We have compared the properties of galaxy groups in the CfA redshift survey to those in the cold dark matter simulations of Davis, Efstathiou, Frenk and White (1985). Redshift catalogs (four realizations) were made from the open universe (unbiased; mass follows light) simulations at expansion factors of 1.8 (Ω=.3, labelled T1) and 3.2 (Ω=.2, labeled T2) relative to initial conditions, and from the biased formation version of the Ω=1 simulation (5 realizations) at expansion factor 1.4. The T1, T2 and biased catalog sets were volume limited at distances of 5000, 3000 and 6500 km s−1 respectively, and magnitude limited (m≤14.5) beyond. They were then randomly culled by 25%, 9% and 10%, respectively, to match the density of comparison versions of the CfA Redshift Survey which were similarly volume limited. We have devised a percolation type grouping algorithm which lets the linking distance on the sky increase with distance in the magnitude limited regions, while keeping the radial velocity linking criteria fixed. We've verified that this produces groups with density contrast uncorrelated with distance and (unlike the Geller-Huchra criteria) M/L uncorrelated with group size for the open models. M/L may, however, show a slight negative correlation with distance.

We simulate the formation of structure on the galactic scale in the cold dark matter, Ω=1 universe.

This is a progress report on a study of the formation of large scale structure in the explosive amplification scenario, using N-body simulations. The simulations start when galaxies of the last generation form. The galaxies are distributed at random in expanding shells around random seeds. They start with an expansion velocity 20% larger than the Hubble velocity, in accordance with the similarity solution that was valid before the gaseous shells fragmented into galaxies. The galaxies are treated thereafter as softened point particles that interact only gravitationally, embedded in an N-body background representing inter-shell gas and dark matter (in variable amounts).

We have studied the properties of rich clusters of galaxies in various cosmological scenarios by comparing high resolution N-body simulations with observations of Abell clusters. The clusters have been simulated in two steps. First, protoclusters are identified in large-scale simulations which represent a wide range of cosmological scenarios (hierarchical clustering, pancake scenarios, and hybrids of the two, spanning a range of power spectra). Then the region around each protocluster is simulated with high resolution, the particles representing L* galaxies. The protoclusters have no spatial symmetry built into them initially. The final clusters are still dynamically young, and of moderate densities, which should be representative of Abell clusters of richness classes 1 and 2.

The need for halos on stability grounds is not at all compelling. Compared to a bulge, a halo is not very efficient in stabilising a disk. Because the effect of a modest halo is small, it is difficult to infer its presence or absence from stability arguments.

Bulge and halo material is often invoked to explain the absence of bars in the majority of disc galaxies, although the amount required is not known, in general, and is sensitive to the shape of the rotation curve. Here we show that the necessary fraction of spherical material is also affected by the degree of random motion amongst the disc stars. Quite moderate velocity dispersion has a strong stabilising influence and our hottest disc is stable without any halo (see also Kalnajs, this volume).

Many mass models of our Galaxy (see e.g. Schmidt 1985 for a review) assume the disc to be nearly axisymmetric. For consistency, therefore, no such model should possess gross non-axisymmetric instabilities. However, most attribute less than half the central attraction at the Sun to bulge and halo material - a situation where bar forming instabilities are frequently found (see e.g. Sellwood 1983).

Heavy halos are probably not axisymmetric. During disk formation, the visible parts of disk galaxies are likely to have aligned their principal axes with those of the surrounding halos, but it is less clear that early-type galaxies are aligned with their halos. Triaxial halos may possibly sustain, or even excite, the warps often seen in the outer parts of disks. Polar rings and ripples around elliptical galaxies provide promising probes of the triaxiality of halo potentials.

In a number of SO galaxies, rings of gas, dust and stars are observed to lie roughly perpendicular to the galactic disc (e.g. Whitmore, these proceedings). The material sometimes forms a fairly broad annulus, and the ring appears nearly flat. Simple estimates suggest that differential precession will destroy a polar ring in much less than a Hubble time, implying that the observed structures have been formed only recently. It is then surprising that some of them are so regular, unless something acts to prevent their disruption.

The discovery of SO galaxies with polar rings makes it possible to directly measure the gravitational potential of a galaxy in three dimensions. Schweizer, Whitmore and Rubin (1983) find a spherical potential in the case of A0136-0801. We have observed three more polar ring galaxies using the 4 meter telescope at CTIO. The following table summarizes the results for these three systems as well as A0136-0801, and figure 1 shows an example of the data.

Shells are often observed around elliptical galaxies (Malin & Carter 1983). Stars in the shells can be regarded as test particles. Therefore for a simple shell morphology (Hernquist & Quinn 1985) the distances between shells allow one to trace the shape of the potential of the host galaxy (Quinn 1984). One can also deduce the distribution of gravitating material. Following this method one concludes that the distribution of luminous matter alone cannot account for the observed shell structure. Depending on the age of the outermost shell one can conclude that either the massive halo terminates at a radius ≃ 5 re ≃ 15 kpc., or that the core of the halo γ≃2.5 kpc, where the halo density is given by ρ≃ {r2 + γ2}−1. In either case, the central density of the halo is no less than an order of magnitude in excess of that expected for a spiral galaxy of comparable luminosity (Figure 1.).

The mass discrepancy, which has led to the notion of dark matter may, in fact, be due to a breakdown of the Newtonian laws which are used to determine the masses of galactic systems. We describe a nonrelativistic theory which departs from Newton's in the limit of small accelerations. When one uses the modified dynamics to deduce gravitational masses, the need to invoke large quantities of dark matter disappears. We outline the theory and give criteria for deciding which systems are expected to exhibit marked departures from Newtonian behaviour. The main body of the talk is a succinct description of the major predictions of the theory regarding dynamics within galaxies.

A new model of filamentary matter fields and voids is proposed. This is a gravitational version of the MIT bag model of hadrons (see a review of DeTar and Donoghue 1983). Bekenstein and Milgrom (1984) have first proposed a gravitational bag model. Their bag is closed but our bag, called a channel, is open.

Theories of galaxy formation via hierarchical clustering of cold dark matter and by fragmentation of gaseous pancakes or shells are reviewed and compared. Dissipative processes are crucial to all theories of galaxy formation, and are discussed in terms of a simple model involving multiple cloud interactions. Stellar energy input is found to play an important role in protogalaxies, both supporting the gas against collapse, thereby prolonging the duration of the active star formation phase, and driving winds from the less massive galaxies. The significance of such processes is explored both for chemical and dynamical evolution and for biasing galaxy formation towards density peaks in the primordial density fluctuation spectrum.

ABSTRACT The mass spectrum of bound baryonic systems (galaxies and globular clusters) is computed as a function of redshift in an Einstein-de Sitter (Ω=1) universe dominated by weakly interacting, cold dark matter. Baryons are assumed to fall into primordial density peaks in the cold particle distribution when the mass in the peaks exceeds the baryon Jeans mass. The distribution of peaks is computed using Gaussian statistics. As the universe expands the baryonic mass attached to a given peak increases because of infall (treated in a spherical approximation), and new peaks of lower amplitude become nonlinear. Globular clusters form first (by z∼40 if the galaxies represent a biased mass distribution). The remaining gas may be reheated to ∼10000 K if a few percent of globular cluster (or Pop. III) stars are very massive. Reheating increases the baryon Jeans mass and delays galaxy formation until z≲10. The present method reproduces the shape (but not the amplitude) of the Schechter galaxy mass function when merging of substructure is included in an approximate fashion.

In an expanding universe neutrinos of mass 10eV form condensates with typical mass 1016 M⊙ and size ∼0.5 Mpc. Visible matter like galaxies and stars are embedded in these and assuming a Maxwellian distribution and collisionless nature of these systems we solve the self consistent Poisson-Vlasov equations. These solutions correctly predict the profiles of luminosity of clusters of galaxies, dwarf, elliptic and spiral galaxies as well as their rotation curves; the embedding picture is supported by M∼R33 relation for astronomical systems as below.

The formation of dwarf, diffuse, metal-poor galaxies, as a result of supernova driven winds, is reexamained in view of the accumulating data on dwarfs in the local group and in the Virgo cluster. The observed drop in both surface-brightness and metallicity with decreasing luminosity is not easily understood if the gaseous protogalaxies are self-gravitating (because they swell after gas-loss), but they are produced naturally inside dominant halos, with a mass-radius relation that indicates ‘cold’ dark matter. The theory predicts for the faint dwarfs an M/L that increases with decreasing luminosity up to 10–100, and a corresponding slow decrease in velocity dispersion down to 5–10 km/s.

The growth of angular momentum in a general clustering scenario is analyzed and its dependence on the primordial density perturbation, δo, is calculated. High density peaks are found to evolve into low angular momentum and low spin parameter (η = J E½ G−1 M−5/2) systems. The basic mechanism behind this anti-correlation is that anisotropic structure, which leads to the growth of angular momentum, is statistically uncorrelated with δo. The collapse time, on the other hand, depends on δo and it is this time scale which determines the angular momentum of bound objects. Three cases are studied: (1) Lagrangian sphere (quasi-linear evolution): J (1σ)/J(3σ) = 3.3 and η (1σ)/η (3σ) = 1.9 where δ is given in σ(= <δ2>1/2)units.

If the universe is dominated by cold dark matter (CDM), had an inflationary phase, and has Ω = 1, then the spectrum of primordial density perturbations can be calculated. Using the spectrum calculated by J. Bardeen, we have found the structure of halos which form around peaks in the density. If the initial density is given by , where ) is a Gaussian process, then the mean run of density around a peak is proportional to the correlation function of . If the mass about a peak comes to equilibrium in near-circular orbits, the exact equilibrium configuration can be calculated. The resulting rotation curve for a 1.5σ perturbation is shown as the curve HB in the figure below. As the baryon mass cools and condenses, it drags the CDM in with it, conserving the adiabatic invariants. Putting a 5×1010 M⊙ exponential disk and a 2×1010 M⊙ bulge at the center of the system, the rotation curve of the resulting compressed dark halo is given by the curve HA. D and B show the disk and bulge contributions, and T gives the net velocity. There are many arguments for wanting large galaxies to form from perturbations rarer than 1.5σ. Our spectrum was normalized by assuming that mass clusters as galaxies do on large scales; if Ω = 1, however, galaxies cannot trace the mass and the amplitude must decrease. The flatness of the rotation curve from the baryon-dominated to the CDM-dominated region comes about, in this case, from the imposition of the phenomenological baryon distribution, but the following argument indicates that the result is general. The ratio of baryonic to dark matter is ∼1/15; the rotation parameter Λ, the ratio of rotation velocity to halo dispersion, is also ∼1/15. When baryons fall though the CDM to the point at which they are rotationally supported, their density increases by (15)3. The CDM density increases by (15)2. Hence, baryon and CDM densities are comparable at the mean baryon radius.

When a pregalactic gas of H and He is heated and reionized, as by a shock wave occurring in the nonlinear collapse of density fluctuations or in the case of explosions in the IGM, the gas cools radiatively and recombines out of equilibrium. The temperature drops faster than the ions can recombine. When the temperature falls below 104K, the residual electron concentration is large enough, as a result, to form H− ions which form H2 molecules, via (H + e → H− + hν) and (H + H− → H2 + e). Molecules also form via (H+ + H → H2+ + hν) and (H2+ + H → H2 + H+). As a consequence, H2 can form with a sufficient concentration (∼10−3) to cool the gas further, by rot-vibrational line excitation and the formation process itself, to ∼102K. This has an important effect on the Jeans mass and fragmentation. We show some illustrative results below for the time-dependent cooling and non-equilibrium recombination and molecule formation. The three cases are as follows: (1) isochoric cooling at hydrogen number density 1 cm−3; (2) isochoric cooling at 3×107 cm−3; (3) isobaric cooling starting at initial density 1 cm−3. At high densities, molecular cooling is suppressed.