Likelihood analysis of the Local Group acceleration

We compute the acceleration of the Local Group using 11 206 IRAS galaxies f rom the recently completed all-sky PSCz redshift survey. Measuring the acce leration vector in redshift space generates systematic uncertainties caused by the redshift-space distortions in the density field. We therefore assig n galaxies to their real-space positions by adopting a non-parametric model for the velocity field that relies solely on the linear gravitational inst ability (GI) and linear biasing hypotheses. Remaining systematic contributi ons to the measured acceleration vector are corrected for by using PSCz moc k catalogues from N-body experiments. The resulting acceleration vector points similar to 15 degrees away from th e CMB dipole apex, with a remarkable alignment between small- and large-sca le contributions. A considerable fraction (similar to 65 per cent) of the m easured acceleration is generated within 40 h(-1) Mpc, with a nonnegligible contribution from scales between 90 and 140 h(-1) Mpc, after which the acc eleration amplitude seems to have converged. The local group acceleration f rom PSCz appears to be consistent with the one determined from the IRAS 1.2 -Jy galaxy catalogue once the different contributions from shot noise have been taken into account. The results are consistent with the gravitational instability hypothesis and do not indicate any strong deviations from the l inear biasing relation on large scales. A maximum-likelihood analysis of the cumulative PSCz dipole is performed wi thin a radius of 150 h(-1) Mpc, in which we account for non-linear effects, shot noise and finite sample size. The aim is to constrain the beta = Omeg a(0.6)/b parameter and the power spectrum of density fluctuations. We obtai n beta = 0.70(-0.2)(+0.35) at 1 sigma confidence level. The likelihood analysis is not very sensitive to the shape of the power spe ctrum, because of the rise in the amplitude of the dipole beyond 40 h(-1) M pc and the increase in shot noise on large scales. There is, however, a wea k indication that within the framework of cold dark matter (CDM) models the observed Local Group acceleration implies some excess power on large scale s.