A wealth of astronomical data indicate the presence of mass discrepancies in the Universe. The motions observed in a variety of classes of extragalactic systems exceed what can be explained by the mass visible in stars and gas. Either (i) there is a vast amount of unseen mass in some novel form — dark matter — or (ii) the data indicate a breakdown of our understanding of dynamics on the relevant scales, or (iii) both. Here, we first review a few outstanding challenges for the dark matter interpretation of mass discrepancies in galaxies, purely based on observations and independently of any alternative theoretical framework. We then show that many of these puzzling observations are predicted by one single relation — Milgrom’s law — involving an acceleration constant a0 (or a characteristic surface density Σ† = a0/G) on the order of the square-root of the cosmological constant in natural units. This relation can at present most easily be interpreted as the effect of a single universal force law resulting from a modification of Newtonian dynamics (MOND) on galactic scales. We exhaustively review the current observational successes and problems of this alternative paradigm at all astrophysical scales, and summarize the various theoretical attempts (TeVeS, GEA, BIMOND, and others) made to effectively embed this modification of Newtonian dynamics within a relativistic theory of gravity.

The availability of the Hipparcos Catalogue triggered many kinematic and dynamical studies of the solar neighbourhood. Nevertheless, those studies generally lacked the third component of the space velocities, i.e., the radial velocities. This work presents the kinematic analysis of 5952 K and 739 M giants in the solar neighbourhood which includes for the first time radial velocity data from a large survey performed with the CORAVEL spectrovelocimeter. It also uses proper motions from the Tycho-2 catalogue, which are expected to be more accurate than the Hipparcos ones. An important by-product of this study is the observed fraction of only 5.7% of spectroscopic binaries among M giants as compared to 13.7% for K giants. After excluding the binaries for which no center-of-mass velocity could be estimated, 5311 K and 719 M giants remain in the final sample. The UV-plane constructed from these data for the stars with precise parallaxes (σ π /π ≤ 20%) reveals a rich small-scale structure, with several clumps corresponding to the Hercules stream, the Sirius moving group, and the Hyades and Pleiades superclusters. A maximum-likelihood method, based on a bayesian approach, has been applied to the data, in order to make full use of all the available stars (not only those with precise parallaxes) and to derive the kinematic properties of these subgroups. Isochrones in the Hertzsprung-Russell diagram reveal a very wide range of ages for stars belonging to these groups. These groups are most probably related to the dynamical perturbation by transient spiral waves (as recently modelled by De Simone et al. 2004) rather than to cluster remnants. A possible explanation for the presence of young group/clusters in the same area of the UV-plane is that they have been put there by the spiral wave associated with their formation, while the kinematics of the older stars of our sample has also been disturbed by the same wave. The emerging picture is thus one of dynamical streams pervading the solar neighbourhood and travelling in the Galaxy with similar space velocities. The term dynamical stream is more appropriate than the traditional term supercluster since it involves stars of different ages, not born at the same place nor at the same time. The position of those streams in the UV-plane is responsible for the vertex deviation of 16.2 • ± 5.6 • for the whole sample. Our study suggests that the vertex deviation for younger populations could in fact have the same dynamical origin. The underlying velocity ellipsoid, extracted by the maximum-likelihood method after removal of the streams, is not centered on the value commonly accepted for the radial antisolar motion: it is centered on U = −2.78 ± 1.07 km s −1 . However, the full data set (including the various streams) does yield the usual value for the radial solar motion, when properly accounting for the biases inherent to this kind of analysis (namely, U = −10.25 ± 0.15 km s −1 ). This discrepancy clearly raises the essential question of how to derive the solar motion in the presence o...