Power spectrum correlations induced by nonlinear clustering

Román Scoccimarro, Matias Zaldarriaga, Lam Hui

    Research output: Contribution to journalArticle

    Abstract

    Gravitational clustering is an intrinsically nonlinear process that generates significant non-Gaussian signatures in the density field. We consider how these affect power spectrum determinations from galaxy and weak-lensing surveys. Non-Gaussian effects not only increase the individual error bars compared to the Gaussian case but, most importantly, lead to nontrivial cross-correlations between different band powers, correlating small-scale band powers both among themselves and with those at large scales. We calculate the power-spectrum covariance matrix in nonlinear perturbation theory (weakly nonlinear regime), in the hierarchical model (strongly nonlinear regime), and from numerical simulations in real and redshift space. In particular, we show that the hierarchical Ansatz cannot be strictly valid for the configurations of the trispectrum involved in the calculation of the power-spectrum covariance matrix. We discuss the impact of these results on parameter estimation from power-spectrum measurements and their dependence on the size of the survey and the choice of band powers. We show that the non-Gaussian terms in the covariance matrix become dominant for scales smaller than the nonlinear scale knl ∼ 0.2 h-1 Mpc-1, depending somewhat on power normalization. Furthermore, we find that cross-correlations mostly deteriorate the determination of the amplitude of a rescaled power spectrum, whereas its shape is less affected. In weak lensing surveys the projection tends to reduce the importance of non-Gaussian effects. Even so, for background galaxies at redshift z ∼ 1, the non-Gaussian contribution rises significantly around l ∼ 1000 and could become comparable to the Gaussian terms depending upon the power spectrum normalization and cosmology. The projection has another interesting effect: the ratio between non-Gaussian and Gaussian contributions saturates and can even decrease at small enough angular scales if the power spectrum of the three-dimensional field falls faster than k-2.

    Original languageEnglish (US)
    Pages (from-to)1-15
    Number of pages15
    JournalAstrophysical Journal
    Volume527
    Issue number1 PART 1
    StatePublished - Dec 10 1999

    Fingerprint

    power spectra
    cross correlation
    matrix
    projection
    galaxies
    cosmology
    perturbation theory
    signatures
    perturbation
    configurations
    simulation
    effect

    Keywords

    • Galaxies: clusters: general
    • Large-scale structure of universe
    • Methods: numerical
    • Methods: statistical

    ASJC Scopus subject areas

    • Space and Planetary Science

    Cite this

    Scoccimarro, R., Zaldarriaga, M., & Hui, L. (1999). Power spectrum correlations induced by nonlinear clustering. Astrophysical Journal, 527(1 PART 1), 1-15.

    Power spectrum correlations induced by nonlinear clustering. / Scoccimarro, Román; Zaldarriaga, Matias; Hui, Lam.

    In: Astrophysical Journal, Vol. 527, No. 1 PART 1, 10.12.1999, p. 1-15.

    Research output: Contribution to journalArticle

    Scoccimarro, R, Zaldarriaga, M & Hui, L 1999, 'Power spectrum correlations induced by nonlinear clustering', Astrophysical Journal, vol. 527, no. 1 PART 1, pp. 1-15.
    Scoccimarro R, Zaldarriaga M, Hui L. Power spectrum correlations induced by nonlinear clustering. Astrophysical Journal. 1999 Dec 10;527(1 PART 1):1-15.
    Scoccimarro, Román ; Zaldarriaga, Matias ; Hui, Lam. / Power spectrum correlations induced by nonlinear clustering. In: Astrophysical Journal. 1999 ; Vol. 527, No. 1 PART 1. pp. 1-15.
    @article{94ca0956910c400a9b27801dc9d1f24e,
    title = "Power spectrum correlations induced by nonlinear clustering",
    abstract = "Gravitational clustering is an intrinsically nonlinear process that generates significant non-Gaussian signatures in the density field. We consider how these affect power spectrum determinations from galaxy and weak-lensing surveys. Non-Gaussian effects not only increase the individual error bars compared to the Gaussian case but, most importantly, lead to nontrivial cross-correlations between different band powers, correlating small-scale band powers both among themselves and with those at large scales. We calculate the power-spectrum covariance matrix in nonlinear perturbation theory (weakly nonlinear regime), in the hierarchical model (strongly nonlinear regime), and from numerical simulations in real and redshift space. In particular, we show that the hierarchical Ansatz cannot be strictly valid for the configurations of the trispectrum involved in the calculation of the power-spectrum covariance matrix. We discuss the impact of these results on parameter estimation from power-spectrum measurements and their dependence on the size of the survey and the choice of band powers. We show that the non-Gaussian terms in the covariance matrix become dominant for scales smaller than the nonlinear scale knl ∼ 0.2 h-1 Mpc-1, depending somewhat on power normalization. Furthermore, we find that cross-correlations mostly deteriorate the determination of the amplitude of a rescaled power spectrum, whereas its shape is less affected. In weak lensing surveys the projection tends to reduce the importance of non-Gaussian effects. Even so, for background galaxies at redshift z ∼ 1, the non-Gaussian contribution rises significantly around l ∼ 1000 and could become comparable to the Gaussian terms depending upon the power spectrum normalization and cosmology. The projection has another interesting effect: the ratio between non-Gaussian and Gaussian contributions saturates and can even decrease at small enough angular scales if the power spectrum of the three-dimensional field falls faster than k-2.",
    keywords = "Galaxies: clusters: general, Large-scale structure of universe, Methods: numerical, Methods: statistical",
    author = "Rom{\'a}n Scoccimarro and Matias Zaldarriaga and Lam Hui",
    year = "1999",
    month = "12",
    day = "10",
    language = "English (US)",
    volume = "527",
    pages = "1--15",
    journal = "Astrophysical Journal",
    issn = "0004-637X",
    publisher = "IOP Publishing Ltd.",
    number = "1 PART 1",

    }

    TY - JOUR

    T1 - Power spectrum correlations induced by nonlinear clustering

    AU - Scoccimarro, Román

    AU - Zaldarriaga, Matias

    AU - Hui, Lam

    PY - 1999/12/10

    Y1 - 1999/12/10

    N2 - Gravitational clustering is an intrinsically nonlinear process that generates significant non-Gaussian signatures in the density field. We consider how these affect power spectrum determinations from galaxy and weak-lensing surveys. Non-Gaussian effects not only increase the individual error bars compared to the Gaussian case but, most importantly, lead to nontrivial cross-correlations between different band powers, correlating small-scale band powers both among themselves and with those at large scales. We calculate the power-spectrum covariance matrix in nonlinear perturbation theory (weakly nonlinear regime), in the hierarchical model (strongly nonlinear regime), and from numerical simulations in real and redshift space. In particular, we show that the hierarchical Ansatz cannot be strictly valid for the configurations of the trispectrum involved in the calculation of the power-spectrum covariance matrix. We discuss the impact of these results on parameter estimation from power-spectrum measurements and their dependence on the size of the survey and the choice of band powers. We show that the non-Gaussian terms in the covariance matrix become dominant for scales smaller than the nonlinear scale knl ∼ 0.2 h-1 Mpc-1, depending somewhat on power normalization. Furthermore, we find that cross-correlations mostly deteriorate the determination of the amplitude of a rescaled power spectrum, whereas its shape is less affected. In weak lensing surveys the projection tends to reduce the importance of non-Gaussian effects. Even so, for background galaxies at redshift z ∼ 1, the non-Gaussian contribution rises significantly around l ∼ 1000 and could become comparable to the Gaussian terms depending upon the power spectrum normalization and cosmology. The projection has another interesting effect: the ratio between non-Gaussian and Gaussian contributions saturates and can even decrease at small enough angular scales if the power spectrum of the three-dimensional field falls faster than k-2.

    AB - Gravitational clustering is an intrinsically nonlinear process that generates significant non-Gaussian signatures in the density field. We consider how these affect power spectrum determinations from galaxy and weak-lensing surveys. Non-Gaussian effects not only increase the individual error bars compared to the Gaussian case but, most importantly, lead to nontrivial cross-correlations between different band powers, correlating small-scale band powers both among themselves and with those at large scales. We calculate the power-spectrum covariance matrix in nonlinear perturbation theory (weakly nonlinear regime), in the hierarchical model (strongly nonlinear regime), and from numerical simulations in real and redshift space. In particular, we show that the hierarchical Ansatz cannot be strictly valid for the configurations of the trispectrum involved in the calculation of the power-spectrum covariance matrix. We discuss the impact of these results on parameter estimation from power-spectrum measurements and their dependence on the size of the survey and the choice of band powers. We show that the non-Gaussian terms in the covariance matrix become dominant for scales smaller than the nonlinear scale knl ∼ 0.2 h-1 Mpc-1, depending somewhat on power normalization. Furthermore, we find that cross-correlations mostly deteriorate the determination of the amplitude of a rescaled power spectrum, whereas its shape is less affected. In weak lensing surveys the projection tends to reduce the importance of non-Gaussian effects. Even so, for background galaxies at redshift z ∼ 1, the non-Gaussian contribution rises significantly around l ∼ 1000 and could become comparable to the Gaussian terms depending upon the power spectrum normalization and cosmology. The projection has another interesting effect: the ratio between non-Gaussian and Gaussian contributions saturates and can even decrease at small enough angular scales if the power spectrum of the three-dimensional field falls faster than k-2.

    KW - Galaxies: clusters: general

    KW - Large-scale structure of universe

    KW - Methods: numerical

    KW - Methods: statistical

    UR - http://www.scopus.com/inward/record.url?scp=0002006966&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=0002006966&partnerID=8YFLogxK

    M3 - Article

    AN - SCOPUS:0002006966

    VL - 527

    SP - 1

    EP - 15

    JO - Astrophysical Journal

    JF - Astrophysical Journal

    SN - 0004-637X

    IS - 1 PART 1

    ER -