Local Gravity versus Local Velocity: Solutions for $\beta$ and nonlinear
  bias
  (abridged) 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 redshift survey (2MRS), yields a prediction of the flows given the
cosmological density parameter, $\Omega$, 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. Our analysis completely avoids the strong error
covariance in the smoothed TF velocities by the use of orthonormal basis
functions and employs elaborate realistic 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, $\propto L^\alpha$, galaxy weighting. We assess
the agreement between the fields as a function of $\alpha$ and
$\beta=f(\Omega)/b$, 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% and 95.4% confidence levels (CLs). For $\beta=0.33$,
we get $\alpha<0.25$ and $\alpha<0.5$, respectively, at the 68.3% and 95.4%
CLs. We set a constraint on the fluctuation normalization, finding $\sigma_8 =
0.73 \pm 0.1$, in very good agreement with the latest WMAP results.
