Large-scale structure of the Universe and cosmological perturbation theory

et al. 2002

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We review the formalism and applications of non-linear perturbation theory (PT) to understanding the large-scale structure of the Universe. We first discuss the dynamics of gravitational instability, from the linear to the non-linear regime. This includes Eulerian and Lagrangian PT, non-linear approximations, and a brief description of numerical simulation techniques. We then cover the basic statistical tools used in cosmology to describe cosmic fields, such as correlations functions in real and Fourier space, probability distribution functions, cumulants and generating functions. In subsequent sections we review the use of PT to make quantitative predictions about these statistics according to initial conditions, including effects of possible non Gaussianity of the primordial fields. Results are illustrated by detailed comparisons of PT predictions with numerical simulations. The last sections deal with applications to observations. First we review in detail practical estimators of statistics in galaxy catalogs and related errors, including traditional approaches and more recent developments. Then, we consider the effects of the bias between the galaxy distribution and the matter distribution, the treatment of redshift distortions in three-dimensional surveys and of projection effects in angular catalogs, and some applications to weak gravitational lensing. We finally review the current observational situation regarding statistics in galaxy catalogs and what the future generation of galaxy surveys promises to deliver.

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“…see Eqs. (128)(129)]. Similar results hold for higher-order N-point correlation functions ξ N [508], and imply that ξ N /ξ…”

Section: Stable Clusteringsupporting

confidence: 62%

Section: Stable Clusteringmentioning

confidence: 53%

Section: Three-point Statistics and Higher Ordermentioning

confidence: 95%

Section: The Velocity-density Relationmentioning

confidence: 96%

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Large-scale structure of the Universe and cosmological perturbation theory

et al. 2002

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“…By expressing the s ‐space velocity in terms of a potential, this relation can now be solved iteratively to obtain the velocity field associated with a given redshift galaxy distribution. Furthermore, our result can simplify calculations of redshift space dynamical relations based on perturbation theory (e.g., Chodorowski 1999).…”

Section: Summary and Discussionmentioning

confidence: 83%

On the vorticity of flow in redshift space

Chodorowski

Nusser

1999

Monthly Notices of the Royal Astronomical Society

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Given an irrotational (vorticity free) velocity field in real space, we prove that, in the distant observer limit and in the absence of multi-valued zones, the associated velocity field in redshift space is also irrotational. The proof does not rely on any approximation to gravitational dynamics. The result can be particularly useful for the analysis of redshift distortions and for reconstruction methods of cosmological velocity fields from galaxy redshift surveys, in the nonlinear regime. Although the proof is restricted to the distant observer limit, we show that the POTENT method can be modified to derive the full real space velocity field as a function of the redshift space coordinate, thus avoiding spatial Malmquist biases.Comment: 3 pages, no figures, minor textual changes; MNRAS, accepte

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Comparing the redshift-space density field with the real-space velocity field

Chodorowski¹

2000

Monthly Notices of the Royal Astronomical Society

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I derive a non‐linear local relation between the redshift‐space density field and the real‐space velocity field. The relation accounts for the radial character of the redshift distortions and is not restricted to the limit of the distant observer. Direct comparisons between the observed redshift‐space density fields and the real‐space velocity fields possess all of the advantages of the conventional redshift‐space analyses, while at the same time they are free of their disadvantages. In particular, neither the model‐dependent reconstruction of the density field in real space, nor the reconstruction of the non‐linear velocity field in redshift space is necessary, the latter being questionable because of its vorticity at second order. The non‐linear redshift‐space velocity field is irrotational only in the distant observer limit, and that limit is not a good approximation for the shallow catalogues of peculiar velocities currently available. Unlike the conventional redshift‐space comparisons, the comparison proposed here does not have to be restricted to the linear regime. Accounting for non‐linear effects removes one of the sources of bias in the estimation of β. Moreover, the non‐linear effects break the Ω–bias degeneracy plaguing all analyses based on linear theory.

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Towards breaking the -bias degeneracy in density--velocity comparisons

Cited by 5 publications

References 49 publications

Large-scale structure of the Universe and cosmological perturbation theory

Large-scale structure of the Universe and cosmological perturbation theory

On the vorticity of flow in redshift space

Comparing the redshift-space density field with the real-space velocity field

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