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 .