HI synthesis observations of the dwarf “regular” galaxy UGC 2259 are presented. This system turns out to be most suitable for our purpose of studying the mass distribution in late-type spirals. It has a symmetrical HI distribution extending over 2 D25 and a regular velocity field which shows no sign of departure from axial symmetry. Despite the fact that UGC 2259 is fainter than most other objects of the same morphological type, its HI properties are typical of what is expected from an Scd galaxy with a MH/LB = 0.43.

We are in the midst of obtaining 21 cm observations of late-type (Sdm through ImV, including BCD) dwarf galaxies in the Virgo Cluster, selected from the Binggeli, Sandage and Tammann catalog (1985, in press). To date, we have observed 174 of these objects; the sample is nearly complete to BT = 17.0. 114 have been detected, and 37 of the strongest emitters have been mapped at 119 spacing to determine HI diameters and rotation curves.

Lower mass limits for particles constituting the dark matter in galaxy halos can be derived from considerations of the initial and final phase space distribution. In the case of massive neutrinos, Tremaine and Gunn (1979) pointed out that the initial fine-grained occupation number of cosmological neutrinos and therefore the final coarse-grained phase space occupation, is less than 0.5. From this they were able to show that if the final neutrino distribution is an isothermal sphere, one can put lower limits on the neutrino mass from assumptions about the core radius of the neutrino sphere.

X-Ray observations of galaxies and clusters can, in principle, trace the binding mass in these systems. I review some of the relevant work. The mass of hot gas in rich clusters is comparable to or exceeds the mass in visible stars. This proportion of gas to stellar material could be universal, although there is no direct evidence that it must be. Studies of the distribution of the gas indicate the presence of dark matter in the envelopes of some dominant cluster galaxies, most notably M87. The M/LB values increase with radius to values of ∼ 400–600 M⊙/L⊙. Uncertainties in the temperature distribution of the gas have hampered these analyses and have made it difficult to draw definitive conclusions about the binding mass in clusters. Recent work on Coma suggests that M/L is falling with radius and the total M/L for the cluster may be as low as ∼ 120. Studies of early type galaxies show that many contain hot gas with temperatures ∼107 K. There is evidence for the existence of cooling flows, and gravity rather than supernovae may be the dominant source of energy that heats the gas. The deduced binding masses for several bright galaxies are uncertain because of the unknown temperature profiles. Values of M/LB ≃ 20–30 within ∼ 30–40 kpc are indicated if one assumes isothermality, but values as low as 5 and as high as 100 are allowed. With better models one may be able to reduce these uncertainties.

X-ray measurements provide an excellent method to determine the amount and distribution of the dark matter in clusters. Unfortunately, accurate temperature profiles, necessary to this method, are currently not available. However, if the intracluster gas is assumed to have a monotonically decreasing temperature, one finds that the dark matter is strongly concentrated to the cluster center, and has a mass which only exceeds the known baryonic mass by a factor of about three. On a second topic, cooling flows are shown to be a very common feature of cluster central and normal elliptical galaxies. The cooling gas is probably ultimately converted into low mass stars.

The distribution of matter condensing out of cooling flows in clusters of galaxies and individual elliptical galaxies has been studied using X-ray data and is found to resemble the expected mass profiles of the underlying galaxies. Most of the cooled gas must create objects of high mass-to-light ratio, although some more normal stars are produced. Cooling flows provide an observable mechanism for the continual formation of dark matter around galaxies. Since the conditions at galaxy formation are similar to those in cooling flows if the gas reaches the virial temperature, we suggest that they are local models of galaxy formation.

The analysis of the X-ray emission from a sample of 55 bright early-type galaxies shows that hot gaseous coronae are a common and perhaps ubiquitous feature of such systems. The X-ray emission can be explained most naturally as thermal bremsstrahlung from hot gas (kT ≈ 0.5–1.5 keV) which may be accumulated from mass loss during normal stellar evolution. The presence of these coronae shows that matter (109−1010 M⊙) previously thought to be expelled in a galactic wind is instead stored in a hot galactic corona which may be heated and powered by supernova explosions. Perhaps the single most important feature of these coronae is that they provide a unique tracer of the gravitational potential in the outer regions of bright early-type galaxies. In this paper we describe the X-ray properties of these coronae (gas mass, temperature, and extent) and discuss their implications for the presence of massive dark halos around individual early-type galaxies. We find total masses of early-type galaxies up to 5 × 1012 M⊙. We estimate mass-to-light ratios for early-type galaxies and find values up to ∼100 (in solar units), similar to those found for the larger dynamical systems of groups and clusters.

In this poster we display the results from a detailed analysis of the distribution of the X-ray emission in early type galaxies. Two major results have come out of the analysis so far:

1. a) The surface brightness radial profiles of isolated elliptical and SO galaxies are smoothly decreasing functions of radius out to a Rmax (similar to the optical radius). Outside Rmax a flattening in the slope is observed, although the exact shape of the profiles at large radii, where the data are poorest, cannot be determined at present.

2. b) For R«Rmax, the X-ray and optical surface brightness profiles are similar (the nuclear region could be an exception). At larger radii, the X-ray profile could be flatter (NGC 4649 and NGC 4472 northern sector) or steeper (NGC 4472 southern sector) than the optical profile, or have a similar shape (NGC 4636).

It is likely that the different profiles reflect the action of slightly different environments and/or a different ambient density around each galaxy, combined with the “history” of each galaxy. The tail in NGC 4472 could be the result of the motion of this galaxy in a dense intracluster medium. The X-ray deficiency in NGC 4649 could be due to either ram pressure stripping or the action of wind in the outer regions of the galaxy.

Recently we have obtained both Hα + [NII] and broad-band red exposures of a number of galaxies with an RCA 320 × 512 CCD at the prime-focus of the 3.6 m CFH Telescope. Figure 1 shows the difference between Hα and red exposures (each with a total integration time of 60 min) of M87 = NGC4486.

In principal, gravitational lenses can be used to study dark matter in a variety of ways. They can provide information on masses of lensing galaxies, circular velocities in halos, the value of Ω in condensed objects, and the constitution of heavy halos (whether they are made of low mass stars or not). They can tell us whether mass and light are distributed equally, provide insights on mass in groups of galaxies and on exotic dark matter such as strings and non zero Λ. As an example, the existance of the normal lens case QSO 2016 with zQ = 3.27 allows one to set the limit qo > −2.3.

Following a few general comments on gravitational lenses from an observer's perspective, the currently available observations of the six known gravitational lenses are summarized. Attention is then called to some regularities and peculiarities of the properties of the known lenses and to how they might be interpreted. The most important conclusions relevant to the dark matter problem which can be obtained from the current observations are that the distributions of mass and light appear to be quite different in at least some of the lensing objects and that objects with projected M/R values about ten times larger than those ordinarily associated with galaxies exist and are not too rare (assuming Λ = 0).

Gravitational interactions allow one to investigate the nature of matter in the universe independent of the properties that make it luminous. Much as studies of the dynamics of galaxies and clusters of galaxies have indicated the presence of dark matter, gravitational lensing provides an independent probe of the large scale distribution of dark matter in the universe.

The average gravitational lens distortion of background galaxy images by foreground galaxies is an independent, non-kinematical measurement of galaxy mass distribution M(r)/r (Tyson, et al. 1984). The upper limit we obtained for the equivalent circular velocity, while small compared with some heavy halo models, is consistent with dynamical estimates for samples of galaxies of all types (e.g. Turner's binary data and the Rubin, et al. rotation curves). For example, for a mean cutoff radius of 65 kpc/h, our 3σ upper limit for the equivalent circular velocity (GM/r)1/2 = 190 km/sec. For a mass cutoff at 190 kpc/h our 2σ upper limit is 175 km/sec. If I weight a sample of asymptotical rotation curve velocities by recent field luminosity functions, I get mean circular velocities less than 170 km/sec.

A review of observational work on dark matter in USSR is given. Dynamically the dark matter can be located (i) in the galactic disk and/or in dwarf galaxies, (ii) in coronas of galaxies and in clusters of galaxies, and (iii) distributed smoothly in voids. The possible amount of matter in all three forms is discussed. Physically dark matter can be baryonic or non-baryonic, in the latter case either hot, warm or cold. Available information on the nature of dark matter is indirect, coming from theories of the formation of structure in the Universe. Two constraints to the formation scenarios are discussed, the galaxian correlation function and their morphology.

The structure of the dominant “dark” component of the Universe may evolve primarily under the influence of gravity. A number of models for the evolution of the Universe make specific predictions for the statistical properties of density fluctuations at early times. N-body simulations can follow the nonlinear development of such fluctuations to the present day. A major difficulty arises because we cannot observe the present mass distribution directly. Recent N-body work has concentrated on models dominated by weakly interacting free elementary particles. Neutrino-dominated but otherwise conventional cosmologies pass rapidly from a smooth distribution to one dominated by lumps with masses greater than those of any known object. Cosmologies dominated by “cold dark matter” produce mass distributions which fit the observed galaxy distribution (i) if Ω = 0.1–0.2 and galaxies follow the mass distribution, or (ii) if Ω = 1, HO < 50 km/s/Mpc and galaxies form preferentially in high density regions. In the latter case, clumps form with flat rotation curves with about the amplitude and abundance expected for galaxy halos.

When one builds a code to simulate numerically a process, the first concern is the range of validity of the results. This can be accessed empirically, though the results can be misleading if the tests are too naive. For particle-mesh codes simulating the gravitational clustering, an analytical theory has been proposed in Bouchet et al. 1985. It yields the numerical dispersion relation of the system in the linear regime, and thus describes how the linear growth rate is affected by the discretisation. The theoretical predictions are in agreement with the results of actual numerical experiments: both show that the results of standart particle-mesh codes should not be trusted at distances smaller than 6 to 8 grid-spacing Δx (depending on the detail of the algorithm).

A flat universe dominated by cold dark matter (CDM) is an attractive arena for the formation of galaxies and large scale structure. Current upper limits on anisotropies of the cosmic microwave background and the standard theory of primordial nucleosynthesis are both compatible with such a universe. Furthermore a flat CDM model in which galaxy formation is biased towards high density regions provides a good match to the observed distribution of galaxies on Megaparsec scales. In collaboration with M. Davis, G. Efstathiou and S.D.M. White, we have carried out a high resolution N-body simulation which shows that this model can also account for the abundance and characteristic properties of galactic halos. The initial conditions for this simulation were based on the results of our previous work which gave both the scaling and overall normalisation of the initial CDM fluctuation spectrum appropriate to the biased galaxy formation model. We simulated a cubic region of present size 14 Mpc (H0 = 50km/s/Mpc) from a redshift of 6 to the present day, with a resolution of 2kpc initially and 14 kpc at the end. We found that by a redshift of 2.5 about 20 clumps with circular speeds exceeding 100 km/s had collapsed near high peaks of the initial linear density field. Between Z = 2.5 and the present most of them remained isolated and accreted extensive outer halos, while others merged into larger systems. The rotation curves of the final smooth systems were impressively flat at large radii resembling the measured rotation curves of spiral galaxies. Furthermore, the abundance of clumps with circular velocities larger than 150 km/s was about the same as the abundance of galaxies brighter than M33 expected in a volume the size of our simulation. Significant transfer of angular momentum to surrounding material occurred as large subclumps merged. Most of this angular momentum was originally invested in the orbital motions of the subclumps. As a result, the central regions of merged objects showed little rotation.

Self-consistent simulations of seven groups are performed from the maximum expansion to the present using Aarseth's N-body code. An initial galaxy consists of 100 stars. Its mass, half-mass radius, and central velocity dispersion are 1, 0.41, and 0.96. Units of mass, length, velocity, and time are 1.4×101 2M⊙, 100 kpc, 245 kms−1 and 4.0×108y. Table 1 gives the elapsed time from the Big Bang to the formation of a multiple merger tm+Tc*/2. For H0=80 kms−1Mpc−1, the Hubble time H0−1=30.6 in our units. Dense groups except B form multiple mergers in a Hubble time.

The void probability function was known from a long time to be an efficient tool in analysing the galaxy repartition (White, Sharp, Schaeffer). We developed a method to determine this quantity with a minimum noise, for any proposed distribution resulting from observations, simulations, or theory. We apply it here to the 2D-CFA catalog. This will be later compared to other 2D galaxy catalogs, to the 3D CFA catalog and to the results of numerical simulations.

Clusters of galaxies are believed to be dominated by dark matter. Some of this matter is presumably bound to galaxies in the form of massive halos, while the rest moves freely in the cluster potential well. The exact fraction of dark matter bound to galaxies is an important datum for models of cluster evolution, since time scales for orbital decay, merging, stripping, etc. are sensitive functions of galaxy mass. In this study we attempt to put a firm upper limit on the amount of dark matter associated with galaxies in clusters, by calculating the response of a galaxy with an initially massive halo to the mean tidal field produced by the overall cluster potential well. If the velocity dispersions of galactic halos are roughly equal to those of luminous galaxies, σg, it is easy to show that the truncated mass of a spherical galaxy orbiting near the center of a cluster is roughly mg ≈ G−1σg3σc−1Rc ≈ 4 × 1011M⊙, where σc and Rc are the cluster velocity dispersion and core radius. The precise value of mg must depend on the orbital geometry, as well as the number of pericenter passages since cluster formation, among other factors.