Abstract. If the universe has closure density and the spectrum of primordial density fluctuations is a power law, the lack of any preferred scale means that the clustering should evolve in a scale invariant manner. These self-similar models allow one to approximately predict the evolution of the clustering in e.g., the ‘standard’ cold dark matter model. I describe how these models yield predictions for the evolution of the cluster populations. Particular attention is given to the range of spectral indices for which the scaling should be valid. I argue than the allowed range is −3 < n < 1, though quite what happens for spectra near the upper bound is somewhat unclear. The cold dark matter power spectrum has spectral index n ≃ −1 on the mass scale of clusters. For this value of n, I find that the comoving density of clusters classified according to virial temperature Tv or by Abell's richness, should show weak positive density evolution ∂log n(Tv, z)/∂z ≃ +0.3. Clusters classified by total X-ray luminosity should show strong positive density evolution ∂log n(Lx, z)/∂z ≃ +3, but the assumptions used to predict the total X-ray luminosity are somewhat questionable. More robust predictions can be made for the halo emission, and I describe an evolutionary test which should be feasible with ROSAT.

INTRODUCTION

Rich clusters have had much impact on cosmological theory. They give the strongest indication that the universe contains copious amounts of dark matter and give an empirical estimate of the baryon to dark matter ratio.

Abstract. I discuss some issues that arise in the attempt to understand what rich clusters of galaxies might teach us about cosmology. First, the mean mass per galaxy in a cluster, if applied to all bright galaxies, yields a mean mass density ∼ 30 percent of the critical Einstein-de Sitter value. Is this because the mass per galaxy is biased low in clusters, or must we learn to live in a low density universe? Second, what is the sequence of creation? There are theories in which protoclusters form before galaxies, or after, or the two are more or less coeval. Third, can we imagine that clusters formed by gravitational instability out of Gaussian primeval density fluctuations? Or do the observations point to the non-Gaussian perturbations to be expected from cosmic strings, or explosions, or even some variants of inflation? These issues depend on a fourth: do we know the gross physical properties of clusters well enough to use them as constraints on cosmology? I argue that some are too well established to ignore. Their implications for the other issues are not so clear, but one can see signs of progress.

THE STATISTICS OF CLUSTERS OF GALAXIES

To draw lessons for cosmology, we need not only the physical properties of individual clusters but also an understanding of how typical the numbers are. The issue here is whether the Abell catalog or any other now available is adequate for the purpose.

Abstract. This article describes the current status of various methods for determining the dark matter distribution in clusters. Despite a great deal of progress recently we still do not have good mass constraints for even one cluster. The reasons for this are discussed. New observational tools and methods of analysis should however lead to some results in the near future.

INTRODUCTION

One of the many interesting aspects of clusters of galaxies is that they appear to contain large amounts of missing mass. The evidence for this has largely been based on the application of the standard virial theorem. More sophisticated approaches which utilize cluster velocity dispersion profiles came to similar conclusions but assumed that the mass distribution in clusters was the same as that of the light (galaxy) distribution. While this may be true it is definitely at present an assumption. Much recent theoretical work has argued for different distributions for the dark and luminous components of the universe. One of the consequences of this is that we should not assume that the mass distribution in clusters parallels the light distribution. Without this assumption it is very difficult to constrain the mass distribution in clusters, and consequently total cluster masses are not as yet well determined (Bailey 1982, The & White 1986, Merritt 1987).

The cluster mass distribution is an important ‘parameter’ in that it directly influences many of the physical processes that occur in clusters.

Abstract. Various observations indicate that the cluster environment can affect the structure and dynamics of galaxies. This review concentrates on the effect the environment can have on three of the most basic properties of a galaxy; the morphological type, the size, and the distribution of mass. A reexamination of the morphology - density relation suggests that the fundamental driver may be related to some global property of the cluster, such as the distance from the cluster center, rather than some local property, such as membership in a local subclump within the cluster. While there is good evidence that the size of a galaxy can be increased (i.e., cD galaxies) or decreased (i.e., early type galaxies near the centers of clusters) by the cluster environment, it is not clear what physical mechanism is responsible. There is tentative evidence that rotation curves of spiral galaxies near the centers of clusters are falling, perhaps indicating that the dark halo has been stripped off. Rotation curves for spiral galaxies in compact groups are even more bizarre, providing strong evidence that the group environment has affected the kinematics of these galaxies.

INTRODUCTION

Perhaps the three most basic questions an extragalactic astronomer might be asked are:

1. Why are some galaxies flattened into disks while others are elliptical in shape?

2. How big are galaxies?

3. How massive are galaxies?

Although we can fill journals with details about galaxies, an astronomer cannot really answer these three basic questions with any confidence.

Abstract. Recent progress in understanding four processes that play a large role in the evolution of clusters of galaxies is reviewed. These are dynamical friction, mergers, collisional tidal stripping and the cluster mean field tide. Recent estimates for the growth rate of the cD galaxy and its frequency of appearance are discussed. In spherical relaxed clusters the theoretical and observational results for the accretion rate of a central massive galaxy seem to be quite consistent. It appears that a major part of the cD formation must occur in subclusters. Recent work on the formation of clusters containing galaxies and dark matter suggests that considerable mass segregation occurs in small subclusters (provided clusters form in a bottom up manner). This appears to be a result of dynamical friction. It may imply that visible clusters are embedded in large dark matter halos and that cluster M/L's have been underestimated.

INTRODUCTION

Clusters of galaxies represent a fascinating, if formidable, challenge for the theorist. Although relatively young in terms of their crossing times (Tcr = R/v), the galaxies are sufficiently large and massive that they interact with each other and the intracluster medium on a timescale comparable to their ages. A sensible way to organize a report on this complicated subject is, by analogy with stellar structure, to report first on the detailed processes which may occur (the ‘hydrodyamics’ and atomic ‘physics’ of the problem) and then to examine the effects of these processes (the analog of ‘evolution’) on the galaxies and the cluster.

Clusters of galaxies are probably the largest gravitationally bound entities in the universe. They offer a laboratory for studying such diverse astrophysical problems as the form of the initial fluctuation spectrum, the evolution and formation of galaxies, environmental effects on galaxies, and the nature and quantity of dark matter in the universe, as well as providing tracers of the large-scale structure. The view that clusters are dynamically relaxed systems has been challenged by the demonstration of significant substructure in the galaxy and X-ray distribution within clusters (see the chapters herein by Geller, Cavaliere & Colafrancesco, Fitchett, Richstone, and Forman). There is, however, still some dissent on the reality of subclustering (see the discussion in West's chapter). New simulations of the formation and evolution of the dark matter and gas distributions in clusters are giving interesting results—their confrontation with observations may yield information on the nature of the initial density fluctuations required to form galaxies and enable us to solve some of the problems in this field (e.g., the so-called “β–discrepancy”). The simulations should also allow for better comparisons between theory and optical and X-ray observations (see the chapters by Cavaliere & Colafrancesco, Evrard and West). The abundance and velocity dispersions of rich clusters, and measurements of their clustering properties and peculiar motions may provide strong constraints on theories of galaxy formation (see the chapters by Kaiser, Peebles and West).

Abstract. N-body simulations of the formation of clusters of galaxies allow a detailed, quantitative comparison of theory with observations, from which one can begin to address two fundamental and related questions:

INTRODUCTION

A wide range of theories have been proposed to explain the origin of galaxies, clusters of galaxies, and the large-scale structure of the universe. Broadly speaking, these can be divided into two classes. Most currently popular models for the formation of structure in the universe are based on the idea of gravitational instability in an expanding universe, in which it is assumed that structure has grown gravitationally from small-amplitude, Gaussian primordial density fluctuations. A second class of cosmogonic scenarios, which will be referred to here as non-Gaussian models, appeal to other processes besides simple gravitational clustering as the driving force behind the genesis of structure.

Within the basic framework of the gravitational instability picture, there are several rival theoretical scenarios that are viable at present. Depending on the the details of the cosmological initial conditions and dominant mass component of the universe, the sequence of formation of structure may have proceeded in quite different ways. If, for instance, the universe is dominated by weakly interacting, non-baryonic particles (i.e., cold dark matter, hereafter CDM) then the formation of structure is expected to proceed hierarchically from small to large scales, with galaxy and cluster formation preceding the collapse of superclusters.

Abstract. A program is proposed for future optical research on clusters of galaxies. This program includes detailed studies of the internal properties of clusters, the connection between clusters and their environment, and the role of clusters in the study of large-scale structure. It is argued that a digital all-sky survey can be feasibly made with a small telescope and a CCD camera, for studies of nearby and intermediate redshift clusters.

INTRODUCTION

Well, we have now heard and seen a large variety of papers on the properties of clusters of galaxies covering topics which range from determining some of their simple “internal” properties, such as dynamical age and mass, through their use as probes of the large-scale-structure of the Universe. Hearing these, it is quite obvious to me that our knowledge of clusters and their place in the Universe has increased tremendously in the last decade—including what some may call a few backward steps with the realization that many, if not most, clusters are dynamically quite complex and probably “young.”

I have been fortunately given the easy task of describing where to go next—always a lot of fun when you have both found out what you don't know and are preparing many new marvelous tools, like the Hubble Space Telescope and suites of new 8-meter class and survey telescopes, with which to attack the problem.

Abstract. Distant clusters provide ideal samples of galaxies in more-or-less standard environments in which to study the evolution of the galaxies themselves, bound structures, the larger-scale environment, and perhaps eventually to provide data for the classical cosmological tests. We review some of the the observational and theoretical aspects of these topics.

INTRODUCTION

Clusters of galaxies at large redshifts provide, in principle, a set of objects whose evolution can be traced directly from epochs as early as z ≈ 1 with present observational capabilities to the present. It seems almost inconceivable that large clusters are destroyed, and although it is quite clear that clusters are still forming, the inner regions of dense clusters must be quite old. Thus if one looks at galaxies in such regions and takes care to sample clusters whose comoving space densities are roughly the same at all epochs, it would seem as if one could define a quite homogeneous sample of galaxies in which the direct forbears of a set of present-day objects could be studied. We are not quite in a position to do that because the cluster catalogs are in such a sad state, but some progress is being made in this direction; we will discuss this at greater length below.

If one could choose clusters at epochs from the present back to large redshifts in some objective way, it would also be possible to study the evolution of the cluster population itself.

While variable star observing is a specialized branch of observational astronomy, the basic procedures of patience and care that apply to all observing also work with variables.

Plan your program in advance, but be flexible, since the sky often offers surprises. Choose your variable carefully. Is the star likely to be visible through your telescope, or is it obviously too faint? At the other extreme, is your star so bright that observing it is a waste of your precious telescope time?

Telescope

Telescope size

This is more of a consideration than most observers realize. In a sense, each variable star has its own best combination of telescope and eyepiece. The general rule is to use only enough power and magnification to see the variable clearly but not have it so bright that it is hard to estimate. Ideally, the variable should be about two magnitudes brighter than the faintest star you can see with your telescope. If it is much fainter than that, you will have a problem of perceiving the star, and if the variable is several magnitudes brighter, so many photons will enter your eye that its sensitivity to subtle magnitude variations will be affected.

At minimum, a star might be fair game for most telescopes smaller than 30 cm (12 inches), but as the star brightens you could use a smaller telescope. (When discussing a telescope size, I refer to the size of the mirror or objective lens.)

Buried deep in the richest part of the winter sky is the magnificent constellation of Orion the Hunter, a group of stars that have a closer relationship than the chance positioning of most constellations. Except for Betelgeuse, most of the bright stars in Orion are roughly the same distance from us. Orion is far more than just a place in the sky, named for a figure from mythology. Orion is a cosmic production plant, whose different divisions show us how stars are made.

The process of star formation is very complicated, but here we can see how it takes place. Young stars in the belt of Orion represent a group of stellar children whose formation is essentially complete. The sword area is a cosmic nursery with some of the stars being less than a million years old. Some astronomers suspect that the area south of the sword, with its hydrogen-rich regions, given another several million years, will coalesce to produce new stars.

In the area where stars are in the process of birth, the highlight is M42, the Orion nebula. The darker your sky, the greater the thrill of such a sight. Here is a nebula whose visual appearance is stunning, whose delicate patterns are exquisite. With a 10 cm (4 inch) telescope, you can make out the beginnings of the complex light and dark gases that share the nebula.

Through the magic of variable stars you now have passed through a looking glass. You have discovered stars passing through the eruptions and inconsistencies of youth and you have visited and drawn comfort from the cosmic wisdom of the aged Mira stars. You have watched the dwarf novae perform and you have looked on as old novae sleep peacefully as the eons after their outbursts pass by.

You passed through the looking glass in a mood of curiosity and I hope you return unsatisfied, demanding more. Through the bibliography, I have suggested certain sources that may help, but the most important source of all is that of the glass of your telescope coupled to the retina of your eye and connected by optic nerve to an inquiring mind searching for answers. Every year new variables are discovered and much more is learned about how these stars behave.

Quite possibly your own observations may add to this knowledge. Possibly also, you will want to pass this on to someone younger.

In the nature of variable stars lies a key to introducing children to astronomy. Stars are individual, they behave in definite ways. They are born, they grow up, they mature, they grow old, and they die. Stars also have moods — sometimes their light output changes. When a star is young it might flicker with the intensity of a rebellious child, unable to decide on its future course.

Variable star astronomy is one field in which an amateur astronomer can still make significant contributions to science. Regardless of the optical tool used, whether it is the naked eye, binoculars, a small or a large telescope, any lover of the stars can play an important role in our understanding of variable stars.

David Levy is truly a lover of stars. He is an avid observer and a discoverer of four comets, the second one found only forty minutes after he finished the final draft of this book! I have known David for over a decade as a member of the AAVSO and as a friend. His enthusiasm and his exuberance for astronomy has always impressed me. When David talks about variable stars, it is as if he is talking about his friends; they are not just stellar objects.

David is keenly aware of the difficulties that a new variable star observer faces. He knows well that, in the beginning, locating variables and estimating their brightnesses takes lots of patience and perseverance. He also knows the joy one feels in making variable star observations. Therefore, he makes every effort to find ways to get his reader interested in variable stars, and to make that first brightness estimate. He helps his reader to find out more about the sky, the wonderful seasonal progression of its appearance, about astronomy as it applies to variable stars, and finally more about the different types of variable stars and the individual members of each type.

Probably

Ask your friend. Especially if by now you are an avid variable star observer, the answer will be yes! So let's take advantage of the situation and perambulate amongst two of the most unusual objects in our corner of the universe, 041619 T Tauri, and 155037 RU Lupi, two stars that represent the carefree conduct of cosmic youth. Both stars are irregular variables and represent stars that are observed in clouds of gas called diffuse nebulae.

T Tauri

Let's begin with T Tauri, the easier of the two, a star that can be watched easily from northern latitudes in the frigid evenings of winter.

If you can find the Hyades, you can find T Tauri. Moving from Delta to 64 Tauri to 4th magnitude 68 Tauri, you proceed to the northeast until you reach Epsilon Tauri, a 3.6 magnitude star (Fig. 20.1). Slightly to the southwest of Epsilon is a group of four stars in the shape of a malformed kite. I use this group as a guide to T Tauri.

Notice the magnitude range of 9.3 to 13.5; I have observed T Tauri for several years and I have never once seen it go fainter than magnitude 10.6 nor brighter than the mid 9's. Most observers have reported it hovering just brighter than 10th magnitude.

But that's only part of the story. T Tauri occasionally can flicker.