Precision Analysis of the Local Group Acceleration

We reexamine likelihood analyses of the Local Group (LG) acceleration, paying particular attention to nonlinear effects. Under the approximation that the joint distribution of the LG acceleration and velocity is Gaussian, two quantities describing nonlinear effects enter these analyses. The first one is the coherence function, i.e. the cross-correlation coefficient of the Fourier modes of gravity and velocity fields. The second one is the ratio of velocity power spectrum to gravity power spectrum. To date, in all analyses of the LG acceleration the second quantity was not accounted for. Extending our previous work, we study both the coherence function and the ratio of the power spectra. With the aid of numerical simulations we obtain expressions for the two as functions of wavevector and sigma_8. Adopting WMAP's best determination of sigma_8, we estimate the most likely value of the parameter beta and its errors. As the observed values of the LG velocity and gravity, we adopt respectively a CMB-based estimate of the LG velocity, and Schmoldt et al.'s (1999) estimate of the LG acceleration from the PSCz catalog. We obtain beta = 0.66^{+0.21}_{-0.07}; thus our errorbars are significantly smaller than those of Schmoldt et al. This is not surprising, because the coherence function they used greatly overestimates actual decoherence between nonlinear gravity and velocity.