We present a self-consistent non-parametric model of the local cosmic velocity field derived from the distribution of IRAS galaxies in the PSCz redshift survey. The survey has been analysed using two independent methods, both based on the assumptions of gravitational instability and linear biasing. The two methods, which give very similar results, have been tested and calibrated on mock PSCz catalogues constructed from cosmological N-body simulations. The denser sampling provided by the PSCz survey compared with previous IRAS galaxy surveys allows an improved reconstruction of the density and velocity fields out to large distances. The most striking feature of the model velocity field is a coherent large-scale streaming motion along the baseline connecting Perseus-Pisces, the Local Supercluster, the Great Attractor and the Shapley Concentration. We find no evidence for back-infall on to the Great Attractor. Instead, material behind and around the Great Attractor is inferred to be streaming towards the Shapley Concentration, aided by the compressional push of two large nearby underdensities. The PSCz model velocities compare well with those predicted from the 1.2-Jy redshift survey of IRAS galaxies and, perhaps surprisingly, with those predicted from the distribution of Abell/ACO clusters, out to 140h(-1)Mpc. Comparison of the real-space density fields (or, alternatively, the peculiar velocity fields) inferred from the PSCz and cluster catalogues gives a relative (linear) bias parameter between clusters and IRAS galaxies of b(c) = 4.4 +/- 0.6. Finally, we implement a likelihood analysis that uses all the available information on peculiar velocities in our local Universe to estimate beta = Omega(0)(0.6)/b = 0.6(-0.15)(+0.22) (1 sigma), where b is the bias parameter for IRAS galaxies

We compute the acceleration of the Local Group using 11 206 IRAS galaxies from the recently completed all-sky PSCz redshift survey. Measuring the acceleration vector in redshift space generates systematic uncertainties caused by the redshift-space distortions in the density field. We therefore assign galaxies to their real-space positions by adopting a non-parametric model for the velocity field that relies solely on the linear gravitational instability (GI) and linear biasing hypotheses. Remaining systematic contributions to the measured acceleration vector are corrected for by using PSCz mock catalogues from N-body experiments. The resulting acceleration vector points similar to 15 degrees away from the CMB dipole apex, with a remarkable alignment between small- and large-scale contributions. A considerable fraction (similar to 65 per cent) of the measured acceleration is generated within 40 h(-1) Mpc, with a nonnegligible contribution from scales between 90 and 140 h(-1) Mpc, after which the acceleration amplitude seems to have converged. The local group acceleration from 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 linear biasing relation on large scales. A maximum-likelihood analysis of the cumulative PSCz dipole is performed within 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 = Omega(0.6)/b parameter and the power spectrum of density fluctuations. We obtain 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 spectrum, because of the rise in the amplitude of the dipole beyond 40 h(-1) Mpc and the increase in shot noise on large scales. There is, however, a weak indication that within the framework of cold dark matter (CDM) models the observed Local Group acceleration implies some excess power on large scales

We present a version of the Fourier-Bessel method Ðrst introduced by Fisher and coworkers and Zaroubi and coworkers with two extensions : (1) we amend the formalism to allow a generic galaxy weight that can be constant, rather than the more conventional overweighting of galaxies at high distances, and (2) we correct for the masked zones by extrapolation of Fourier-Bessel modes rather than by cloning from the galaxy distribution in neighboring regions. We test the procedure extensively on N-body simulations and Ðnd that it gives generally unbiased results but that the reconstructed velocities tend to be overpredicted in high-density regions. Applying the formalism to the PSCz redshift catalog, we Ðnd that b \ 0.7 ^0.5 from a comparison of the reconstructed Local Group velocity to the cosmic microwave background dipole. From an anisotropy test of the velocity Ðeld, we Ðnd that b \ 1 cold dark matter models normalized to the current cluster abundance can be excluded with 90% conÐdence. The density and velocity Ðelds reconstructed agree with the Ðelds found by Branchini and coworkers on most points. We Ðnd a back infall into the Great Attractor region (Hydra-Centaurus region), but tests suggest that this may be an artifact. We identify all the major clusters in our density Ðeld and conÐrm the existence of some previously identiÐed possible ones.

In 1989, Peebles showed that in the gravitational instability picture galaxy orbits can be traced back in time from a knowledge of their current positions, via a variational principle. We modify this variational principle so that galaxy redshifts can be input instead of distances, thereby recovering the distances. As a test problem, we apply the new method to a Local Group model. We infer M \ (4È8) ] 1012 depending on cosmology, implying that the dynamics of the outlying Local Group dwarfs are M _ consistent with the timing argument. Some algorithmic issues need to be addressed before the method can be applied to recover nonlinear evolution from large redshift surveys, but there are no more difficulties in principle.