In the earlier chapters of this book, alongside the descriptions of observational hardware and techniques, I have tried to provide a picture of the Moon and of lunar science past and present. Necessarily this ‘picture’ has been painted with a rather broad brush. To really get to know the Moon, one must be prepared to examine it in finer detail. To that end, this chapter presents a selection of 48 specific features/areas of the Moon. Taken together, these provide a representative selection of the types of lunar formation one may encounter at the eyepiece of one's telescope.

Why the particular selection that follows? I can only say that this has been my personal choice. I have tried to cover the fullest possible range of lunar features. You will find descriptions of craters both grand and small, conventional and unusual in their profile. Mountains, valleys, domes, rilles (both sinuous and linear), mare flood-plains and other types of terrain are also described. In some of the sections broad areas are described. A few sections concentrate on particular features of special interest. Altogether, over two hundred named formations are examined. Many are the ‘old favourites’ of novice and experienced observers. Others are more ‘off the beaten track’. Sometimes I have provided detailed descriptions. Other times I have only provided sketchy details and leave you, the reader – and I hope the observer – to find out things for yourself.

Pulsation is the astronomer's word for vibration or oscillation. Every physical object has natural patterns or modes of vibration, each with a corresponding period – the time required for one vibration. We commonly observe this in musical instruments. A bugler can make the air column in a bugle vibrate in different modes or harmonics, with different periods which we perceive as different pitches. A violin string can vibrate in several pitches at once, producing a complex sound which may be pleasant or not, depending on the quality of the violin and the skill of the musician. It is tempting to call pulsation ‘the music of the spheres’, especially as most stars are spherical; the sun is spherical to 1 part in 100 000. This concept comes from an excellent recent review article on stellar pulsation, part of a conference in July 2005, and published in Communications in Asteroseismology, volume 147:

http://www.univie.ac.at/tops/CoAst/archive/cia147.pdf

Pulsation modes

Stars are, to a first approximation, spherical. The simplest form of pulsation is radial pulsation – a simple, spherically symmetric in-and-out expansion and contraction. A star has an infinite number of modes of radial pulsation. The simplest is called the fundamental mode. In this mode, all parts of the star expand together and contract together, in unison. The next-simplest mode is the first overtone. In this mode, there is a nodal sphere in the star, where the material remains at rest. When the part of the star outside this sphere is expanding, the part inside is contracting, and vice versa. In the second overtone mode, there are two nodal spheres, where the material remains at rest.

Sometime, far back in prehistory, people first began watching the sky. They must certainly have noted the daily and yearly motions of the sun, the waxing and waning of the moon, and perhaps even the wanderings of the planets. They might even have noted changes in the stars, not changes of position but changes of brightness. There are hundreds of these variable stars among the naked-eye stars, and the changes of some of them are so striking that they could not escape the notice of a careful eye.

Written records of skywatching begin in the Near East around 2000 BC, and in the Far East around 1000 BC. Unwritten records may also exist: paintings, rock and bone carvings, alignments of giant stones. The study of these has been called archaeoastronomy. The interpretation of any ancient records is a challenge to both the astronomer and the historian, and many interesting books and articles have been written on the topic.

The Babylonians laid the foundations of Western astronomy through their mathematics and through their systematic observations of the sun, moon, planets, and stars (albeit for astrological purposes). Babylonian astronomy was absorbed into Greek culture, where it eventually led to ‘models’ of the visible universe. In some schools of philosophy, these models were intended as mathematical conveniences, designed only to represent or predict solar, lunar, or planetary motions. In other schools, these models took on wider significance: they were intended to represent physical reality. Aristotle (384–322 BC), for instance,

The roots of this book go back over forty years. As an undergraduate in 1960, I was exposed to the variable star research at the David Dunlap Observatory of the University of Toronto. Mentors such as Don Fernie, Jack Heard, and Helen Sawyer Hogg brought the field to life. As a graduate student, I sampled both theory (with Pierre Demarque) and observation (with Don Fernie). Then I was fortunate to obtain a faculty position at the University of Toronto's brand-new Erindale Campus in Mississauga, west of Toronto. I was concerned with teaching, supervising students, and building a new university campus.

My research continued, and my graduate teaching responsibility was a course on variable stars. This book evolved from that course. The 1970s were in many ways the ‘golden age’ of variable stars at the University of Toronto. A dozen graduate students undertook M.Sc. and/or Ph.D. these on variable stars. The David Dunlap Observatory, being a ‘local’ observatory under our control, enabled both large-scale surveys, and long-term studies to be carried out – both of which are almost impossible at modern-day national observatories. The observatory was equipped with both a 1.88m spectroscopic telescope, and 0.6m and 0.5m photometric telescopes, and many of these thesis projects combined these techniques in a very effective way. I learned much from these graduate students, and owe much to my colleagues, including a succession of Directors of the David Dunlap Observatory – who were also Chairs of the Department of Astronomy and Astrophysics.

All of the types of stars in this chapter could probably be fitted in, arbitrarily, elsewhere in this book. But they are not easily categorized, so we discuss them here – and admit that ‘pigeon-holding’ variable stars is not simple.

Be stars – Gamma Cassiopeiae variables

Be stars are defined as non-supergiant stars with temperatures between about 10 000K and 30 000K which have shown emission lines in their spectra on at least one occasion. As the definition suggests, the spectra of Be stars can vary with time (figure 9.1), as can their brightness. In the GCVS4, variable Be stars are known in most cases as Gamma Cassiopeiae (GCAS) variables, after the prototype, but others are arbitrarily classified as BE. About 20 per cent of B stars are Be stars and, because these stars are very luminous, there are about 200 of them among the 10 000 naked-eye stars. This makes them one of the most conspicuous classes of variables. See Percy (2001) for a brief review of Be stars, and Smith et al. (2000) for a recent conference proceedings. For current research information, the Be Star Newsletter, published by a working group of the IAU, is very useful:

http://www.astro.virginia.edu/˜dam3ma/benews/

The emission lines in the spectra of Be stars arise in a disc of gas around the star. One thing that distinguishes Be stars from normal B stars is their rapid rotation – typically up to 500 km s−1 at their equator. This reduces the effective gravity at the equator, and makes it easier for other processes, such as radiation pressure and possibly pulsation, to produce a slowly expanding, outwardly spiralling disc of gas above the equator.

AAVSO: American Association of Variable Star Observers

AGB: asymptotic giant branch (in the Hertzsprung–Russell diagram)

AGN: active galactic nucleus

ASAS: All-sky Automated Survey

AU: astronomical unit

BAA: British Astronomical Association

BC: bolometric correction

BV: Bamberg variable

CCD: charge-coupled device

CGRO: Compton Gamma-Ray Observatory (satellite)

CDS: Centre de Données astronomiques de Strasbourg

COROT: COnvection, ROtation, and planetary Transits (satellite)

CSV: Catalog of Suspected Variable Stars

CTTS: classical T Tauri stars

CV: cataclysmic variable

EUVE: Extreme Ultraviolet Explorer (satellite)

GAIA: Global Astrometric Interferometer for Astrophysics (satellite)

GALEX: GALaxy evolution EXplorer (satellite)

GCVS: General Catalogue of Variable Stars

GPB: Gravity Probe B (satellite)

GRB: gamma-ray burst

HC: heliocentric correction

HD: Henry Draper (catalogue);: HDE: HD Extension

H-R: Hertzsprung-Russell; H-R diagram;

HST: Hubble Space Telescope (satellite)

IAU: International Astronomical Union

IBVS: IAU Information Bulletin on Variable Stars

IR: infrared

IUE: International Ultraviolet Explorer (satellite)

JD: Julian Date

LMC: Large Magellanic Cloud (galaxy)

L∩: solar luminosity - 3.85 x 1026 Watts

MACHO: MAssive Compact Halo Object (also project of this name)

MOST: Microvariability and Oscillations of STars (satellite)

M∩: solar mass - 1.9891 x 1030 kg

NASA: National Aeronautics and Space Administration (US)

NSF: National Science Foundation (US)

NSV: New Catalog of Suspected Variable Stars

O - C: observed - computed (method)

OGLE: Optical Gravitational Lensing Experiment

PL: period–luminosity (relation)

PMS: pre-main sequence

RA: right ascension; Dec.: declination

RASNZ: Royal Astronomical Society of New Zealand ROSAT: Röntgen Satellite

Eruptive variables are considered to include any variables which flare up relatively quickly, and fade more slowly. They include flare stars which brighten in seconds, and some types of novae and symbiotic stars which may take months or even years to brighten. This class sometimes even includes R Coronae Borealis stars, which are the inverse of eruptive variables! In the GCVS4, this class includes many types of pre-main sequence stars, and also S Doradus, Gamma Cassiopeiae, and erupting Wolf-Rayet stars. In eruptive variables, there is generally a sudden input of energy into a star, or part of a star, and we see the star's response – a violent outburst.

Flare stars

Flare stars, also known as UV Ceti stars, are dwarf K and M stars (mostly the latter) which randomly and unpredictably increase in brightness within seconds to minutes, by up to several magnitudes, then slowly return to normal (figures 7.1, 7.2). In the GCVS4 they are classified as UV, or UVN if they are associated with pre-main sequence stars, or RS if they occur in an RS Canum Venaticorum binary system. These flares are qualitatively similar to those on the sun. The flares are one aspect of activity on these stars; emission lines in both the visible and ultraviolet spectra, and X-ray emission from a hot (up to 10 000 000 K) corona are others. So flare stars are generally classified as dMe, the ‘e’ referring to the presence of emission lines in the spectrum. Some flare stars are also BY Draconis variables (section 4.5); this is yet another manifestation of their activity.

Although a substantial fraction of stars belong to binary or multiple star systems, most of these are wide binaries; the average separation of the stars is tens or hundreds of times greater than the average distance of the earth from the sun. These are usually seen as visual binaries, if they are nearby. They are not usually variable in brightness for geometric reasons, because, with such large separations, they are unlikely to eclipse as seen from the earth, or to influence each other. Close binary stars, however, are usually variable in some way. That is because the probability of an eclipse is greater, for geometric reasons. And the degree of physical interaction is much greater.

Normally, close binaries will not be visual binaries, but techniques such as optical interferometry and adaptive optics will gradually enable astronomers to ‘see’ the two components of some close binaries. Visual binaries, spectroscopic binaries, and eclipsing binaries will increasingly overlap.

For an excellent introduction to close binary stars, see Hilditch (2001).

Overview

Eclipsing variables (figure 5.1) are binary stars in which the observer sees the orbit almost edge-on. One star periodically eclipses the other and, at these times, the total brightness of the pair decreases. The brightness change is a geometrical effect; there is not necessarily any physical or intrinsic change in the stars. (In close binary stars, however, there may be.)

Binary stars are of interest for several reasons. First of all, at least half of all stars are binary or multiple stars, so they are a normal occurrence in our universe.

Variable stars and astronomical research

Throughout this book, we have described the basics of variable star astronomy, the many ways in which variable stars have increased our understanding of the universe, the frontier areas of this field, and the questions that remain. What part will variable stars play in astronomical research in the next generation? Here are a few possibilities:

• The sun is the nearest and most important star, because its energy output and its activity both affect the earth, and life on it. It may be ‘average’ and relatively benign, but the nature and cause of its activity are still poorly understood. Study of other sun-like stars will continue to help.

• Sky surveys will continue to expand in terms of depth and continuity of coverage, turning up rare stars which are ‘Rosetta stones’ for understanding the processes which occur in stars.

• Continued studies of pulsars – especially binary pulsars – will provide unique information about the laws of physics which apply in the most extreme environments in the universe.

• Optical interferometry and the GAIA astrometric satellite will usher in a new era in ‘precision astrophysics’ by measuring the physical properties of stars to better than 1 per cent.

• Asteroseismological satellites such as MOST and COROT will provide stringent tests of theories of the structure and evolution of stars.

• Faint, distant supernovae will lead to a better understanding of the nature of dark energy.

In section 2.19, we outlined what was presently known about star formation, and the early evolution of stars. There are several types of variability which are specifically or predominantly found among young stars. Most or all of these would be found in a given star, such as the sun, at various times in its pre-main-sequence (PMS) lifetime. We must always remember that the universe we see is a snapshot of millions of stars, seen at various random stages of their evolution. The PMS stage lasts only a few million years, so stars spend only a small fraction of their lifetime in it. But every star passes through this stage once.

PMS variables are often called nebular variables, because, being young, they are usually found in or near the nebulae from which stars are born. Or they may be called Orion population because the Orion region is a nearby, active site of star formation. One of the challenges in studying these stars is the fact that they are usually found within clouds of gas and dust, which will obscure or hide them at visible wavelengths. Radio observations have therefore been useful, and new sub-millimeter and mid-IR facilities such as the Atacama Large Millimeter Array and the James Webb Space Telescope, respectively, will be ideally suited for studying star formation.

A PMS star could also be an eclipsing or rotating variable, if it had a close companion, or a spotted surface. It could even be a pulsating variable, if it was located in an instability strip. We shall concentrate here on types of objects, and of variability, which are unique to PMS stars.

Only in theory are stars bland, featureless spheres. In the case of the sun, we can directly observe its complex, ever-changing surface – sunspots, flares, magnetic fields, low-level pulsation, and seething convection cells – bubbles of rising and falling gas. On other stars, we cannot ‘see’ the appearance, but we can deduce it.

As the star rotates, regions of different brightness (and colour, and magnetic field strength, and other properties) will pass into the observer's field of view, and these properties will appear to vary. The period of variation is the period of rotation. Since all stars rotate, any star with a patchy surface will be a rotating variable, unless the patches are symmetrical about the axis of rotation, or unless the axis of rotation points at the observer. The variations will be both photometric and spectroscopic.

What causes a star to have a patchy surface? Rotation itself causes a star to be slightly oblate, and to be slightly cooler at the equator and hotter at the poles. But this effect is symmetric about the axis of rotation. A binary companion can cause patches: it distorts the star, and causes ‘gravity darkening’ and a reflection effect; this is discussed in section 5.4.6. Ellipsoidal variables are sometimes considered to be rotating variables. In this case, a star is distorted into an egg shape by the tidal gravitational effect of a companion star. The axis of the ‘egg’ points to the companion, and appears to rotate as the star orbits the centre of mass of the system.

Variable stars are stars, first of all. They can be studied and understood in the same way as non-variable stars, except that they have the advantage that they can ‘talk’ to us through their variability. If we can understand their language, then we can learn more about them than we can about non-variable stars. All of this information comes through ‘the message of light’ (and its relatives). We measure the direction, intensity, wavelength, and polarization of the light from the stars. In this chapter, we will describe how astronomers can understand stars through observation and theory. This is a collaboration between those who build the instruments that astronomers use, the observers who use them, the theoreticians who develop the laws of physics and astrophysics, and those who use modelling and simulation to apply those laws to real stars.

For an excellent introduction to all aspects of stars, see the monograph by Kaler (1997), and Kaler's website:

http://www.uiuc.edu/˜kaler/sow/sow.html

Another option is to consult one of the many introductory astronomy textbooks which are designed for university students. Some of these textbooks are divided into two volumes, one being on stars and galaxies.

Positions

Stars seem fixed to the celestial sphere, as it appears to revolve around the earth in its daily motion. The position of a star is given by its declination and right ascension, which are analogous to latitude and longitude on earth. The declination is the angular distance of the star north or south of the celestial equator, which is the projection of the earth's equator on to the sky.