The spatial distribution of galaxies is compared with model distributions. It is demonstrated that giant and dwarf galaxies in the Local Supercluster occupy statistically identical regions. Various tests suggest that galaxy formation is biased since all unbiased model distributions are in conflict with observed distribution of galaxies. Multifractal analysis shows that a cold dark matter dominated universe with biased galaxy formation has a fairly constant fractal dimension over a broad range of scales. This contrasts with the observed distribution which does not show simple fractal features.

Observations and interpretation of the observations of the large-scale galaxy distribution prompt a number of profound questions to which we do not yet have clear answers. In this discussion I review two of the questions discussed during the symposium.

Modern N-body techniques allow the study of galaxy formation in the wider context of the formation of large-scale structure in the Universe. The results of such a study within the cold dark matter cosmogony are described. Dark galactic halos form at relatively recent epochs. Their properties and abundance are similar to those inferred for the halos of real galaxies. Massive halos tend to form preferentially in high density regions and as a result the galaxies that form within them are significantly more clustered than the underlying mass. This natural bias may be strong enough to reconcile the observed clustering of galaxies with the assumption that Ω = 1.

This talk is concerned with one of the most important class of theories of Large Scale Structure (hereafter LSS) based on two principal assumptions. It is supposed that (i) the main process is gravitational instability in expanding universe and (ii) the primordial perturbations a r e small Gaussian density fluctuations. Both assumptions are natural in inflationary model of the very early universe as well as in cosmological models dominated by Dark Matter (DM) in the form of Weakly Interacting Massive Particles (WIMPs). Other possible models of LSS formation are discussed by N. Turok, J. Ostriker and A. Dekel.

The hot big bang theory of the early universe is rather well established. Among its successful predictions are the Hubble expansion, the microwave background radiation and the abundances of the light elements. It also fits in rather nicely with ideas from particle physics. According to these ideas (which are firmly based on experiment) at high energies particle interactions become more symmetrical and the apparently complicated particle spectrum today becomes very simple. It is an appealing notion that such a state of high symmetry was actually realised in the very early universe at very high temperatures, and the symmetry was broken as the universe expanded and cooled.

We address, by means of Numerical Simulations, one of the main issues of the Cosmic String Galaxy Formation Scenario, namely the existence of a scaling solution, which is crucial to the very existence of the scenario. After a brief discussion of our numerical technique, we present our results which, though still preliminary, offer the best support to date of this scaling hypothesis.

Processes of the formation and the evolution of the large-scale structure are discussed in the framework of unstable dark matter models. Six numerical models are presented. The projected distribution of simulated galaxies on the sky, wedge diagrams, correlation functions and the mean linear scale of voids are presented. Physical background of the hypothesis of unstable particles and possible observational tests are discussed. The level of the microwave background fluctuations is estimated analytically. Special attention is given to late stage of supercluster evolution and galaxy formation.

In this talk, I will discuss a few particular topics, rather than attempting a general review of the formation of disk galaxies. First recall the basic structure and kinematics of a disk galaxy like the Milky Way. The Table below lists the four main structural components as they are presently understood, and gives typical masses, and (if known) the characteristic rotational velocities (at the sun) and the radial velocity dispersion for each component. For more details, see Freeman (1987).

The study of galaxy evolution with large lookback times is dominated by two difficult issues. The first is a technical matter. Even the most luminous galaxies are faint (mr < 19) at significant lookback times (z ≳ 0.5), and so spectrophotometric observations of average galaxies challenge our present telescope and detector technology. The second issue is the selection of objects in an unbiased way in order to assemble a representative sample of galaxies at the remote epoch. It is far too easy to chase only exotic objects whose very peculiarity has brought them to our attention. Though observations of such objects may be fascinating and revealing, they may tell us little about the evolution of an typical galaxy like our own.

Large scale structures up to 5h−1 mpc, the galaxy-galaxy correlation length and the size of typical galaxy groups and clusters, can be produced quite naturally from explosions originating in young galaxies (Ostriker and Cowie, 1981: “OC”) or quasars (Ikeuchi, 1981: “I”) with energy output of 1061 ergs. But very large-scale structure in the 25 mpc −50 mpc range possibly indicated by cluster-cluster correlations (Bahcall, 1987a), can only be produced by much more energetic events of 1065 ergs which are far beyond the output of any objects currently known. This follows simply from the dimensional arguments which give R = c(Eσ/t2)0.2 implicit in the classic Seldov-Taylor solution and cosmological analogs (cf Ostriker, 1986). Thus very large scale structure can only be produced by explosions if many small ones can coalesce suitably at early epochs (OC) or single giant events are produced by exotic objects such as superconducting cosmic strings (Ostriker, Thompson and Witten 1986: “OTW”). If however these large events do occur, then many specific properties of very large-scale structures will be produced quite naturally (cf Bahcall, 1987b, Weinberg, Ostriker and Dekel, 1987 “WOD”). Before discussing these points, it is appropriate to say a few words on the importance of hydrodynamics in general and explosions in particular, since the latter will certainly be a consequence of galaxy formation even if they are not the primary cause.

A large new sample of absorption redshifts derived from the C IV doublet in the spectra of 56 QSOs has been used to study the evolution and clustering tendencies of the heavy element absorbers (thought to be galaxies). The new data have been compared with more extensive existing data for the more common Lyman α forest lines (thought to be produced by intergalactic clouds). Little or no clustering is observed in the Lyman α forest lines; moreover, there is no evidence for voids in their distribution. Clustering has been detected in the heavy element redshifts on scales Δv ≥ 200 km s−1 where relative motions of clouds within galaxies are unlikely to dominate. The degree of clustering inferred at z ≈ 2 is of the order expected on the simplest model for the evolution of galaxy clustering in cosmic time. The recent discovery of similar concentrations of absorption features extending over Δz ∼ 0.2 in the spectra of widely separated QSOs on the sky provides evidence for very large structures, probably filaments or sheets of galaxies, extending over 100 Mpc (co-moving). The Lyman α forest and heavy element redshifts evolve very differently. The Lyman lines show a rapid increase in density with increasing z, while the C IV doublets show a decrease. This result emphasizes that there are two discrete populations of absorbers. The decrease in C IV line density may be due to the effects of the onset of stellar nucleosynthesis in galaxies.

The properties of the MgII absorption line systems detected in quasar spectra are briefly summarized. If these absorption systems arise in intervening galaxies, one can estimate their characteristic size and luminosity, and predict their identification rate. Results of a search for the absorbers is presented for a sample of 13 MgII systems at 0.16 ≤ z ≤ 0.79. Strong constraints on the luminosity function are derived from the high actual identification rate and observed galaxy luminosities. Other properties of these absorbing galaxies are discussed, especially their spectral type and spatial environment.

Quasar clustering has now been confirmed at a high level of significance, and there is evidence for its evolution. A review is given of these developments, and of other evidence related to the evolution of structure.

We present correlation function results from galaxy and QSO redshift surveys. The galaxy correlation function shows evidence for a possible ‘shoulder’ feature in ξ(s) at s = 2h−1 Mpc. At scales between 10 and 100h−1Mpc the correlation function remains close to zero and shows no evidence for any large scale galaxy clustering. The QSO correlation function detects strong QSO clustering for scales s < 10h−1 Mpc. At larger scales (10 < s < 1000h−1 Mpc) no evidence of significant QSO clustering is seen.

Deep radio source surveys made with the VLA at 6 cm wavelength show that the radio source count continues to converge down to microjansky flux densities, although there is some evidence of a flattening of the count in the range between 10 and 100 microjansky. The weak sources may be primarily an evolving population of active spiral galaxies.

We will briefly review the following questions: 1) is there compelling evidence for the existence of dark matter in individual disk galaxies?, 2) where is this dark material?, 3) how much of it is there?, and 4) what is its shape?

Analyses of rotation curves of spiral galaxies show that the amount of dark matter in a galaxy can exceed the amount of luminous matter by a factor of 4. Lenticular galaxies also appear to have dark halos, but conflicting results have been obtained for ellipticals. Data for double spiral galaxies confirm the results from rotation curves and suggest that the dark halos do not extend much beyond 5 optical radii R25.

We begin by reviewing the history of Aaronson's entry into the study of dark matter and velocity dispersions. A short review of mass estimations and dark matter in spirals, small groups of galaxies, dwarf irregulars, and dwarf spirals follows. We then discuss velocity dispersions in the five dwarf spheroidals Fornax, Carina, Sculptor, Draco, and Ursa Minor. A new velocity histogram for Draco and Ursa Minor is shown. We then end with some questions and theoretical and observational needs.