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

Abstract

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.

Cosmological parameters from the comparison of peculiar velocities with predictions from the 2M++ density field

“…After constructing β dependent predictions of peculiar velocities, Branchini et al (2012) in turn estimate β by minimizing the scatter of predicted 2MASS absolute magnitudes about a universal luminosity function and find β = 0.323 ± 0.083. Davis et al (2011) expand the velocity field in spherical harmonics and fit the inverse TF relation to SFI++ finding β = 0.33 ± 0.04. The TF data span a range of distances, and because the effective bias changes with distance it is difficult to compare this directly with our number-weighted result β * = 0.44 ± 0.02.…”

“…As noted by Davis et al (2011), the SFI++ TF relation has a kink in the faint end (M > −20), and an asymmetric distribution of outliers about the expected velocity width parameter η ≡ log(W ) − 2.5 (Springob et al 2007). As we will be fitting for the inverse TF relation, we will account for the outliers and deviation from linearity of the relation by excluding galaxies with redshift-distance magnitudes fainter than -20.…”

“…By measuring σ8,g directly from the redshift data, one can eliminate b and constrain the degenerate cosmological parameter combination f σ8 = βσ8,g. Using this method of velocity-velocity comparison, a number of recent studies have constrained this parameter combination (Pike & Hudson 2005;Davis et al 2011;Branchini et al 2012;Turnbull et al 2012).…”

The linear growth of structure in theRh=ctuniverse

“…Over the past several decades, f (z) has been measured using a range of techniques and surveys, including 2dFGRS (Peacock et al 2001), VVDS (Guzzo et al 2008), quasar clustering and Ly α clustering (Ross et al 2007;da Angela et al 2008;Viel et al 2004), and in peculiar velocity surveys at z ∼ 0 (Davis et al 2011;Hudson et al 2012). For example, growth rate measurements may be made using the galaxy two-point correlation function, which yields a value of the parameter β ≡ f /b.…”

“…of the changing growth rate as the Universe evolves (Peacock et al 2001;Viel et al 2004;Jain and Zhang 2007;Ross et al 2007;da Angela et al 2008;Guzzo et al 2008;Song and Koyama 2009;Song and Percival 2009;Davis et al 2011;Hudson and Turnbull 2012;Macaulay et al 2013;Alam et al 2016).…”