The competition between CDM and MOND to account for the ‘missing mass’ phenomenon is asymmetric. MOND has clearly demonstrated that a characteristic acceleration a0 underlies the data and understanding what gives rise to a0 is an important task. the reason for MOND's success may lie in either the details of galaxy formation, or an advance in fundamental physics that reduces to MOND in a suitable limit. CDM has enjoyed great success on large scales. the theory cannot be definitively tested on small scales until galaxy formation has been understood because baryons either are, or possibly have been, dominant in all small-scale objects. MOND's predictive power is seriously undermined by its isolation from the rest of physics. in view of this isolation, the way forward is probably to treat CDM as an established theory to be used alongside relativity and electromagnetism in efforts to understand the formation and evolution of galaxies.

It has long been known that Newtonian dynamics applied to the visible matter in galaxies and clusters does not correctly describe the dynamics of those systems. While this is generally taken as evidence for dark matter it is in principle possible that instead Newtonian dynamics (and with it General Relativity) breaks down in these systems. Indeed there have been a number of proposals as to how standard gravitational dynamics might be modified so as to correctly explain galactic dynamics without dark matter. I will review this general idea (but focus on “MOdified Newtonian Dynamics”, or “MOND”), and discuss a number of ways alternatives to dark matter can be tested and, in many cases, ruled out.

Newtonian mechanics indicates that galaxies and galaxy clusters are much more massive than we would have guessed from their luminosities, with the discrepancy being generally attributed to dark matter halos. An alternative hypothesis is that accelerations in very weak gravitational fields are larger than predicted by Newton's laws, and there is no need for dark matter. Even though we do not currently have a satisfactory theory associated with this rival hypothesis, we can ask whether any observational tests could rule it out or prefer it over the dark matter hypothesis. Current evidence suggests that neither hypothesis enjoys a decisive advantage over the other. If dark matter turns out to be the correct interpretation however, then theories of galaxy formation face some quite severe fine-tuning problems.

I review the observational side of the present state of the debate about the dark matter in galaxies, with emphasis on the core/cusp problem in low surface brightness galaxies, and the question of maximum/sub-maximum disks in spiral galaxies. Some remarks are made about the dwarf spheroidals around the Milky Way, and about elliptical galaxies.

This is a summary of the discussion in Panel I of IAU Symposium 220 on Dark Matter in Galaxies. the panel topics and panellists were as follows – Cusps Theory: Julio Navarro; Cusps Observations: Erwin de Blok, Rob Swaters; Substructure Observations: Mario Mateo; Substructure Theory: James Taylor, Shude Mao. in addition to the talks by the panellists and the discussion among them, there was a good deal of discussion with the audience. Despite the differences of opinion expressed I think a consensus emerged, and I try to summarize it here.

I report recent results of numerical simulations designed to study the inner structure of Cold Dark Matter (CDM) halos. This work confirms the proposal of Navarro, Frenk & White (NFW) that the shape of ACDM halo mass profiles differs strongly from a power law and is approximately independent of mass. the logarithmic slope of the spherically-averaged density profile, as measured by β = –d ln ρ/d ln r, decreases monotonically towards the center, becoming shallower than isothermal (β < 2) inside a characteristic radius, r–2, and shows no evidence for convergence to a well-defined asymptotic value (β0) at the center. the dark mass contained within the innermost radius resolved by the simulations places strong constraints on β0; cusps as steep as r–1.5 are clearly ruled out in our highest resolution simulations. A profile where the radial dependence of the slope is a simple power law, β(r) ∝ rα, approximates the structure of halos better than the NFW profile and so may minimize errors when extrapolating our results inward to radii not yet reliably probed by numerical simulations. We compare the spherically-averaged circular velocity (Vc) profiles to the rotation curves of low surface brightness (LSB) galaxies in the samples of de Blok et al. and Swaters et al. the Vc profiles of simulated CDM halos are generally consistent with the rotation curves of LSB galaxies, but there are also some clearly discrepant cases. This disagreement has been interpreted as excluding the presence of cusps, but it may also just reflect the difference between circular velocity and rotation speed likely to arise in gaseous disks embedded within realistic triaxial halos.

Low Surface Brightness (LSB) galaxies are dominated by dark matter. High-resolution rotation curves suggest that their total mass-density distributions are dominated by constant density cores rather than the steep and cuspy distributions found in Cold Dark Matter (CDM) simulations. the data are best described by a model with a soft core with an inner power-law mass-density slope α = 0.2 ± 0.2. However no single universal halo profile provides an adequate description of the data. the observed mass profiles appear to be inconsistent with ACDM.

Systematic effects on HI and Hα long-slit observations make a measurement of the inner slope of the dark matter density distribution difficult to determine. Halos with constant density cores and ones with r–1 profiles both appear consistent with the data, although constant density cores generally provide better fits. High-resolution, two-dimensional velocity fields remove most of the systematic effects, yet as a result of noncircular and random motions the inner slopes still cannot be accurately measured. Halo concentration parameters provide a more useful test of cosmological models because they are more tightly constrained by observations. the concentration parameters for LSB galaxies appear consistent with, but on the low end of the distribution predicted by CDM.

The Cold Dark Matter (CDM) hierarchical structure formation theory predicts substructures in dark matter halos. the number of predicted subhalos seems to exceed the observed number of luminous satellite galaxies. Gravitational lenses can be used to probe luminous or dark substructures. Image positions and flux ratios in broad-band (including radio and optical) and emission lines can all be used to probe substructures on different mass scales. the observed gravitational lenses appear to require a few percent of the mass surface density in substructures within the mass range of 104M⊙ − 109M⊙. Numerical simulations predict roughly the same mass fraction in substructures within the virialised region. But at typical image positions (a few percent of the virial radius), the predicted surface mass density in substructures appears to be lower than required. Both observations and numerical simulations are somewhat uncertain at present so it is not yet clear whether the discrepancy is severe.

Models of structure formation based on cold dark matter predict that most of the small dark matter haloes that first formed at high redshift would have merged into larger systems by the present epoch. Substructure in present-day haloes preserves the remains of these ancient systems, providing the only direct information we may ever have about the low-mass end of the power spectrum. We describe some recent attempts to model halo substructure down to very small masses, using a semi-analytic model of halo formation. We make a preliminary comparison between the model predictions, observations of substructure in lensed systems, and the properties of local satellite galaxies.

We investigate the structure of the dark matter halo formed in the cold dark matter scenarios by N-body simulations with parallel treecode on GRAPE cluster systems (Fukushige, Kawai, Makino 2003). We simulated 8 halos with the mass of 4.4 × 1014M⊙ to 1.6 × 1015M⊙ in the SCDM and LCDM model using up to 30 million particles. With the resolution of our simulations, the density profile is reliable down to 0.2 percent of the virial radius. Our results show that the slope of inner cusp within 1 percent virial radius is shallower than −1.5, and the radius where the shallowing starts exhibits run-to-run variation, which means the innermost profile is not universal.

Many quasars that are gravitationally lensed exhibit flux ratio “anomalies” that cannot be explained under the hypothesis that the lensing potential is smooth on scales smaller than 1 kpc. Micro-lensing by stars is a natural source of granularity in the lens potential. the character of the expected fluctuations due to Micro-lensing depends sensitively on the relative surface densities of micro-lenses (stars) and smoothly distributed (dark) matter. Observations of flux ratios may therefore be used to infer the ratio of stellar to dark matter along the line of sight – typically at impact parameters 1.5 times the half light radius. Several recently discovered systems have anomalies that would seem to be explained by Micro-lensing only by demanding that 70-90% of the matter along the line of sight be smoothly distributed.

We have studied the mass distribution in the lensing galaxy 2237+0305 using constraints from both gravitational lensing and photometric and spectroscopic observations. We find that with sufficient dynamical information we can constrain the mass-to-light ratio of the luminous components and determine the dynamical contribution of the disk. in addition, future observations should allow us to place constraints on the shape of the dark matter halo and its inner slope.

Using our semi-linear inversion method, we measure the mass profile of the lens galaxy in the Einstein ring system 0047–2808. The lens is modeled as a baryonic component following the observed light embedded in a generalised dark matter NFW halo. The semi-linear method makes full use of the information content in the ring image. We determine a B-band mass to light ratio for the baryons of 2.33+0.30–0.62h M⊙/LB⊙ (99% CL), accounting for 54% of the total projected mass within the Einstein radius of 1.16″. The inner logarithmic slope of the halo is found to be 0.65+0.73–0.31 (99% CL). We find that the halo is fairly well aligned with the light but has only half the ellipticity.

We report on the final microlensing result from one survey (VATT/Columbia) monitoring stars in M31, and the initial results of a larger study (MEGA), which together seem to indicate the presence of a microlensing halo component comprising a significant fraction of the dark matter in M31.

Microlensing surveys have ruled out that the dark halos of the Milky Way and M31 are composed entirely of massive compact halo objects (MACHOs) for a wide range of MACHO masses. We have tried using the Subaru telescope to improve the limit on Moon-mass MACHOs, which is the lowest decade in MACHO mass that can be probed by microlensing. Unfortunately, only a half-night of Subaru data was obtained and this is not enough; at least 2 nights of data are required. the current limit is based on nearly 6 years of observations with smaller telescopes.

I discuss current and future applications of pixel lensing: the microlensing of unresolved stars. Pixel lensing is the tool of choice for studying the MACHO dark matter content of external galaxies like Andromeda (M31), and is at the heart of an ambitious new proposal to undertake a census of low-mass stars and brown dwarfs in the M31 bulge.

The latest results of the Eros2 experiment are presented. the search for gravitational microlensing events toward the Galactic Center and toward the Magellanic Clouds yielded an optical depth τbulge = 0.94 ± 0.29 × 10–6, and a strong limit, combining all Eros analyses, on the composition of the halo. Less than 25% of a standard halo can be composed of MACHOs with a mass range [10–7, 1] M⊙ at the 95% C.L.

We assess to what extent the claimed signature of planetarymass compact objects in the long-term optical light curves of quasars really can be explained by the dark matter populations allowed in the currently favoured ΩM = 0.3, ΩΛ = 0.7 cosmology. Revised upper limits on the cosmological density of planetary-mass compact objects inferred from the statistics of quasar light curves and the equivalent widths of quasar emission lines are also presented.