  In maximum-likelihood analyses of the Local Group (LG) acceleration, the
object describing nonlinear effects is the coherence function (CF), i.e. the
cross-correlation coefficient of the Fourier modes of the velocity and gravity
fields. We study the CF both analytically, using perturbation theory, and
numerically, using a hydrodynamic code. The dependence of the function on
Omega_m and the shape of the power spectrum is very weak. The only cosmological
parameter that the CF is strongly sensitive to is the normalization sigma_8 of
the underlying density field. Perturbative approximation for the function turns
out to be accurate as long as sigma_8 is smaller than about 0.3. For higher
normalizations we provide an analytical fit for the CF as a function of sigma_8
and the wavevector. The characteristic decoherence scale which our formula
predicts is an order of magnitude smaller than that determined by Strauss et
al. This implies that present likelihood constraints on cosmological parameters
from analyses of the LG acceleration are significantly tighter than hitherto
reported.
