Key outstanding questions regarding dark matter are formulated, as a backdrop to the upcoming discussions at this meeting. A major issue involves how many species of dark matter there are, and whether both baryons and non-baryons are implicated in cosmological dark matter. How is dark matter distributed relative to baryons on all scales? Are voids really empty? And finally, is there high-amplitude structure in the matter distribution of the universe on scales ∼100 Mpc, and, if so, how can it be accounted for in terms of known, plausible physical processes?

The Poisson and Vlasov equations are solved self-consistently for realistic Galaxy models which include multiple disk components, a Population II spheroid, and an unseen massive halo. The total amount of matter in the vicinity of the Sun is determined by comparing the observed distributions of tracer stars, samples of F dwarfs and of K giants, with the predictions of the Galaxy models. Results are obtained for a number of different assumed distributions of the unseen disk mass. The major uncertainties, observational and theoretical, are estimated. For all the observed samples, typical models imply that about half of the mass in the solar vicinity must be in the form of unobserved matter. The volume density of unobserved material near the Sun is about 0.1M⊙pc−3; the corresponding column density is about 30M⊙pc−2. This so far unseen material must be in a disk with an exponential scale height of less than 0.7 kpc. If the unseen material is in the form of stars with masses less than 0.1M⊙, then the nearest such object is about 1 pc away and has a proper motion of more than 1 arcsecond per year.

Two years ago, Seitzer and Tyson began a program of 4-meter prime focus CCD observations at CTIO, with the aim to develop techniques for imaging and photometry to the theoretical limit of that telescope and overall 52% efficiency: 26.6 J mag, 26 R mag, 25 I mag. Color-magnitude plots show that the limiting magnitudes for detection are 28 J mag, 27 R mag, and 25.3 I mag. Each of our CCD fields covers about 12 sq. arcmin., with total exposure time about 7000 sec. in each of the three bands (see Boeshaar and Tyson 1985). Processed images are put on a VAX 11/780 and the FOCAS v.3.2 automated detector and classifier is run. In order to determine the probability of detection and photometric errors as a function of magnitude, FOCAS is rerun many times on artificial images made by adding in real star and galaxy images, dimmed many magnitudes, at random locations on the CCD sky frame. Over 2000 objects are detected in every high galactic latitude CCD field, less than 50 of which are classified as stars. Most of the faint galaxies are very blue (due to evolution), making it possible to search for infrared excess stars in the presence of so many galaxies.

Analysis of the detailed photometric, kinematic and chemical properties of stellar populations constrains the formation history of the Galaxy. We have completed a photometric survey and initiated a spectroscopic survey, obtaining radial velocities and abundances for volume complete samples of spheroid dwarfs in situ, to distances of a few kpc. Three fields under study are those for which Chiu (Ap. J. Suppl. 1980) obtained proper motions - SA 57 (NGP), SA51 (anticenter field) and SA68. Two of these fields are on the sun - Galactic center meridional plane (SA57 and SA51) so that (U,V) and (V,W) components of space motion respectively may be derived on the basis of the proper motions alone, once distances have been obtained. Our initial distance estimates are from Chiu's photometry and population classes, which are based on the position of the star on the reduced proper motion diagram.

The Palomar-Green Survey produced statistically complete samples of hot white dwarfs and subdwarfs, from which the local mass density of these objects can be determined. The luminosity function of hot hydrogen-atmosphere white dwarfs (DA's) was recently re-determined by Fleming, Liebert, and Green (1985, Ap. J., submitted). The contribution of each of the 353 objects to the local space density was calculated from the ensemble of limiting magnitudes and a spectroscopically or photometrically derived absolute magnitude. The local surface density of white dwarfs with MV < 12.75 (log L/L⊙ > −3.1; TE > 9000 K) is 0.32 ± 0.03 pc−2. Assuming an exponential disk with scale height 250 pc, we derive the differential luminosity function in the figure; the total volume density is 0.65 ± 0.06 per 1000 pc3. He atmosphere degenerates add another 20%.

Many of the “observations” of dark matter involve the application of the virial theorem or more sophisticated dynamical models to bound gravitational systems. Such studies often adopt a certain mass function and assume that the system is in a state near equipartition. In many cases though the data are not sufficient to determine the mass function or justify the equipartition assumption. Open clusters provide excellent case studies of systems which are relaxed and which have a large observable stellar-mass range, approaching an order of magnitude in the nearest young clusters. As a result open clusters have recently been the subject of extensive dynamical study.

We use a Galaxy model including three components for the ‘seen’ stellar matter (Robin, Crézé, 1985). A scenario of star formation and evolution in the disc constrains the age distribution within each spectral type and luminosity range. The model fits available star counts. We add the ‘seen’ interstellar matter with local density 0.04 M⊙ pc−3 and scale height 140 pc. Thus the total observed local density is 0.085 M⊙ pc−3.

The line-of-sight velocity field has been determined for all 80 FV stars within 15 degrees of the North Galactic Pole (NGP) with measured and constant velocities, and measured distances, from the catalogs of Hill et al. (1976, 1982). These data are a subset of the data used in a determination of Kz by Bahcall (1984). Procedures were as described by Goulet and Shuter (1984). The velocity field is depicted in Figure 1, and the magnitude of the velocity residuals is plotted in Figure 2.

From a new photometric and spectroscopic survey of high proper motion stars, combined with previously published work, we find that the local value of the escape velocity from the Galaxy exceeds 500 km s−1. This gives direct dynamical evidence that the total Galactic mass exceeds the mass inside the solar orbit by a factor of at least five.

From the observed rotation curves of Sa, Sb, and Sc spiral galaxies, it is possible to deduce a dozen constraints on the nonluminous matter in spirals. Within the optical image, the dark matter is less concentrated than the luminous, and contributes about 1/2 of the mass, for spirals of all Hubble types and luminosities.

Our group has now obtained rotation curves for 80 spiral galaxies, Hubble types Sa through Sd. As described in Rubin et al. (Ap. J. 289, 81; 1985), the forms of these rotation curves are similar for all Hubble types. Given this observational fact, we have chosen to analyze the mass distributions for these galaxies under the assumption that the mass distributions for all spirals can be described by the same three-dimensional form, here taken to be spherical for simplicity. The mass distribution forms for 71 of these galaxies can be placed into a simple classification scheme based on the curvature of mass distribution form in a log(radius) - log (integral mass) diagram. The three most common mass forms among this continuum are termed Types I, II and III, the forms of which are displayed below (see also the discussion by Rubin elsewhere in this Symposium).

The observational evidence on the discrepancy between the mass distribution in galaxies derived from HI rotation curves and that derived from the distribution of light is reviewed. In the outer parts the discrepancy is such that in some galaxies there is at least three times as much dark matter as luminous matter. This is a direct consequence of the nearly constant circular velocity far beyond the edge of the visible part of the galaxy, as derived from the motion of HI. The discrepancy is clearly present already near the edge of the visible disk (R25). In the inner regions, i.e. inside approximately 2.5 disk scale-lengths, no dark matter is required, but its presence can not be ruled out. There is no evidence for a dependence on galaxy luminosity or morphological type. These results suggest a strong coupling between luminous matter and dark matter within individual galaxies, and among galaxies as well. Finally attention is drawn to the large-scale asymmetries in the outer parts of galaxies and to possible implications for the vertical distribution of dark matter.

We present preliminary results of the analysis of WSRT observations of the edge-on spiral NGC 4565 (Sancisi 1985). The neutral hydrogen layer of this galaxy extends to 1.3 R25, permitting to trace the rotation curve outside the optical edge of the system, and is warped in the outer parts.

At Westerbork, we have mapped the distribution and motions of HI in about twenty gas-rich SO and SO/a galaxies, with resolutions of order 30 arcsec. Gas-rich SO's often have most of their HI in an outer ring, with diameters between 0.9 and 2.5 times the optical (D0). Assuming circular shape and motions for this ring, radius R, and a spherical distribution of matter, we derive the inclination and rotation speed of the ring, the amount of mass MT(R) interior to it and the corresponding ratio MT/LB0 to blue luminosity.

The issue of “dark matter” in astronomy is extremely confusing. Difficulties exist on two levels. First there are the, in principle, straightforward scientific questions of measurement. A certain region of space is studied, and by some technique, the mass within it is determined. Separately the energy output in some wavelength band from the region is measured and then, with due allowance for distance uncertainties, a “mass-to-light” ratio is determined. These measurements are difficult, with the results affected both by small number statistical uncertainties (as when using globular clusters to determine the mass of the galactic halo), measurement errors (as with binary galaxies), and systematic questions of interpretation (as with X-ray emitting gas around galaxies). Ultimately, with patience and skill these problems have been reduced and, as we shall see in subsequent sections of this report, there exists moderate agreement among observers concerning the large mass (∼ 1012 M⊙) and high mass-to-light ratio (M/LB > 100 M⊙/L⊙) for material integrated over distances in the range (30 kpc < r < 300 kpc) from the centers of giant galaxies.