Journal Article

Local gravity versus local velocity: solutions for β and non-linear bias

Marc Davis, Adi Nusser, Karen L. Masters, Christopher Springob, John P. Huchra and Gerard Lemson

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 413, issue 4, pages 2906-2922
Published in print June 2011 | ISSN: 0035-8711
Published online May 2011 | e-ISSN: 1365-2966 | DOI: http://dx.doi.org/10.1111/j.1365-2966.2011.18362.x
Local gravity versus local velocity: solutions for β and non-linear bias

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We perform a reconstruction of the cosmological large-scale flows in the nearby Universe using two complementary observational sets. The first, the SFI++ sample of Tully–Fisher (TF) measurements of galaxies, provides a direct probe of the flows. The second, the whole sky distribution of galaxies in the 2MASS (Two Micron All Sky Survey) redshift survey (2MRS), yields a prediction of the flows given the cosmological density parameter, Ω, and a biasing relation between mass and galaxies. We aim at an unbiased comparison between the peculiar velocity fields extracted from the two data sets and its implication on the cosmological parameters and the biasing relation. We expand the fields in a set of orthonormal basis functions, each representing a plausible realization of a cosmological velocity field smoothed in such a way as to give a nearly constant error on the derived SFI++ velocities. The statistical analysis is done on the coefficients of the modal expansion of the fields by means of the basis functions. Our analysis completely avoids the strong error covariance in the smoothed TF velocities by the use of orthonormal basis functions and employs elaborate mock data sets to extensively calibrate the errors in 2MRS predicted velocities. We relate the 2MRS galaxy distribution to the mass density field by a linear bias factor, b, and include a luminosity-dependent, ∝Lα, galaxy weighting. We assess the agreement between the fields as a function of α and β=f(Ω)/b, where f is the growth factor of linear perturbations. The agreement is excellent with a reasonable χ2 per degree of freedom. For α= 0, we derive 0.28 < β < 0.37 and 0.24 < β < 0.43, respectively, at the 68.3 per cent and 95.4 per cent confidence levels (CLs). For β= 0.33, we get α < 0.25 and α < 0.5, respectively, at the 68.3 per cent and 95.4 per cent CLs. We set a constraint on the fluctuation normalization, finding σ8= 0.66 ± 0.10, which is only 1.5σ deviant from Wilkinson Microwave Anisotropy Probe (WMAP) results. It is remarkable that σ8 determined from this local cosmological test is close to the value derived from the cosmic microwave background, an indication of the precision of the standard model.

Keywords: cosmological parameters; dark matter; large-scale structure of Universe

Journal Article.  12964 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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