Local group velocity versus gravity: Nonlinear effects

We use numerical simulations to study the relation between the velocity of the Local Group (LG) and its gravitational acceleration. This relation serves as a test for the kinematic origin of the CMB dipole and as a method for estimating ß= Ω^0.6/b. We calculate the misalignment angle between the two vectors and compare it to the observed value for the PSCz survey. The latter value is beyond the upper limit of the 90% confidence interval for the angle; therefore, the nonlinear effects are unlikely to be responsible for the whole observed misalignment. We also study the relation between the amplitudes of the LG velocity and gravity vectors. In an Ω = 1 Universe, the smoothed gravity of the LG turns out to be a biased low estimator of the LG (unsmoothed) velocity. In an Ω = 0.3 Universe, the estimator is biased high. The discussed biases are, however, only a few per cent, thus the linear theory works to good accuracy. The gravity-based estimator of the LG velocity has also a scatter that limits the precision of the estimate of β in the LG velocity-gravity comparisons. The random error of β due to nonlinear effects amounts to several per cent.