Local Group velocity versus gravity: the coherence function

In maximum-likelihood analyses of the Local Group (LG) acceleration, the object describing non-linear 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 Ω_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 σ ₈ of the underlying density field. A perturbative approximation for the function turns out to be accurate as long as σ ₈ is smaller than about 0.3. For higher normalizations we provide an analytical fit for the CF as a function of σ 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.