The Correlation Function in Redshift Space: General Formula with Wide‐Angle Effects and Cosmological Distortions

Matsubara, Takahiko

doi:10.1086/308827

Cited by 97 publications

(142 citation statements)

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“…Szalay, Matsubara, & Landy (1998) derived a formula of velocity distortions in the linear two-point correlation function with the wide-angle effect. Matsubara (2000) derived the most general formula of the linear two-point correlation function in which the velocity distortions, the AP effect, and the wide-angle effect are all included in a unified formula. All the previous formulae for the linear two-point correlation function are limiting cases of the last formula.…”

Section: Bayesian Analysis Of the Galaxy Distribution In Redshift Surmentioning

confidence: 99%

“…In the context of CMB analysis, Bond (1995) introduced an equivalent method that is called the signal-to-noise ratio (S/N) eigenmode method. The KL method is now recognized as one of the most promising methods to tackle large data sets of the cosmological surveys (Tegmark, Taylor, & Heavens 1997;Tegmark et al 1998;Taylor et al 2001) and has been successfully applied to the Las Campanas Redshift Survey (LCRS; Matsubara, Szalay, & Landy 2000), the Sloan Digital Sky Survey (SDSS; Szalay et al 2003;Pope et al 2004), and the ROSAT-ESO FluxLimited X-Ray (REFLEX) Galaxy Cluster Survey (Schuecker et al 2002). A variant, simplified method, which is called the pseudo-KL eigenmode method, is applied to the IRAS PointSource Catalog Redshift Survey (PSCz; Hamilton, Tegmark, & Padmanabhan 2000), the 2dF Galaxy Redshift Survey (Tegmark, Hamilton, & Xu 2002), and SDSS (Tegmark et al 2004).…”

Section: Introductionmentioning

confidence: 99%

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Eigenmode Analysis of Galaxy Distributions in Redshift Space

Matsubara

Szalay

Pope

2004

ApJ

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Eigenmode analysis is one of the most promising methods of analyzing large data sets in ongoing and nearfuture galaxy surveys. In such analyses, a fast evaluation of the correlation matrix in arbitrary cosmological models is crucial. The observational effects, including peculiar velocity distortions in redshift space, light cone effects, selection effects, and effects of the complex shape of the survey geometry, should be taken into account in the analysis. In the framework of the linear theory of gravitational instability, we provide the methodology to quickly compute the correlation matrix. Our methods are not restricted to shallow redshift surveys: arbitrarily deep samples can be dealt with as well. Therefore, our methods are useful in constraining the geometry of the universe and the dark energy component, as well as the power spectrum of galaxies, since ongoing and nearfuture galaxy surveys probe the universe at intermediate to deep redshifts, z $ 0:2 5. In addition to the detailed methods to compute the correlation matrix in three-dimensional redshift surveys, methods to calculate the matrix in two-dimensional projected samples are also provided. Prospects for applying our methods to likelihood estimation of the cosmological parameters are discussed.

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Section: Bayesian Analysis Of the Galaxy Distribution In Redshift Surmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Eigenmode Analysis of Galaxy Distributions in Redshift Space

Matsubara

Szalay

Pope

2004

ApJ

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“…The Fisher information matrix approach is one example of this (Tegmark 1997 ;Tegmark, Taylor, & Heavens 1997 ;Goldberg & Strauss 1998 ;Taylor & Watts 2000). This approach is sound and will lead to very accurate results when applied to forthcoming surveys such as SDSS and 2dF ; the computational e †ort can be successfully minimized in those cases via data compression techniques, e.g., via the Karnhunen-"" signal-to-noise ÏÏ eigenmodes (Vogeley & Szalay Loe`ve 1996 ;Matsubara, Szalay, & Landy 2000), quadratic compression into high-resolution powers (Tegmark 1997 ;Tegmark et al 1997Padmanabhan, Tegmark, & Hamilton 2001), etc. There is, on the other hand, a case to be made for combining di †erent galaxy redshift surveys and extracting information jointly from them, as an ensemble, prior to comparing them with di †er-ent kinds of data sets.…”

Section: Introductionmentioning

confidence: 99%

Overconstrained Dynamics in Galaxy Redshift Surveys

Susperregi

2001

ApJ

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The least-action principle (LAP) method is used on four galaxy redshift surveys to measure the density parameter and the matter and galaxy-galaxy power spectra. The data sets are PSCz, ORS, Mark III, ) m and SFI. The LAP method is applied on the surveys simultaneously, resulting in an overconstrained dynamical system that describes the cosmic overdensities and velocity Ñows. The system is solved by relaxing the constraint that each survey imposes upon the cosmic Ðelds. A least-squares optimization of the errors that arise in the process yields the cosmic Ðelds and the value of that is the best Ðt to the ) m ensemble of data sets. The analysis has been carried out with a high-resolution Gaussian smoothing of 500 km s~1 and over a spherical selected volume of radius 9000 km s~1. We have assigned a weight to each survey, depending on their density of sampling, and this parameter determines their relative inÑu-ence in limiting the domain of the overall solution. The inÑuence of each survey on the Ðnal value of ) m , the cosmographical features of the cosmic Ðelds, and the power spectra largely depends on the distribution function of the errors in the relaxation of the constraints. We Ðnd that PSCz and Mark III are closer to the Ðnal solution than ORS and SFI. The likelihood analysis yields to 1 p ) m \ 0.37^0.01 level. PSCz and SFI are the closest to this value, whereas ORS and Mark III predict a somewhat lowerThe model of bias employed is a scale-dependent one, and we retain up to 42 bias coefficients in ) m .b rl the spherical harmonics formalism. The predicted power spectra are estimated in the range of wavenumbers h Mpc~1, and we compare these results with measurements recently reported in the 0.02 [ k [ 0.49 literature.

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“…Several applications of this effect are proposed (Nair 1999;Nakamura, Matsubara & Suto 1998;Popowski et al 1998;Yamamoto, Nishioka & Suto 1999). To maximally extract the cosmological information from the survey data, the likelihood analysis combined with a data reduction technique like the Karhunen-Loève transform has been quite successful at low redshifts (Vogeley & Szalay 1996;Szalay, Matsubara & Landy 1998;Matsubara, Szalay & Landy 2000). We expect it to be just as useful at intermediate-to-high redshifts here.…”

Section: Introductionmentioning

confidence: 96%

“…As the depth and the sampling rate of redshift surveys increase, redshift-space clustering depends on the cosmological constant through the cosmological redshift distortions (Ballinger, Peacock & Heavens 1996;Matsubara & Suto 1996;Matsubara 2000). Several applications of this effect are proposed (Nair 1999;Nakamura, Matsubara & Suto 1998;Popowski et al 1998;Yamamoto, Nishioka & Suto 1999).…”

Section: Introductionmentioning

confidence: 99%

Constraining the Cosmological Constant from Large-Scale Redshift-Space Clustering

Matsubara

Szalay²

Statistical Challenges in Astronomy

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We show how the cosmological constant can be estimated from redshift surveys at different redshifts, using maximum-likelihood techniques. The apparent redshift-space clustering on large scales ( > ∼ 20 h −1 Mpc ) are affected in the radial direction by infall, and curvature influences the apparent correlations in the transverse direction. The relative strengths of the two effects will strongly vary with redshift. Using a simple idealized survey geometry, we compute the smoothed correlation matrix of the redshiftspace correlation function, and the Fisher matrix for Ω M and Ω Λ . These represent the best possible measurement of these parameters given the geometry. We find that the likelihood contours are turning, according to the behavior of the angular-diameter distance relation. The clustering measures from redshift surveys at intermediate-to-high redshifts can provide a surprisingly tight constraint on Ω Λ . We also estimate confidence contours for real survey geometries, using the SDSS LRG and QSO surveys as specific examples. We believe that this method will become a practical tool to constrain the nature of the dark energy.

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The Correlation Function in Redshift Space: General Formula with Wide‐Angle Effects and Cosmological Distortions

Cited by 97 publications

References 46 publications

Eigenmode Analysis of Galaxy Distributions in Redshift Space

Eigenmode Analysis of Galaxy Distributions in Redshift Space

Overconstrained Dynamics in Galaxy Redshift Surveys

Constraining the Cosmological Constant from Large-Scale Redshift-Space Clustering

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