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

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, , 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, proportional to L alpha, galaxy weighting. We assess the agreement between the fields as a function of alpha and beta = f()/b, where f is the growth factor of linear perturbations. The agreement is excellent with a reasonable chi 2 per degree of freedom. For alpha = 0, we derive 0.28 < beta < 0.37 and 0.24 < beta < 0.43, respectively, at the 68.3 per cent and 95.4 per cent confidence levels (CLs). For beta = 0.33, we get alpha < 0.25 and alpha < 0.5, respectively, at the 68.3 per cent and 95.4 per cent CLs. We set a constraint on the fluctuation normalization, finding Sigma(8) = 0.66 +/- 0.10, which is only 1.5 Sigma deviant from Wilkinson Microwave Anisotropy Probe (WMAP) results. It is remarkable that Sigma(8) 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.