We report the final redshift release of the 6dF Galaxy Survey (6dFGS), a combined redshift and peculiar velocity survey over the southern sky (|b| > 10°). Its 136 304 spectra have yielded 110 256 new extragalactic redshifts and a new catalogue of 125 071 galaxies making near‐complete samples with (K, H, J, rF, bJ) ≤ (12.65, 12.95, 13.75, 15.60, 16.75). The median redshift of the survey is 0.053. Survey data, including images, spectra, photometry and redshifts, are available through an online data base. We describe changes to the information in the data base since earlier interim data releases. Future releases will include velocity dispersions, distances and peculiar velocities for the brightest early‐type galaxies, comprising about 10 per cent of the sample. Here we provide redshift maps of the southern local Universe with z≤ 0.1, showing nearby large‐scale structures in hitherto unseen detail. A number of regions known previously to have a paucity of galaxies are confirmed as significantly underdense regions. The URL of the 6dFGS data base is http://www-wfau.roe.ac.uk/6dFGS.

We study velocity moments of elliptical galaxies in the Coma cluster using Jeans equations. The dark matter distribution in the cluster is modelled by a generalized formula based upon the results of cosmological N‐body simulations. Its inner slope (cuspy or flat), concentration and mass within the virial radius are kept as free parameters, as well as the velocity anisotropy, assumed independent of position. We show that the study of line‐of‐sight velocity dispersion alone does not allow us to constrain the parameters. By a joint analysis of the observed profiles of velocity dispersion and kurtosis, we are able to break the degeneracy between the mass distribution and velocity anisotropy. We determine the dark matter distribution at radial distances larger than 3 per cent of the virial radius and we find that the galaxy orbits are close to isotropic. Due to limited resolution, different inner slopes are found to be consistent with the data and we observe a strong degeneracy between the inner slope α and concentration c; the best‐fitting profiles have the two parameters related with c= 19−9.6α. Our best‐fitting Navarro–Frenk–White profile has concentration c= 9, which is 50 per cent higher than standard values found in cosmological simulations for objects of similar mass. The total mass within the virial radius of 2.9h−170 Mpc is 1.4 × 1015h−170 M⊙ (with 30 per cent accuracy), 85 per cent of which is dark. At this distance from the cluster centre, the mass‐to‐light ratio in the blue band is 351h70 solar units. The total mass within the virial radius leads to estimates of the density parameter of the Universe, assuming that clusters trace the mass‐to‐light ratio and baryonic fraction of the Universe, with Ω0= 0.29 ± 0.1.

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Using the standard dynamical theory of spherical systems, we calculate the properties of spherical galaxies and clusters whose density profiles obey the universal form first obtained in high‐resolution cosmological N‐body simulations by Navarro, Frenk & White (NFW). We adopt three models for the internal kinematics: isotropic velocities, constant anisotropy and increasingly radial Osipkov–Merritt anisotropy. Analytical solutions are found for the radial dependence of the mass, gravitational potential, velocity dispersion, energy and virial ratio and we test their variability with the concentration parameter describing the density profile and amount of velocity anisotropy. We also compute structural parameters, such as half‐mass radius, effective radius and various measures of concentration. Finally, we derive projected quantities, the surface mass density and line‐of‐sight as well as aperture‐velocity dispersion, all of which can be directly applied in observational tests of current scenarios of structure formation. On the mass scales of galaxies, if constant mass‐to‐light is assumed, the NFW surface density profile is found to fit Hubble–Reynolds laws well. It is also well fitted by Sérsic R1/m laws, for but in a much narrower range of m and with much larger effective radii than are observed. Assuming in turn reasonable values of the effective radius, the mass density profiles imply a mass‐to‐light ratio that increases outwards at all radii.

Elliptical galaxies are modelled with a four‐component model: Sérsic stars, Λ‐cold dark matter (ΛCDM), a β‐model for the hot gas and a central black hole, with the aim of establishing how accurately can one measure the total mass within their virial radii. Dark matter (DM) is negligible in the inner regions, which are dominated by stars and the central black hole. This prevents any kinematic estimate (using a Jeans analysis) of the inner slope of the DM density profile. The gas fraction rises, but the baryon fraction decreases with radius, at least out to 10 effective radii (Re). Even with line‐of‐sight velocity dispersion (VD) measurements at 4 or 5Re with 20 km s−1 accuracy and perfectly known velocity anisotropy, the total mass within the virial radius (rv≡r200) is uncertain by a factor of over 3. The DM distributions found in ΛCDM simulations appear inconsistent with the low VDs measured by Romanowsky et al. of planetary nebulae between 2 and 5Re. Some of Romanowsky et al.'s orbital solutions for NGC 3379 imply a dark matter content at least as large as cosmologically predicted, and the lower M/L values of most of their solutions lead to a baryonic fraction within rv that is larger than the universal value. Replacing the Navarro–Frenk–White (NFW) DM model by the new model of Navarro et al. decreases the VD slightly at a given radius. So, given the observed VD measured at 5Re, the inferred M/L within rv is 40 per cent larger than that predicted by the NFW model. Folding in the slight (strong) radial anisotropy found in ΛCDM (merger) simulations, which is well modelled (much better than with the Osipkov–Merritt formula) with , the inferred M/L within rv is 1.6 (2.4) times higher than for the isotropic NFW model. Thus, the DM model and radial anisotropy can partly explain the low planetary nebula VDs, but not in full. The logarithmic slope of the VD at radii of 1–5Re, which is insensitive to radius, is another measure of the DM mass within the virial radius, but it is similarly affected by the a priori unknown DM mass profile and stellar velocity anisotropy. In an , single integral expressions are derived for the VDs in terms of general radial profiles for the tracer density and total mass, for various anisotropic models (general constant anisotropy, radial, Osipkov–Merritt and the model above).

Mass modelling of spherical systems through internal kinematics is hampered by the mass / velocity anisotropy degeneracy inherent in the Jeans equation, as well as the lack of techniques that are both fast and adaptable to realistic systems. A new fast method, called MAM-POSSt, is developed and thoroughly tested. MAMPOSSt performs a maximum likelihood fit of the distribution of observed tracers in projected phase space (projected radius and lineof-sight velocity). As in other methods, MAMPOSSt assumes a shape for the gravitational potential (or equivalently the total mass profile). However, instead of postulating a shape for the distribution function in terms of energy and angular momentum, or supposing Gaussian line-of-sight velocity distributions, MAMPOSSt assumes a velocity anisotropy profile and a shape for the three-dimensional velocity distribution. The formalism is presented for the case of a Gaussian 3D velocity distribution. In contrast to most methods based on moments, MAMPOSSt requires no binning, differentiation, nor extrapolation of the observables. Tests on cluster-mass haloes from ΛCDM dissipationless cosmological simulations indicate that, with 500 tracers, MAMPOSSt is able to jointly recover the virial radius, tracer scale radius, dark matter scale radius and outer or constant velocity anisotropy with small bias (<10% on scale radii and <2% on the two other quantities) and inefficiencies of 10%, 27%, 48% and 20%, respectively. MAMPOSSt does not perform better when some parameters are frozen, and even particularly worse when the virial radius is set to its true value, which appears to be the consequence of halo triaxiality. The accuracy of MAMPOSSt depends weakly on the adopted interloper removal scheme, including an efficient iterative Bayesian scheme that we introduce here, which can directly obtain the virial radius with as good precision as MAM-POSSt. Additional tests are made on the number of tracers, the stacking of haloes, the chosen aperture, and the density and velocity anisotropy models. Our tests show that MAMPOSSt with Gaussian 3D velocities is very competitive with other methods that are either currently restricted to constant velocity anisotropy or 3 orders of magnitude slower. These tests suggest that MAMPOSSt can be a very powerful and rapid method for the mass and anisotropy modeling of systems such as clusters and groups of galaxies, elliptical and dwarf spheroidal galaxies.

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Understanding galaxy formation is one of the most pressing issues in cosmology. We review the current status of galaxy formation from both an observational and a theoretical perspective, and summarize the prospects for future advances.