The galaxy density field as extracted from the IRAS 1.2 Jy redshift survey is compared to the mass density field as reconstructed by the POTENT method from the Mark III catalog of peculiar velocities. The reconstruction is done with Gaussian smoothing of radius 12 h −1 Mpc, and the comparison is carried out within volumes of effective radii 31−46 h −1 Mpc, containing ≈ 10−26 independent samples. Random and systematic errors are estimated from multiple realizations of mock catalogs drawn from a simulation that mimics the observed density field in the local universe. The relationship between the two density fields is found to be consistent with gravitational instability theory in the mildly nonlinear regime and a linear biasing relation between galaxies and mass. We measure β I ≡ Ω 0.6 /b I = 0.89 ± 0.12 within a volume of effective radius 40 h −1 Mpc, where b I is the IRAS galaxy biasing parameter at 12 h −1 Mpc. This result is only weakly dependent on the comparison volume, suggesting that cosmic scatter is no greater than ±0.1. These data are thus consistent with Ω = 1 and b I ≃ 1. If b I > 0.75, as theoretical models of biasing indicate, then Ω > 0.33 at 95% confidence. A comparison with other estimates of β I suggests scale-dependence in the biasing relation for IRAS galaxies.

A B S T R A C TWe simulate the formation and evolution of the local galaxy population, starting from initial conditions with a smoothed linear density field which matches that derived from the IRAS 1.2-Jy galaxy survey. Our simulations track the formation and evolution of all dark matter haloes more massive than 10 11 M ( out to a distance of 8000 km s 21 from the Milky Way. We implement prescriptions similar to those of Kauffmann et al. to follow the assembly and evolution of the galaxies within these haloes. We focus on two variants of the CDM cosmology: a LCDM model and a tCDM model. Galaxy formation in each is adjusted to reproduce the I-band Tully-Fisher relation of Giovanelli et al. We compare the present-day luminosity functions, colours, morphology and spatial distribution of our simulated galaxies with those of the real local population, in particular with the Updated Zwicky Catalog, with the IRAS PSCz redshift survey, and with individual local clusters such as Coma, Virgo and Perseus. We also use the simulations to study the clustering bias between the dark matter and galaxies of differing type. Although some significant discrepancies remain, our simulations recover the observed intrinsic properties and the observed spatial distribution of local galaxies reasonably well. They can thus be used to calibrate methods which use the observed local galaxy population to estimate the cosmic density parameter or to draw conclusions about the mechanisms of galaxy formation. To facilitate such work, we publicly release our z ¼ 0 galaxy catalogues, together with the underlying mass distribution.

We present an improved POTENT method for reconstructing the velocity and mass density fields from radial peculiar velocities, test it with mock catalogs, and apply it to the Mark III Catalog. Method improvments: (a) inhomogeneous Malmquist bias is reduced by grouping and corrected in forward or inverse analyses of inferred distances, (b) the smoothing into a radial velocity field is optimized to reduce window and sampling biases, (c) the density is derived from the velocity using an improved nonlinear approximation, and (d) the computational errors are made negligible. The method is tested and optimized using mock catalogs based on an N-body simulation that mimics our cosmological neighborhood, and the remaining errors are evaluated quantitatively. The Mark III catalog, with ~3300 grouped galaxies, allows a reliable reconstruction with fixed Gaussian smoothing of 10-12 Mpc/h out to ~60 Mpc/h. We present maps of the 3D velocity and mass-density fields and the corresponding errors. The typical systematic and random errors in the density fluctuations inside 40 Mpc/h are \pm 0.13 and \pm 0.18. The recovered mass distribution resembles in its gross features the galaxy distribution in redshift surveys and the mass distribution in a similar POTENT analysis of a complementary velocity catalog (SFI), including the Great Attractor, Perseus-Pisces, and the void in between. The reconstruction inside ~40 Mpc/h is not affected much by a revised calibration of the distance indicators (VM2, tailored to match the velocities from the IRAS 1.2Jy redshift survey). The bulk velocity within the sphere of radius 50 Mpc/h about the Local Group is V_50=370 \pm 110 km/s (including systematic errors), and is shown to be mostly generated by external mass fluctuations. With the VM2 calibration, V_50 is reduced to 305 \pm 110 km/s.Comment: 60 pages, LaTeX, 3 tables and 27 figures incorporated (may print the most crucial figures only, by commenting out one line in the LaTex source

We estimate the power spectrum of mass density fluctuations from peculiar velocities of galaxies by applying an improved maximum-likelihood technique to the new all-sky SFI catalog. Parametric models are used for the power spectrum and the errors, and the free parameters are determined by assuming Gaussian velocity fields and errors and maximizing the probability of the data given the model. It has been applied to generalized CDM models with and without COBE normalization. The method has been carefully tested using artificial SFI catalogs. The most likely distance errors are found to be similar to the original error estimates in the SFI data. The general result that is not very sensitive to the prior model used is a relatively high amplitude of the power spectrum. For example, at k = 0.1 h Mpc −1 we find P (k)Ω 1.2 = (4.4±1.7)×10 3 (h −1 Mpc) 3 . An integral over the power spectrum yields σ 8 Ω 0.6 = 0.82 ± 0.12. Model-dependent constraints

We present extensive tests of the fast action method (FAM) for recovering the past orbits of mass tracers in an expanding universe from their redshift-space coordinates at the present epoch. The tests focus on the reconstruction of present-day peculiar velocities using mock catalogues extracted from high-resolution N-body simulations. The method allows for a self-consistent treatment of redshift-space distortions by direct minimization of a modified action for a cosmological gravitating system. When applied to ideal, volume-limited catalogues, FAM recovers unbiased peculiar velocities with a one-dimensional, 1sigma error of similar to220 km s(-1), if velocities are smoothed on a scale of 5 h(-1) Mpc. Alternatively, when no smoothing is applied, FAM predicts nearly unbiased velocities for objects residing outside the highest density regions. In this second case the 1sigma error decreases to a level of similar to150 km s(-1). The correlation properties of the peculiar velocity fields are also correctly recovered on scales larger than 5 h(-1) Mpc. Similar results are obtained when FAM is applied to flux-limited catalogues mimicking the IRAS PSCz survey. In this case FAM reconstructs peculiar velocities with similar intrinsic random errors, while velocity-velocity correlation properties are well reproduced beyond scales of similar to8 h(-1) Mpc. We also show that FAM provides better velocity predictions than other, competing methods based on linear theory or the Zel'dovich approximation. These results indicate that FAM can be successfully applied to presently available galaxy redshift surveys such as IRAS PSCz