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.

Learning to see is the most important skill in all visual observing, and variable star observing provides very good training in seeing. Quickly, without looking up, describe to yourself in detail the wall behind you. How are the pictures arranged? Which are colored? Where is every lamp outlet? Think of all else that is relevant.

Chances are you may have had difficulty remembering everything, but if you are alert you can train your mind to observe closely these common scenes and remember them. If you have trouble visualizing what is on the wall in your room, will you have better luck with a field of stars in space?

Let's carry this a step further. Suppose you've just walked into your friend's house, and all of a sudden the lights flash on and 15 people yell “Surprise!” Do you think you might have an easier time remembering who was there and where each was standing? Apparently, when the unusual happens, it causes your mind to snap into an increased state of sensitivity. Your mind is capable of increased observational skill when it concentrates. Your mind and eye will be very important in your career as an observer.

Seeing is an art to be developed, a beautiful capability within you that must be nurtured and cultivated. When it blossoms, the quality of your observations, whether they involve describing the wall of your room or the brightness of a star, will increase dramatically.

Just to get an idea of what variable star observing is all about, here are two active, easily found stars that we will observe informally, before we know too much. The first is Delta Cephei, an ideal star to begin with for several reasons. It is part of a bright and compact star group, it is usually around magnitude 4, and it is an active star, always offering something interesting for you to watch.

Delta Cephei's variation was discovered by John Goodricke in 1784 (see chapter 30), and it is the star for which all the Cepheid variables are named. The variation in this giant star is small but extremely regular with a period of several days. It is also typical that this star enjoys a leisurely decline to minimum that is followed by a rapid rise to maximum.

At maximum, Delta Cephei is easily visible at magnitude 3.5, and at minimum it shines at 4.4. If you observe every night or two you will soon see how it falls, then rises, week after week.

Notice the two stars Zeta and Epsilon on Fig. 6.1 and in the sky. Which is brighter? Let us give Zeta Cephei an arbitrary value of “1” and Epsilon a value of “5”. Each night estimate the brightness of Delta Cephei as follows:

1. 1 — as bright as Zeta

2. 2 — slightly fainter than Zeta

3. 3 — halfway between Zeta and Epsilon

4. 4 — slightly brighter than Epsilon

What else does the sky have that varies? Besides stars, there are other objects worth noting. Some are easily visible, and others are beyond the reach of all but the most powerful telescopes and detectors. They range in distance from a few million kilometres to billions of light years.

Variable nebulae

In the constellation of Monoceros is a variable star called R. It varies irregularly by about half a magnitude around 11. However, the star is usually very hard to see. The reason is that it is embedded in a nebula which also varies in brightness! This object is known as Hubble's variable nebula, NGC 2261, after the Mount Wilson astronomer who in 1916 discovered that it varies in brightness, size, and even shape. The variation does not seem to follow the brightness changes in R Mon, and they do not occur with any regularity.

R Monocerotis and its nebula probably represent a planetary system in an early stage of formation. At least two other variable nebulae are known, NGC 1555 in Taurus, and a tiny wisp in Corona Austrina, NGC 6729, the home of R Coronae Austrinae. (See p. 151.)

Active galaxies

Innocently displaying some irregular brightness changes are a number of objects that have recently been identified as the cores of galaxies. The Seyfert galaxies are spiral galaxies with starlike nuclei that are very bright and slightly variable.

As this season opens, the excitement of Orion is now at our disposal in the early evening. R Leonis is a fine star, and then you can move your thoughts and your telescope to RY Leonis, a long period star that is easy to find.

Next, move over to the Big Dipper region, to a small region that houses the “Dipper Trio”. It consists of two long period variables, T and RS Ursae Majoris, with closely matched periods, and S UMa with a shorter period but altogether a brighter star. Spring also offers perhaps the most unusual dwarf nova of all, Z Camelopardalis, a star whose exploding fluctuations are often interrupted by standstills.

Lynx

072046 Y Lyncis. Red and bright, this semiregular has a half magnitude range from 7.2 to 7.8 and a possible but imperfectly defined period of about 110 days. To find this star with your binoculars, go about 13 degrees east of Beta Aurigae. Difficult to follow usefully because of its small range. Observe it only once a month, no Moon, constant observing conditions from one observation to another, same pair of binoculars, and watch out for the Purkinje effect. The more you keep observing conditions constant, the more accurate your Y Lyn picture will be. Level 2.

061359 U Lyncis. Mira star. Range 9.5–14.4; period 436 days. Level 3.

This part of the book contains stars that have not been described in earlier chapters. It is intended to help you plan an observing program by introducing you to a selection of interesting variable stars. By reading through these chapters, you should find some stars that you will enjoy watching. The finder charts are intended to help in finding the location of a variable star. Once you have decided on a program, I suggest that you order a complete set of charts for each star you choose and be careful to plan in advance the best time and equipment for observing them. The order in which the different constellations are presented in each chapter represents a vague and somewhat arbitrary eastward movement across the sky.

For each star, I have included the range, period and a code that specifies level of difficulty:

1. 1 = very easily found and estimated

2. 2 = a good star for beginners

3. 3 = some challenge, either in finding or in estimating

4. 4 = quite difficult

5. 5 = recommended only for advanced observers with larger instruments

Different sources provide different values for maxima, minima, and ranges of many variable stars, especially those with uncertain variations. In most cases I have used the values given in the General Catalogue of Variable Stars by B. V. Kukarkin et al., Fourth Edition.

This season is variable time, with a cast of variables probably better than at any other time during the year. We still have the fine variables of the Milky Way, while toward the east, a different group of variables is gaining prominence.

This is also the time to get your fellow astronomy club members excited about the challenging field of variables. Fall is the time for renewal in many northern hemisphere astronomy clubs, where after the summer break, monthly programs and dark-of-the-Moon star parties are taking place once again. If you are fanatical about variables, you may be aware that this field of observing is not the most popular among the amateurs who attend astronomy club meetings. Observations of the changing light output of these distant suns are perceived to lack the luster of the Messier hunt or the glossy galaxy photo, and even the thrill of the meteor watch. Now is the time to insist that variables are fun.

Now we can observe Algol in all its glory, and use it as a motivation to start observing other eclipsing binaries. Two other easily found, easily observed stars are Delta Cephei, and its neighbor Mu Cephei, a huge red giant sun with totally irregular and unpredictable variations.

Another exciting star is RU Pegasi, a dwarf nova. You never know exactly when the next outburst will take place! While RU Peg may be one of the most exciting stars of fall, it surely is not the most famous.