APPENDIX A Astronomical Terminology

A: 1 Introduction

When we disco ver a new type of astronomical entity on an optical image of the or in a -astronomical record, we refer to it as a new object. It need not be astar. It might be a , a , or perhaps a of interstellar . The word "object" is convenient because it allows us to discuss the entity before its true character is established. seeks to provide an accurate description of all natural objects beyond the 's . From to time the of an object may change, or its might become altered, or else it might go through some other kind oftransition. We then talk about the occurence of an event. attempts to explain the sequence of events that mark the of astronomical objects. A great variety of different objects populate the . Three ofthese concern us most immediately in everyday : The that our atmosphere during the and establishes the moderate needed for the existence oflife, the Earth that forms our habitat, and the that occasionally lights the sky. Fainter, but far more numerous, are the that we can only see after the Sun has set. The objects we detect can be divided into two groups. Many ofthem are faint, and we would not be able to see them if they were not very close to the Sun; others are bright, but at much larger . The first of objects, taken together with the Sun, comprise the . They form a gravitationally bound group orbiting a common center of . Within the Solar System the Sun itself is of greatest astronomical interest in many ways. It is the one that we can study in great detail and at close range. Ultimately it may reveal precisely what nuclear processes take place in its center and just how a star derives its . Complementing such , the study of , , and 576 Appendix A

may ultimately reveal the ofthe Solar System and the origins oflife. Both of these are fascinating problems.

A:2 The Sun

The Sun is a star. Stars are luminous bodies whose range from about 1032 to 1035 g. Their in the visual part ofthe spectrum normally lies in the range between 10-4 and 104 the Sun's energy outflow. The surface temperatures of these stars may range from no more than '" 1, 000 K to about 50,000 K. Just how we can determine the relative brightness of stars will be seen later in this Appendix. The determination oftemperatures is discussed in Chapter 4. The Sun, viewed as astar, has the following features: (a) Its radius is 6.96 x 10 10 cm. Although occasional prominences jut out from the solar surface, its basic shape is spherical. The equatorial radius is only a fractional amount larger than the polar radius: [(req - rpoI)/r] ~ 6 X 10-6 (Di86). (b) The Sun emits a total of3.9 x 1033 erg S-I. Nearly half ofthis is visible, but an appreciable fraction of the power is emitted in the near and near parts ofthe spectrum. Solar X-ray and radio emission make only slight contributions to the totalluminosity. (c) The Sun's mass is 1.99 x 1033 g. (d) Three principal layers make up the Sun's atmosphere. They are the , , and corona. (i) The photosphere is the layer from which the Sun's visible emanates. It has a of ab out 6,000 K. (ii) The chromosphere is a layer some ten to fifteen thousand kilometers thick. It separates the relatively cool photosphere from the far hotter corona. (iii) The corona extends from 1.03 R0 , or about 20,000 km above the photo• sphere, out to at least several solar radii. The outer boundary has not been defined. The corona is not a static structure; its outer edge merges continuously into the interplanetary that streams outward from the Sun at of several hundred kilometers per . This streaming, ionized gas, mainly and , is called the solar . The temperature of the corona is '" 1.5 x 106 K. (e) and groups, cool regions on the solar surface, move with the Sun as it rotates, and allow us to determine a 27 -day period. This period is only an apparent rotation rate as viewed from the Earth which itself the Sun. The actual with respect to the is only about 25! days at a of 15 0 and varies slightly with latitude; the solar surface does not rotate as asolid shell. The Sun exhibits an II- during which time the number of sunspots increases to a maximum and then declines to a minimum. At minimum the number of spots on the Sun may be as low as zero. At maximum the number of individual sunspots or members of a sunspot group mayamount to 150. There are special ways of counting to arrive at this sunspot number and a continuous record is kept through the collaborative effort of a number of . A:3 The Solar System 577

The ll-year cycle is actually only half of a longer 22-year cycle that takes into account the polarity and arrangement of magnetic fields in sunspot pairs. (f) A variety of different events can take place on the Sun. Each type has a name of its own. One of the most interesting is a jlare, a brief burst of light near a sunspot group. Associated with the visible flare is the emission of solar , X -rays, ultraviolet radiation, and radio . Flares are also associated with the emission of of electrons and protons that constitute a large component added to the normal . After a day or two, required for the Sun-to-Earth at a of'" 10 3 km S-1 , these particles can impinge on the Earth's ( and ), giving rise to magnetic and aurorae. These disturbances tend to corrugate the ionosphere and make it difficult to reflect radio waves smoothly. Since radio depends on smooth, continuous ionospheric , reliable radio communication is sometimes disrupted for as long as a day during such magnetic storms.

A:3 The Solar System

A variety of different objects the Sun. Together they make up the Solar System (Fig. A.l). The Earth is representative ofplanetary objects. Planets are large bodies orbiting the Sun. They are seen primarily by reflected . The majority emit hardly any radiation by themselves. In order of increasing from the Sun, the planets are , , Earth, , , , , , and . All the planets orbit the Sun in one direction; this direction is called direct. Bodies moving in the opposite direction are said to have retrograde orbits. Table 1.3 gives same of the more important data ab out planets. It shows that the different planets are characterized by a wide range of , surface temperature and , magnetic field strength, and other properties. One of the aims of astrophysics is to understand such differences, perhaps in terms of the history of the solar system. Besides the nine planets we have listed, there are many more minor planets, or , orbiting the Sun. Most ofthem travel along paths lying between the orbits of Mars and Jupiter, a region known as the asteroidal belt. The largest is . Its radius is 350 km. Its mass is about one ten-thousandth that ofEarth. A number ofobjects collectively known as Centaurs are intermediate in between typical comets and small icy planets or planetary . They have short-lived orbits intermingled with those ofthe outer planets. Their are estimated at 30 to 200 km and they appear to be drawn from the Kuiper beft, a region beyond the outer planets inhabited by perhaps a hundred thousand objects with diameters greater than 100 km and orbits between 50 and 100 AU. Discovered as the first ofthis group in 1992, is 1992QB1, with a diameter of 180 km and a stable, nearly about the Sun, some 14 AU beyond Neptune. More recently a number of comets have also been discovered at these distances, and 578 Appendix A

90· I

FIGURE A.l. Cornparison of planetary, asteroidal, and short-period cornetary orbits. Al• though the Earth, Mars, and Jupiter have nearly circular orbits, the orbits of asteroids, , Hermes, Eros, Apollo, Kepler, and Hidalgo are appreciably eccentric, as are those ofcornets Encke, Pons--Winnecke, Ternpel-Swift, Whippie, Tuttle--Giacobini-Kresak, and Biela. Cornets are narned after their discoverers. Many cornets and asteroids have aphelion distances near Jupiter's orbit, and Jupiter has a controlling infiuence on the shape of the orbits and rnay have "captured" cornets frorn parabolic orbits into short-period orbits. estimates suggest that the may contain several hundred million to a billion smaller cometary bodies (St96). Many of the smaller known asteroids, whose orbits lie mainly between Mars and Jupiter, have diameters of the order of a kilometer. These objects number A:3 The Solar System 579 in the thousands and there must be many more orbiting masses that are too small to have been observed. Among these are bodies that might only be a few meters in diameter or smaller. From time to time, some of these approach the Earth and survive the journey through the atmosphere. Such an object that actu• ally impacts on the Earth's surface is called a . Meteorites are studied with great interest because they are a direct means of learning about the physi• cal and chemical history of at least a small class of extraterrestrial Solar-System objects. Even smaller than the meteorites are grains of that also the Sun along orbits similar to those of planets. When a dust grain enters the atmosphere, much of it may burn, through heat generated by friction and its high initial . The becomes luminous through and can be observed as a meteor, historically called a shooting star. In contrast to meteoritic material, meteoric matter does not generally reach the Earth's surface in recognizable form. However, some fragments do appear to survive and are believed to contribute to a shower offine dust that continually rains down on the Earth. Most ofthis dust has a micrometeoritic origin. are micron- or submicron-sized grains of interplanetary origin that drift down through the atmosphere and impinge on the Earth's surface. They have a large surface-to- and are easily slowed down in the upper atmosphere without becoming excessively hot. Once they have lost speed they gradually drift down through the air. Some of these grains may be formed in the burn-up of larger meteors; others may come in unchanged from interplanetary space. Collections of these grains can be made from the arctic snows or deep ocean sediments, far from sources of industrial smoke. The identification of this extraterrestrial mass is not simple. It is difficult to distinguish meteoritic matter from dust generated in, say, volcanic explosions. Some researchers have claimed that the amount of material deposited on the Earth each day is ofthe order ofseveral tons, though the bulk ofthis is thought to lie in asteroidal impacts occurring only once in a few million . A cloud of micrometeoritic dust exists in the space between the planets and possibly also as a tenuous dust belt about the Earth. The dust reflects sunlight and gives rise to a glow known as the . The zodiacallight can be seen, on very clear days, as a tongue-shaped glow jutting up over the western after or the eastern horizon before . The glow is concentrated about the , the plane in which the Earth orbits the Sun. Interplanetary dust grains can also be detected on impact on interplanetary space probes. We recognize that these planetary and interplanetary objects continually interact. Planets and their satellites have often collided with asteroids. The surfaces of Mercury, the Moon, and asteroids, are pockmarked by impact craters. The Earth too shows vestiges of such bombardment; but our atmosphere erodes away and destroys outlines in a time ofthe order ofseveral million years, whereas on the Moon times are of the order of billions of years. A giant asteroid is believed to have collided with the Earth about 4.5 ago, tearing out a big chunk that became the Moon. The impacts of this and other large asteroids 580 Appendix A may have led to great climatic changes and the of wide-ranging forms oflife. We should notice that in talking about planets, meteorites, meteors, and microm• eteoritic dust grains we are enumerating different-sized members of an otherwise homogeneous group. The major difference between these objects is their size. Other differences can be directly related to size. For example, it is clear that plan• ets may have while micrometeorites do not. But this difference arises because only massive objects can retain a surrounding blanket of gas. The grav• itational attraction of small grains just is not strong enough to retain at temperatures encountered in interplanetary space. The different names, given to these different-sized objects, have arisen because they were initially discovered by a variety of different techniques; and although we have known the planets, meteorites, meteors, and other interplanetary objects for a long time, we have just recently come to understand their origin and interrelation. A set of objects similar to the planets are the satellites or . A orbits about its parent planet and these two objects together orbit ab out the Sun. In physical makeup and size, satellites are not markedly different from planets. The planet Mercury is only four times as massive as our Moon. , one of Jupiter's satellites, , one ofSatum's satellites, and , one ofNeptune's satellites, all are neady twice as massive as the Moon. Titan even has an atmosphere. Many other satellites are less massive; they look very much like asteroids. An extreme of the moon phenomenon is provided by the rings of Satum, Jupiter, and Uranus, consisting of clouds of fine dust - micrometeoritic grains, all orbiting the parent planet like minute interacting moons. Evidently there are great physical similarities between satellites and planetary objects of comparable size. The main difference lies in the orbital motion of the two classes of objects. It is interesting that an asteroid could be captured by Jupiter to become one of its satellites. The reverse process might also be possible. The somewhat vague distinction between planets and interplanetary objects is not unique. Differences between stars and planets are also somewhat vague. We talk about binaries in which two stars orbit about a common center of . Often one ofthese objects is much smaller than the other, sometimes no more than a few thousandths as massive. Jupiter has about one thousandth the mass of the Sun. Stars are bodies sufficiently massive to generate high temperatures and pres• sures in their interior, where nuclear reactions can convert into . Intermediate between giant planets and stars somewhat less massive than the Sun are brown dwarfs which, though not sufficiently massive to convert hydrogen into helium can, for a short period, gain energy through the conversion of , 7Li, and 3He, before settling down and radiating slowly through gravitational con• traction. The dividing line, below which conversion of hydrogen into helium is not possible, lies at 0.08 MG' This distinction in mass separates brown dwarfs from stars. The dividing line between planets and brown dwarfs lies at roughly 0.075 MG '" 75 M" where M J is themass ofJupiter. Belowthismass, the hydro• static pressure at a body's center is insufficient to overcome the Coulomb pressures A:4 Stellar Systems and 581 that normally prevent so lids from being compressed. Planet-sized bodies are not sufficiently massive to overcome Coulomb . Brown dwarfs do overcome these forces but are kept from indefinite collapse by degeneracy pressures discussed in Chapter 8 (Ku97a). We should still mention one final elass of objects belonging to the Solar System: the comets. Their orbits are neither strictly planetary, nor are they at all similar to those of satellites. Some comets have elliptic orbits about the Sun. Their periods may range from a few years to many hundreds ofyears. Other comets have nearly parabolic orbits and must be reaching the Sun from the far reaches of the Solar System. Comets are objects which, on approaching the Sun from large distances, disintegrate through solar heating: gases that initially were in a frozen state are evaporated off and dust grains originally held in place by these volatile substances become released. The dust and gas, respectively, are seen in refiected and re-emitted sunlight. They make the appear diffuse (Fig. A.2). Comet tails are produced when the freshly ionized gas and dust are repelled from the Sun, respectively, by the solar wind and by the pressure of sunlight. The dust from a comet tail produces a when the Earth passes through the remnants ofthe tail. The Solar System may contain as many as 10 11 comets, most ofthem in a giant eloud stretching into interstellar space but still gravitationally bound to the Sun. This is named after , the Dutch who originally proposed its existence.

A:4 Stellar Systems and Galaxies

Before we turn to a description of individual stars, we should first consider the groupings in which stars occur. Stars are often assembled in a number of characteristic configurations, and we elassify these systems primarily according to their size and appearance. Many stars are single. Others are accompanied by no more than one companion; such pairs are called binaries . Depending on their separation and , binary stars can be elassified as visual, spectroscopic, or eclipsing. The limit of visual resolution of a binary is given by available optical techniques. Refinements are continually being made, but interferometric techniques now allow us to resolve stars only milliarc• apart. For smaller separations, we cannot use interferometric techniques. The two stars in such a elose pair constitute a spectroscopic binary and have to be resolved indirectly by means of their differing spectra. We sometimes encounter a special but very important type of spectroscopic binary in which the stars orbit about each other roughly in a plane that contains the observer's line of sight. One star may then be seen eelipsing the other and a change in brightness is observed. An eelipse ofthis kind becomes probable only when the two companions are very elose together, no more than a few radii apart. We call such systems eclipsing binaries. Binaries are important because they provide the only means of deter- 582 Appendix A

(a) (b)

(e) (d)

(e) FlGURE A.2. (a) The , NGC 224, Messier 31, a spiral with two smaller eompanion galaxies, one ofwhieh, the elliptieal galaxy NGC 205, is shown enlarged (d). The barred (b) is NGC 1300. Its spiral classifieation is SBb. These three pietures were photographed at the Mount Wilson . The (e) is (M3), also known as NGC 5272. The eomet (e) is eomet Brooks, and the photograph was taken on Oetober 21, 1911. Only the region of the eomet around the head is shown. Photographs (e) and (e) were taken at the Liek Observatory. A:4 Stellar Systems and Galaxies 583

mining accurate mass values for stars (other than the Sun). How these masses are determined is shown in the discussion of orbital motions (Section 3:5). Close binaries are also important because if one of the two stars begins to expand, as it moves onto the -giant branch ofthe Hertzsprung-Russell diagram (Section A:5(g) and Figs. 1.4 and 1.6), the surface material may become more strongly attracted to the companion star. Ifthe companion is compact, the infalling material can radiate X-rays on impact. Portions of the previously in its interior are revealed. This allows us to check for systematic production of the heavy elements in the star and thus also to test the of chemical evolution and energy production in stars (Section 8: 13). Binary stars are not the only known close configurations. There exist many temaries consisting of three stars; and higher multiple systems are not uncommon. Perhaps one in every five "stars" shows evidence ofbeing a binary and about one in every 20 "stars" shows evidence ofbeing a higher-order system. For stars more massive than the Sun, these fractions are considerably higher; single stars occur only in one third of the observed cases. Sometimes stars form an aggregate ofhalf a dozen or a dozen members. This is called a stellar group. There also exist stellar associations that are groups of some 30 stars mutually receding from one another. Associations appear to have had a common point of origin in the past. They are thought to have been formed together and to have become separated shortly after formation. By observing the size ofthe association and the rate at which it is expanding, we can determine how long ago the expansion started and how old the stars must be. Two principal groupings are called clusters: galactic clusters and globular clus• ters. The galactic clusters usually comprise 50 to several hundred stars loosely and amorphously distributed but moving with a common velocity through the sur• rounding field of stars. In contrast, globular clusters (Fig. A.2) are much larger, containing several hundred thousand stars and having a very striking spherical (globular) appearance. Stars in a cluster appear to have had a common origin. We think they were formed during a relatively short time interval, long ago, and have had a common history. Clusters are not just populated by single stars. Binaries and higher multiples and groups of stars often form small subsystems in clusters. Normally stars and clusters are members of galaxies. These are more or less well-defined, characteristically shaped systems containing between 108 and 10 12 stars (Fig. A.2). Some galaxies appear elongated and are called elliptical or E galaxies. Highly elongated ellipticals are classed as E7 galaxies. If no can be detected and the galaxy has a circular appearance, it is called a globular galaxy and is classified as EO. Other numerals, between 0 and 7, indicate increasing apparent elongation. The observed elongation need not correspond direcdy to the actual elongation ofthe galaxy because the observer on Earth can only see a given galaxy in a fixed projection. Elliptical galaxies show no particular structure except that they are brightest in the center and appear less dense at the periphery. In contrast, spiral galaxies (S) and barred spiral galaxies (SB) show a strong spiral structure. These galaxies are denoted by a symbol 0, a, b, or c following the spiral designation to indicate 584 Appendix A increasing openness ofthe spiral arrns. In this notation, a compact spiral is desig• nated SO and a barred spiral with far-flung spiral arrns and quite open structure is designated SBc (see Figs. A.2 and 12.7(a).) Not all galaxies can be described by designations, E, S or SB. Some are more randomly shaped. Such galaxies are classified as irregular and designated by the symbol Ir. Peculiar galaxies of one kind or another are denoted by a letter p following the type designation, for example, E5p. Galaxies do not contain stars alone. In some spiral galaxies the total mass of interstellar gas and dust is comparable to the total observed. Dust clouds can be detected through their extinction, which obscures the view of more distant stars. Dust also absorbs optical and ultraviolet radiation and re-emits at long infrared . This process is so effective that some galaxies radiate far more strongly in the infrared than in all other spectral ranges combined. Gas also may be detected in absorption or through emission of radiation. Through spectroscopic studies in the radio, infrared, visible, ultraviolet, and X-ray domains of the spectrum, many , , and have been identified, and the temperature, , and ofsuch gases has been determined. In comparing galaxies on a or images obtained by means of a charge-coupled device, CCD, we expect nearby galaxies to appear larger than more distant objects; this means that the of a regular galaxy can be taken as a rough indicator of its distance. When the spectra of different galaxies are correlated with distance, we find that a few nearby galaxies have -shifted speCtra; but all the more distant galaxies have spectra that are systematically shifted toward the red part ofthe spectrum. Galaxies at larger apparent distances, as judged from their diameters or brightness, are increasingly red-shifted. This correlation is so weIl established that we now take an of a remote galaxy's red shift as a standard indicator of its distance. Galaxies are not the largest aggregates in the Universe. There exist many pairs and groups of galaxies. Figures 1.11 and A.2(f) show such groupings. Our Galaxy, the to which the Sun belongs, is a member of the that contains somewhat more than two dozen galaxies. The Andromeda and the Galaxy are the largest members and together account for most ofthe mass (Table 1.4). Larger clusters 0/galaxies containing up to several thousand galaxies also exist. Groupings on a larger scale include filamentary structures composed of tenuous chains of galaxies, enormous voids surrounded by denser concentrations - walls of galaxies and possibly - entire groupings of clusters of galaxies. Beyond that scale, no further clustering is apparent. On the largest scales, the Universe can best be described as consisting of randomly grouped aggregates and voids. The scheme of classification of galaxies leaves a number of borderline cases in doubt. Small EO galaxies are not appreciably different from the largest globu• lar clusters. Merging galaxies sometimes cannot be distinguished from irregular ones; and the distinction between a group or a cluster of galaxies mayaiso be a matter of taste. But the classification is useful nevertheless; it gives handy A:5 Brightness of Stars 585 names to frequently found objects without making any attempt to provide rigorous distinctions. Crossing the vast spaces between the galaxies are quanta of electromagnetic radiation and highly energetic cosmic ray particles that travel at almost the . These are the carriers of information that permit us to detect the existence of the distant objects. There is one overwhelming feature that characterizes the galaxies. Everywhere, at large distances, the spectra of galaxies and clusters of galaxies appear shifted toward the red, long , end of the spectrum. The farther we look, the greater is the red shift. We attribute the red shift to a high recession velocity. The galaxies appear to be flying apart. The Universe expands!

A:5 Brightness of Stars

(a) The Scale One of the first things we notice after a casuallook at the sky is that some stars appear brighter than others. We can visually sort them into different brightness groups. In doing this, it becomes apparent that the can clearly distinguish the brightness oftwo objects only if one ofthem is approximately 2.5 times as bright as the other. The factor of2.5 can therefore serve as a rough indicator of apparent brightness, of apparent visual magnitude, mv of stars. Stars offirst magnitude, mv = 1, are brighter by a factor of,....., 2.5 than stars of second magnitude, mv = 2, and so on. The magnitude scale extends into the region of negative values; but the Sun, Moon, Mercury, Venus, Mars, Jupiter, occasional bright comets, and the three stars, , , and ot Centauri are the only objects bright enough to have apparent visual magnitudes less than zero. Normally it would be cumbersome to use a factor of 2.5 in computing the relative of stars of different magnitudes. Since this factor has arisen not because of some feature pecu1iar to the stars that we study, but is quite arbitrari1y dependent on a property ofthe eye, we are tempted to discard it altogether in favor of a pure1y decimal system; but a brightness ratio of 10 is not usefu1 for visual purposes. As a result, a compromise that accommodates some ofthe advantages of each ofthese systems is in use. We define a magnitude in sucha way that stars, whose brightness differs by precisely five magnitudes, have a brightness ratio of exact1y 100. Since 100 1/ 5 = 2.512, we still have reasonable agreement with what the eye sees, and for computational work we can uSe standard to the base 10.

(b) Color The observed brightness of a star depends on whether it is seen by eye, recorded on a photographic plate, or detected by means of!l radio . For dif• ferent astronomical objects the ratio öf radiation emitted in the visible and 586 Appendix A radio regions of the spectrum varies widely. The spectrum of an object can be roughly described by observing it with a variety of different detectors in several different spectral regions. The apparent magnitudes obtained in these measure• ments can then be compared. Several standard filters and instruments have been developed for this purpose so that we may compare and contrast data from observatories all over the . The resulting brightness indicators are listed below:

m u denotes visual magnitude. m pg denotes photographie magnitude. While photographic plates have now been all but displaced by detector arrays, the need for standardization to follow long-term trends has required the maintenance oftraditional wavelength bands in modem . The photographic plate is more sensitive to blue light than the eye; nowadays this brightness is usually labeled B, for blue. m pg and m pu are older notations. V or m pu denotes photovisual magnitude obtained with a photographic plate and a special filter used to pass light and reject some ofthe blue light. This brightness is generally denoted by V for visual. U denotes the ultraviolet magnitude obtained with a particular ultraviolet transmitting filter (Table A.I). I denotes infrared magnitude obtained in the photographic part ofthe infrared. At longer wavelengths photographic plates are no longer sensitive, but a number of infrared spectral magnitudes have been defined so that results obtained with indium antimonide, mercury cadmium telluride, and other infrared detectors might be compared bydifferent ob servers. These magnitudes are labeled J, K, L, M, N,and Q. Table A.I lists the wavelengths at which these magnitudes are determined. mbol denotes the total ofan object integrated over all . This bolometrie magnitude is the brightness that would be measured by a - a detector equally sensitive to energy radiated at any wavelength.

TABLE A.I. Effective Wavelength for Standard Brightness Measurements.

Effective I Effective Symbol Wavelength Symbol Wavelength

U 0.36JLm K 2.2JLm B 0.44 L 3.4 V 0.55 M 5.0 R 0.70 N 10.2 I 0.90 Q 21 J 1.25

I JLm (micron or micrometer) = 10-6 m = 10-4 cm = 104 A (Angstroms). A:5 Brightness of Stars 587


.I 4 •• . 61- ". -: S: I. • ... - .. ".;. V 8 ...... - -.:... •. •,. Y\t . • 10- -:ftt: .. - -s:~ . '.; ...., . 12- .•.r:;J.- .i .:-,...... - 14,• I I 1 1 I 1 .1 -0.2 o 0.2 04 0.6 0.8 1.0 1.2 14 B-V FIGURE A.3. Color-magnitude diagram of the cluster stars, after correction for interstellar extinction effects. The Pleiades cluster contains some ofthe most recently formed stars in the Galaxy (after Mitchell and Johnson (Mi57b)).

(e) The difference in brightness as measured with different filters gives an indication of a star's color. The ratio ofblue to yellow light received from a star is given by the difference in magnitude - of the brightness - of the star measured with blue and visual filters. This quantity is known as the color index:

C = B - V. Differences such as U - B are also referred to as color indexes. Figure A.3 shows a color-magnitude diagram for the young Pleiades . The comparison of involved in producing a reliable color index can only be achieved if we can standardize detectors and filters used in the measurements. And even then errors can creep into the comparison. For this reason some standard stars have been selected to define a point where the color index is zero. These stars are denoted by the spectral-type symbol AO (see Section A:6).

(d) Bolametrie Correetion Normally the bolometric brightness of a star can only be obtained by means of observations spanning the entire spectrum. The bolometrie eorreetion, Be, is de• fined as the difference between the bolometric and visual magnitudes of astar. The is always positive 588 Appendix A

(e) F or many purposes we need to know the absolute magnitude rather than the appar• ent brightness of astar. We define the absolute magnitude of a star as the apparent magnitude we would measure if the star were plaeed a distanee of 10 pe from an observer. (1 pe = 3 x 10 18 em. See Seetion 2:2.) Suppose the distanee of a star is r pe. Its brightness diminishes as the square of the distanee between star and observer. The apparent magnitude of the star will therefore be greater, by an additive term logz.5 rZ/ rJ, than its absolute magnitude.

r Z r m = M + logz.5 2" = M + 5 log - , ro ro where the logarithm is taken to the base 10 when no subseript appears. Sinee ro = 10 pe, we have the further relation for the , Mo, Mo == m - M = 510gr - 5. (A-l) Thus far no attention has been paid to the extinetion oflight by interstellar dust. The apparent magnitude is diminished through extinetion and a positive faetor A has to be subtraeted from the right side ofequation (A-l) to restore M to its proper value

M = m + 5 - 5 log r - A. (A-2) Obtaining the star's distanee, r, is often less diffieult than assessing the interstellar extinetion A. We diseuss this diffieulty in Seetion A:6(a) below. The deteetor and filter used in obtaining the apparent magnitude m in equation (A-2) determines the value of the absolute magnitude M. We ean therefore use subseripts, v, pg, pu, and bol for absolute magnitudes in exaetly the same way as for apparent magnitudes.

(f) Luminosity Onee we have obtained the bolometrie absolute magnitude of astar, we ean ob• tain its total radiative emission, or luminosity, L, direetly in terms of the :

log (LL(J = 2~5 [Mbo10 -Mbo1 ] • (A-3)

The luminosity ofthe Sun, L 0 , is 3.8 X 1033 erg see-1 and the solar bolometrie magnitude, Mbol0, is 4.6. The luminosity of stars varies widely. A ex• plosion ean be as bright as all the stars in a galaxy for abriefinterval ofa few days. The brightest stable stars are a million times more luminous than the Sun. At the other extreme, a dwaif may be a faetor of a thousand times fainter than the Sun; and brown dwarfs, stars with masses ranging down to ~ M(2)60, may have A:6 Classification of Stars 589

10-7 L 0 ~ L ~ 10-4 L 0 as they settle down to contract and slowly radiate away gravitational , over billions ofyears (Ku97a).

(g) The Hertzsprung-Russell Diagram One ofthe most useful diagrams in all astronomy is the Hertzsprung-Russell, H-R diagram. It presents a comparison of brightness and temperature plotted for any chosen class of stars. Chapter 2 shows that the diagram is valuable in estimating the dimensions of galaxies and intergalactic distances; more important, such H-R diagrams, obtained for different stellar age groups, provide the main empirical foundation for the theory of . H-R diagrams can take many different forms. The color index is an indicator of a star's surface temperature, as shown in Chapter 4. Hence the abscissa sometimes is used to show a star's color index, and we then speak of a color-magnitude diagram. The ordinate can show either Mv, or MboI, or luminosity. When only a comparison of stars all of which are known to be equally distant is needed, it suffices to plot the apparent magnitude. Figure A,3 shows such a plot ofthe Pleiades cluster stars. Figure 1.6 plots the characteristics of M3, an old globular cluster in our Galaxy. The Pleiades are among the most recently born Galactic stars. This difference is refiected in the difference ofthe two diagrams. These two figures, as weIl as Fig. 1.3, show that stars are found to fall only in a few select areas ofthe H-R and color-magnitude diagrams. The largest number of stars cluster about a fairly straight band called the . This is particularly clear for the Pleiades cluster. The main sequence runs from the upper left to the lower right end ofthe diagram, or from bright blue down to faint red stars. To the right and above the main sequence (Fig. 1.4) lie bright red stars along a track called the red-giant branch. There is also a thatjoins the far end ofthe red-giant branch to the main sequence. These two branches show up particularly in Fig. 1.6. In the horizontal branch, we find some stars that periodically vary with brightness. Finally, some faint stars lie below and to the left of the main sequence. The rest of the diagram is usually empty.

A:6 Classification of Stars

(a) Classification System The classification ofstars is a complex task, primarily because we find many special cases hard to fit into a clean pattern. Currently a "two-dimensional" scheme is widely accepted. One of these "dimensions" is a star's spectrum; the other is its brightness. Each star is assigned a two-parameter classification code. Although the object of this section is to describe this code, we should note that the ultimate ofthe classification scheme is an extensive collection of spectra such as those 590 Appendix A

Co? 1:0 Q Q '< ....::3 < n 1> n C C ::J C ., ("') S S S ., Cl Cl

=He H8 -He Ca-



S A G) 1> CD -+aJ ~ (]l -..J" (]l =r--, <.0 Cl _. ()J ()J- ()J ()J ()J rv ::J\O 0 0 0 0 0 0 0 cn=r. -+ 0 0 0 0 0 Oro 0 3 ..,

FIGURE A.4. Schematic diagram of spectra oftypical stars representing different spectral types. The number of stars brighter than the eighth magnitude in each c1ass is listed on the right, next to the star's spectral type. (With the permission ofthe , ofChicago.) shown in Fig. AA. Each spectrum is representative of a particular type of star. Stars are classified primarily according to their spectra, which are related to their color. Although the primary recognition marks are spectral, the sequence of the classification is largely in terms of decreasing stellar surface temperature - that is, a shift in the star's radiation to longer wavelengths. The bluest com• mon stars are labeled 0, and increasingly red stars are classed according to the A:6 Classification ofStars 591

sequence (Table A.2)

Q S p B A F G K M W ° R N Blue White Yellow Red

{BlUiSh} { Yellowish } Orange White White

Over 99% of all stars belong to the basic series B, A, F, G, K, and M. Stars with designation 0, R, N, and S are comparativelyrare and so also arethe spectral types: Q denotes novae - stars that suddenly brighten by many orders of magnitude becoming far brighter than any nonvariable star. P denotes planetary nebulae, hot stars with surrounding envelopes of intensely ionized gases. W refers to Wolf• Rayet stars, intensely hot stars that exhibit broad emission bands ofionized , nitrogen, and helium. These stars appear to consist of a nuclear-processed interior exposed by extreme surface mass loss. The classes Rand N denote stars containing unusually strong molecular bands of diatomic carbon, C2, and cyanogen, CN. The S stars are characterized by bands oftitanium oxide, TiO, and zirconium oxide, ZrO. Stars classed as W, 0, Bare sometimes said to be early types, while stars of class G, K, M, R, N, S are designated late types. Globular cluster stars, and stars that make up the Galaxy's spherical halo, are primarily late type stars. Stars in the Milky Way plane are a mixture of early and late types, respectively, referred to as population 11 and population 1 stars. The transition from one spectral class to another proceeds in ten smaller steps. Each spectral class is subdivided into ten subclasses denoted by Arabic numerals after the letter. A5 lies interrnediate between spectral types AO and A9; and FO is just slightly redder than A9. The classification scheme also allows us to denote a star's luminosity class by placing a Roman numeral after the spectral type. Each ofthese luminosity classes has aname: I Supergiant II III Normal Giant IV V Main Sequence sd wd White Dwarf

The Sun has spectral type GI V indicating that it is a yellow main sequence star. Sometimes we find classes I, 11, and III collected under the heading "giant" while stars of group V are called "dwarfs." Letters "g" or "d" are placed in front 592 Appendix A

TA8LE A.2. Spectral Classification of Stars."

Type Main Characteristics Subtypes Spectral Criteria Typical Stars

Q : sudden bright- T Pyx ness increase by 10 QCyg to 12 magnitudes P : NGC6720 hot star with NGC6853 intensely ionized gas envelope W Wolf-Rayet stars: 8road emission of Om to OVI, Nm to HO 191765 hot stars Nv, CII to CIV, and Hel and HeIl. 0 Hot stars, OIl A 4650 dominates 80 +35°4013 continuum strong HeIl A 4686 dominates} emission 80 +35°4001 inUV Lines narrower lines 80 +36°3987 (05 to 09) Absorption lines dominate; only HeIl, Cn in emission {Pup, A Cep SiIV A4089 at maximum 29CMa On A 4649, HeIl A 4686 strong rCMa 8 Neutral helium 80 Cm/4650 at maximum e Ori dominates 81 Hel A 4472 > On A 4649 ß CMa,ßCen 82 Hel lines are maximum .5 Ori, a Lup 83 HeIl lines are disappearing Jl.4 Ori, a Pav 85 Si H128 > He A 4121 19 Tau, cfJ Vel 88 A 4472 = Mg A 4481 ß Per,.5 Gru 89 Hel A 4026 just visible A Aql, A Cen A Hydrogen lines AO 8almer lines at maximum aCMa decreasing from A2 CaIlK= O.4H.5 S CMa,1 Cen maximum at AO A3 K= 0.8 H8 a PsA, r 3 Eri A5 K> H.5 ß Tri, a Pic F Metallic lines FO K=H+H8 .5 Gem,a Car becoming F2 G band becoming noticeable 1l"Sgr noticeable F5 G band becoming continuous aCMi,p Pup F8 8almer lines slightly stronger ß Vir, a For than in Sun G Solar-type GO CaA 4227 = H8 a Aur, ß Hya spectra G5 Fe A4325 > Hy on small-scale plates K Gem,a Ret K Metallic lines KO Hand K at maximum strength a 800, a Phe dominate K2 Continuum becoming weak in blue ß Cnc, v Lib K5 G band no longer continuous aTau M TiO bands TiO bands noticeable a Ori,a Hya 8ands conspicuous p Per, y Cru Spectrum fluted by the strong bands WCyg,RXAqr variables, Hy, H.5 X Cyg, 0 Cet R,N CN, CO, C2 bands CN, CO, C2 bands appear instead ofTiO. R stars show pronounced Hand K lines. S ZrO bands ZrObands RGem " Compiled mainly from Keenan in Stars and Stellar Systems, K.A. Strand (ed.), with permission from the University ofChicago Press (Ke63) (based on Cannon and Pickering (Ca24)) and also from Allen (Al55). This table, which is based on the Henry Oraper classification scheme, is a rough guide to the spectral features of stars. The classification of stars, however, remains on ongoing process and changes occur. (With the permission of Athlone Press ofthe University ofLondon, 2nd ed. © c. W. Allen, 1955 and 1963, and with the permission ofthe University ofChicago Press.) A:6 Classification of Stars 593

of the spectral class symbol to denote these types. Similarly placed letters "sd" and "w", denote subdwarfs and white dwarf stars. Another classification feature concems supergiants, which are often separated into two luminosity classes Ia and Ib depending on whether they are bright or faint. A letter "e" following a spectral classification symbol denotes the presence of emission lines in the star's spectrum. There is one exception to this rule. The combination Oe5 denotes 0 stars in the range 05 to 09; it has no further connection with emission. A letter "p" following the spectral symbol denotes that the star has some form of peculiarity. The color designation (stellar spectral type) given here is nearly linear in the color index B - V. It is not however linear in V - V nor do the V - V values decrease monotonically with increasingly late spectral type. Small differences in color indexes exist for giants and main sequence stars of the same spectral type. This unfortunate difficulty has arisen for historical reasons. We might still see how well stellar colors approach those of a blackbody. The closeness offit is shown in Fig. A.5, called a color-color diagram. Four factors are responsible for the rather large deviations from a blackbody. (i) For stars around spectral type A, where the fit to the blackbody spectrum is poorest, absorption by hydrogen atoms in their first excited states produces a deviation. We talk about the Balmer jump in connection with the sharp rise in absorption at wavelengths corresponding to the Balmer continuum produced by these excited atoms in the outer atmosphere of astar. (ii) Cool stars have H- ions in the outer atmospheres. These ions absorb radiation selectively, making the star appear bluer. (iii) The relatively high abundance of in population I stars produces a number of absorption lines that change the color of astar, moving it toward the lower right of Fig. A.5. (iv) Finally, no star looks completely , because its outer layers are not equally opaque at all wavelengths. Light at different wavelengths therefore reaches us from different depths within the star, and these levels are at differ• ent temperatures. The resulting spectrum of therefore corresponds to a mixture of temperatures, rather than to blackbody radiation at one well-defined temperature. Determination of the spectral type of a star by means of its color index alone would be very difficult, since proper account would have to be taken ofthe changes in color produced by interstellar dust. Small dust grains tend to absorb and scatter blue light more strongly than red. Light from a distant star therefore appears much redder than when emitted. To discover the true color index ofthe star a correction has to be introduced for interstellar reddening. However, in order to make this correction, we have to know how much interstellar dust lies along the line of sight to a given star, and to what extent a given quantity of dust changes the color balance. None ofthis information is normally available. Instead, we have to make use of a circular line of reasoning. We know that nearby stars of any given spectral type exhibit characteristic absorption or emission lines in their spectra. Since these stars are near, there is little intervening interstellar dust, and their spectra can be taken to be unreddened. We can therefore draw up tables listing 594 Appendix A

-0 .8

o U-B

0 .8


2 .1

2.4 B-V

FIGURE A.5. The relation between the color systems U - Band B - V for unreddened main-sequence stars (dots) and little reddened supergiants and yellow giants (crossed dots). The li ne along which blackbody radiators would fall is also shown (after Johnson and Morgan (J053».

the spectralline features of each color c1ass. A distant star can then be c1assed in terms of its spectrallines rather than its color index and the color index can be used to verify the c1ass assignment. If the color is redder than expected, we have an indication of reddening by interstellar dust. Whether dust is actually can then be checked - in many instances - by seeing whether other stars in the immediate neighborhood of the given object all are reddened by about the same amount. If they are, we have completed the analysis. The results give the correct spectral identification of stars in the chosen region and, in addition, we are given the extent to which interstellar dust changes the color index. A similar analysis can also be applied to determine the extent to which the overall brightness of the star is diminished through extinction by interstellar dust. This analysis allows us to determine the amount of obscuration in all the spectral ranges for which observations exist. As already stated, the color and spectrum ofa star depends on its surface temper• ature. Table A.3 gives the for representative stars and Figure A.6 relates a star's temperature to its color. As discussed in Chapter 4, the effective temperature is measured in terms ofthe radiant power emitted by the star over unit surface area. A:6 Classification of Stars 595

SUPERGIANTS 0380 AO FO GO KO MO 111 I I I I I I I GIANTS 0380 AO FO GO KO MO 111 1 I 1 I I I I 1 1 MAIN SEOUENCE 0380 AO FO GO KO MO M8 111 I I ! ! I ! I I I I

4.8 4.7 4.6 4.5 4.4 4.3 4.2 4.1 4.0 3.9 Supergiants 0 i3.8 o 0 I- : 3.7 , 01 .... 0 .Q 3.6 o 0 .. 3.5 ."'-. 00 Giants 3.4 'o~ 3.3 o ~.h • 0... .... 3.2 - "0 3.1 0 .. 00 0 .:.., 3.0 • Main-sequence Stars 2.9 .. ' ...... 2.8 00 .. 2.7 2.6 -0.5 0.0 0.5 1.0 1.5 2.0 B-V FIGURE A.6. Effective temperatures and colors for all stars separated by luminosity dass. For darity, temperatures of giants, subgiants, and main-sequence stars are lowered by 0.3 in log Te!! with respect to the next more luminous dass. The lines are shown to help guide the eye along the steep portions ofthe curve (after Flower (Fe96)).

By analyzing the spectra of stars we can obtain their speed of rotation from the broadening of stellar spectrallines. If the axis of rotation of a star is inclined at an i relative to the line of sight we obtain a measure of Ve sin i, where Ve is the equatorial velocity ofthe star. Only those stars whose axes are perpendicular to the line of sight will exhibit the full due to the rotation of the star; but by analyzing the distribution of line widths, we can statistically determine both the rotational velocity and the distribution function of the angle i (Hu65). As far as we can tell, rotation axes of stars are randomly oriented with respect to the Galaxy's rotation axis. Table A.4 gives some typical values of V e for different types of stars. Figure 1.9 shows the angular for unit stellar mass for these stars. 596 Appendix A

TABLE A.3. Effective Stellar Temperatures.a

Main-Sequence Subgiants Giants Supergiants V IV III 11 Ib Ia Types Te (0 K) 04 48670 48180 47690 08 38450 37090 35730 BO 33340 31540 25700 B5 15400 14800 13100 AO 10000 9700 10200 A3 8500 FO 7200 F5 6700 6600 6500 6350 6200 GO 6000 5720 5500 5350 5050 OS 5520 5150 4800 4650 4500 KO 5120 4750 4400 4350 4100 K5 4350 3700 3600 3500 MO 3750 3500 3400 3300 M2 3350 3100 2050 a Adapted from Keenan (Ke63), Böhm-Vitense (Bö81), and Vacca et al. (Va96). See also text.

TABLE AA. for Stars ofLuminosity Class III and V (after Allen Al64).

Mean Ve (lans-I ) Spectral Type III V 05 190 BO 95 200 B5 120 210

AO 140 190 A5 170 160 FO 130 95

F5 60 25 GO 20 < 12 K,M < 12 < 12

(b) Variable Stars Two main types ofvariable stars can be listed. Extrinsic variables can be: (i) elose binary stars whose combined brightness varies because one star the other; or (ii) stars that are eclipsed by, or periodically illuminate, ejecta or remnants of the matter from which these young stars formed - T- Tauri variables, named after the star in which these features were first detected. Intrinsic variables are stars whose luminosity actually changes with time. The brightness variations may be repetitive as for periodic variables, erratic as for irregular variables, or the behavior may be semiregular. The distinction is not A:6 Classification of Stars 597

TAßLE A.5. Properties ofPulsating Variables.

Mean brightness Range of Spectral Type Mvand Remarks Period, P Type variation I'1Mv RR Lyrae

always clear-cut. A brief summary ofsome characteristics ofthe pulsating variables is given in Table A.5. The brighter ofthese stars are important in the construction of a reliable cosmic distance scale. Other types ofintrinsic variables include exploding stars such as novae, recurrent novae, supernovae, dwarfnovae, and shell stars. The brightness ofa nova rises 10 to 12 magnitudes in a few . The return to the star's previous low brightness may take no more than a few , or it may take a century. Both extremes have been observed. The absolute photographic brightness at maximum is ab out - 7. Recurrent novae brighten by about 7.5 magnitudes at periods of several decades. Their peak brightness is ab out the same as that of ordinary novae. The brightness decline usually takes 10 to 100 days but sometimes is outside this range. Supernovae are ab out ten magnitudes brighter than novae. The brightness may become as great as that of a whole galaxy. Two types have been recognized. Supernovae of type 11 exhibit spectral lines of hydrogen in their optical spectra, while supernovae oftype I do not. SNe I occur in all galaxies, where they have the spatial distribution of older stars; typically their absolute magnitude is Mv = -16 at maximum. SNe 11 occur only in the arms of spiral galaxies, are associated with populations ofyoung stars, and have Mv = -14 at maximum. The two types of supernovae can be subdivided into several subtypes, but roughly 80% of SN e I are of a type designated as SN Ia, whose light curves are all remarkably similar. This makes them useful distance indicators. On exploding, a supernova can thrust about one ofmatter into inter• stellar space at initial speeds oftens ofthousands ofkilometers per second. Often these gaseous shells persist as supernova remnants for several thousand years. On photographic plates they appear as filamentary arcs surrounding the point of initial explosion. 598 Appendix A

Dwaifnovae brighten by about four magnitudes to a maximum absolute bright• ness of Mv + 4 to +6. Their spectral type normally is A. Their outbursts are repeated every few weeks. Shell stars are B stars having bright spectrallines. The stars seem to shed shells. A rise in brightness of one magnitude can occur. Flare stars sporadically brighten by '" I magnitude over intervals measured in tens of minutes. They then relapse. These stars are yellow or red dwarfs of low luminosity. The ftares may weil be similar to those seen on the Sun, except that they occur on a larger scale. In extreme cases the star brightens a hundred fold. stars are stars that suddenly dirn by as much as eight mag• nitudes and then within weeks return to their initial brightness. At maximum the spectrum is of class R, rich in carbon. The variable stars are not very common, but they are interesting for two reasons. First, some of the variable stars have a well-established brightness pattern that allows us to use them as distance indicators (see Chapter 2). Second, the intrinsic variables show symptoms ofunstable conditions inside a star or on its surface. In that sense the variable stars provide important clues to the structure of stars and to the energy balance or imbalance at different stages of stellar evolution. Novae, T-Tauris, and some stars at the extreme end of the giant branch, the stars, AGB, are found to be strong emitters of infrared radiation. The novae and AGB stars eject material that forms dust on receding from the parent star, while T- Tauris are largely embedded in the dust clouds from which they formed.

A:7 The Distribution of Stars in Space and Velocity

We judge the radial of stars by their shifts. Transverse velocities can be obtained for nearby stars from the - the across the sky - and from their distance, if known. We find that stars of different spectral type have quite different motions. Stars in the have low relative velocities, while stars that comprise the have large velocities relative to the Sun. In practice there is no clear-cut discontinuity between these populations (Ku54). This is ratherweIl illustrated bythe continuous variation in velocities given in Table A.6. A star's velocity is correlated with its the mean height above the Galactic plane. By noting the distribution of stars in the solar neighborhood, we at least obtain some idea about how many stars of a given kind have been formed in the Galaxy. If we can compute the li fe span of astar, as outlined in Chapter 8, then we can also judge the rate at which stars are born. For the short-lived stars such birth rates represent current formation rates; and we can look for observational evidence to corroborate estimates of longevity once the spatial number density of a given type of star has been established (Fig. A. 7). Such studies are still in relatively prelimi• nary stages, because we are not quite sure what the appearance of a star should be A:8 , Radio Stars, and X-Ray Sources 599

TABLE A.6. Stellar Velocities Relative to the Sun, and Mean Height Above Galactic Plane.a

VelocitY' , v Density, p Height, h Objects kms-I 10-3 M0 Pc-3 pc Interstellar clouds large clouds 8 small clouds 25 Early main sequence stars: 05-B5 50 1O} 0.9 B8-B9 12 60 A~A9 15 1 115 F~F9 20 3 190 Late main sequence stars: F5-GO 23 G~K6 25 12 } 350 K8-M5 32 30 Red-giant stars: K~K9 21 0.1 270 M~M9 23 0.01 High-velocity stars: RR Lyrae variables 120 10-5 Subdwarfs 150 1.5 Globular clusters 12~180 10-3 a Stellar velocities collected by Spitzer and Schwarzschild from other sources (Sp51a). , p, and heights, h, after (Al64). (With the permission ofthe Athlone Press ofthe University ofLondon, 2nd ed.© C.w. Allen 1955 and 1964.) b Root mean square value for component ofvelocity projected onto the Galactic plane. at birth, particularly if it is still surrounded by some of the dust from which it has been formed (Section 1 :4) (Da67).

A:8 Pulsars, Radio Stars, and X-Ray Sources

(a) Pulsars Isolated pulsars are radio sources that emit pulsed radiation with clocklike reg• ularity. Except for half a dozen to a dozen sources, pulsars have thus far been identified primarily in the radio wavelength region. The central star in the or the powernll gamma-ray emitter , both of which emit visible light as weB as gamma rays, are notable exceptions. Where pulsars are companions to giant stars, whose atmosphere they are tidaBy stripping away, they can also be strong, intermittent, X-rays sources. For isolated pulsars the regularity of the pulses is constant to about one part in 108 per year. Pulses are typically spaced anywhere between a few milliseconds and a few seconds apart. Within each pulse, there are subpulses that march, relative to the overall en• velope, with regularities both in their phase and in their changing sense of 600 Appendix A

FIGURE A.7. Present formation rate, 0/, ofbright stars per square ofarea (projected onto the Galactic plane) during 10 10 yr. The mass of stars of different brightness is shown (after M. Schmidt (Sc63)).

. The coherence and pulse rates already tell us that the source is small compared to normal stars. We are dealing with neutron stars, stars whose cores consist of closely packed, degenerate neutrons. In such a star the mass of the Sun is packed into a volume about 10 km in diameter. The most widely accepted model for the pulsars has a rotating with aperiod equal to the interval between the main pulses. The method of generating the pulses, however, has not yet been settled. In all , the radiation is emitted in a direction tangential to the charged particles moving with the rotating star and, hence, there is a loss of and a corresponding slowdown of the star's rotation and of the pulse rate. Careful measurements indeed show this slowdown in a number ofpulsars (G068)*. Pulsars mayaIso be the sources ofhighly relativistic particles and thus contribu• tors to the Galactic cosmic ray component. However, the extent ofthis contribution is not known and may be minor. From time to time a discontinuous change in the period can also occur, apparently due to a structural change the star undergoes. Other puzzling features are giant pulses, thousands of times brighter than a normal pulse, but appearing only about once in ten thousand pulses; null pulses, where there is no intensity at all; sudden changes in the pulse structure, with an equally sudden flipping back to the original pulsing mode. A small number of pulsars are associated with known supernova remnants. One is in the . Another is a star in the Crab nebula, remnant of a supernova seen in 1054 AD. It was identified as the stellar remnant of the A:8 Pulsars, Radio Stars, and X-Ray Sources 601 supernova, more than 25 years before the pulsar's discovery. The now pulses every 33 msec. Using the present slowdown rate, we can make a rough linear extrapolation of the Crab pulsar's period, backward in time, and see that this is indeed a remnant of the object that exploded in 1054 AD. Slower pulsing pulsars are thought to be appreciably older. Within the past two decades a class ofbinary pulsars has been discovered - two compact sources orbiting each other. Many are neutron-star / neutron-star binaries. The constancy of their periods can be better than one part in 10 10 per year. The fastest known emits pulses with a periodicity of only 1.5 ms. One interesting feature of the pulsars is the arrival time of pulses at different radio . Although equally spaced, these pulses arrive at slightly different times because the ofthe and of any outer layers of the pulsar is slightly different for different radio frequencies. This allows us to compute the number of electrons along the line of sight to the object. We can then make a rough estimate of its distance and radio luminosity (Section 6: 11). The pulsars - many hundreds are by now known - are concentrated toward the plane ofthe Galaxy (see Fig. 6.6).

(b) Radio Stars The first to be discovered was the Sun (Re44). Its radio emission is very weak and we detect it clearly only because it lies nearby. For more than a decade after the Sun's detection, all discovered radio sources were extragalactic radio galaxies or , or involved nebulosities such as supernovae or ionized hydrogen regions in the Galaxy. However, in recent years, several new classes of radio stars have been observed. Besides pulsars, novae and X-ray emitting stars have also been detected at radio frequencies. Red supergiants, red dwarfflare stars, and blue dwarf companions to red supergiants have also been studied. Most ofthese objects are faint at radio wavelengths.

(c) X-Ray Stars The most readily observed X-ray sources are Galactic. Figure A.8 shows a clus• tering of the sources about the Galactic plane. These sources are associated with stars and fall into several groups. (i) The Crab pulsar emits extremely regular X-ray pulses with a 33 millisecond period. This is somewhat of an exception, but the gaseous surrounding the Crab is quite typical in being a bright X-ray source. (ii) X-3 is a source that pulses semiregularly. For periods of a day and a halfit pulses with aperiod that slowly increases from 4.84 to 4.87 s. Then it suddenly drops in intensity in aperiod of an , only to start all over again half a day later. Sources of this kind appear to be close binary stars. (iii) A variety of X-ray sources have a puzzling regularity to their brightness changes on sc ales of seconds. 0\ o N v,'VO Ctu"er Clul'er of GaJaJCies 0'GaIP~$ ScoX·' :g 81nuy' X"IY cto Soolel ::I Ex HVa 0- Call1ClysmlC ~ . VariarM (U Gern) > MxB '~29 Burst...

YZCMI Cyg X-3 Flarl St. r Blnaty X'fa)' I,nd "'(3), Source

Ca." 'I ·F·'1 .~. ). Supernova [_ '1 l'' t "'~V' " '\" ' I',. -r •"~·~f' •• _ ' _ *.- J' ' i;::'/ 'J . ....j i Remnant ... Croll ~_ . X Per -..... Binlry ondPuta. x-,ay PulW and Be 511'

Accrellng Binar... ." NGC 6624 Gx 339-4 Lorge Mooo"an", Cioud SS433 Burst., Slack Hole CaodiCIale lMe Accreting binary PKS 2'~30< In'SUpefnoYl BL Llcertae Remnanl 0bjec1 "'=tiYtGall1CY

FIGURE A.8. The X·ray sky. Map ofthe X-ray sky known in 1987 plotted in galactic coordinates. Note the concentration toward the and galactic plane. Bright sources are shown as larger . Anumber of individual sources are identified both by their respective catalogue designations and by source type. By 1997, the roughly 106 registered extragalactic sources would have totally filled this plot. (With the permission of Kent S. Wood and the Naval Research Laboratory, as weil as of Jay M. Pasachoffand W.B . Saunders, Co). A:9 Quasars and Active Galactic Nuc1ei, AGNs 603

(iv) Novalike sources fiare up for a or so and then die away. (v) Many X-ray stars are associated with neutron stars (Pa96). Some might also be associated with black holes, stars in an ultimate state of collapse (Section 8: 19). As the sensitivity of X-ray instrumentation has improved many classes of ordinary stars have also been detected. Millions of extragalactic sources also emit X-rays. The first to be observed was M87, a spherical galaxy that emits radio waves and strikingly exhibits jets of relativistic particles apparently shot out from its center. The central in massive clusters is often embedded in a halo ofhot, X-ray emitting gas, possibly ejecta spewed out ofthe galaxy by supernova explosions. Many quasars, radio galaxies and Seyfert galaxies also are powerful X-ray sourees.

A:9 Quasars and Active Galactic Nuclei, AGNs

These objects are listed separately because their is not yet properly understood. Quasars have many features in common with some types of radio galaxies; in particular, the visible spectra bear a strong resemblance to the nuclei of Seyfert galaxies, which are spiral galaxies with compact nuclei that emit strongly in the infrared and exhibit highly broadened emission lines from ionized gases. In both the quasars and Seyfert nuclei, we find highly ionized gases with spectra indicating temperatures of the order of 105 to 106 K and number densities '" 10 6 cm-3. The conditions resemble those found in the solar corona. In the quasars and Seyfert nuclei the spectra of these gases show velocity differences of the order of 1,000 or 2,000 km s-I , indicating either: (a) that gases are being shot out ofthese objects at high velocity; (b) that they are falling in at high speed; (c) that there is fast rotation; or (d) that there is a great deal of turbulent motion present. Most likely, a combination of two or three factors is involved. The quasars and active nuclei of Seyfert galaxies sometimes show brightness variations on a time scale of hours. These highly luminous nuclei are, therefore, believed to either radiate into narrowly collimated beams emanating from rotating sourees, or to be less than a few light-hours or days '" 10 14 to 10 16 cm in diameter. This argument assumes that the brightness changes are coherent, while actually we may be observing independent outbursts in different portions of a rather larger object. Quasars have spectra that are highly red-shifted, indicating that they are at extreme distances and hence must be extremely luminous to appear as bright as they do. Only extreme infrared galaxies, whose peak emission occurs at wavelengths of'" 100 J.lm, are comparably luminous. Some may radiate more than 1046 erg S-I - a hundred times more than our galaxy. Since the size of these objects is so small, the must be some ten orders of magnitude greater than that ofnormal galaxies. Extremely high X-ray luminosity also characterizes many quasars and active galactic nuclei, AGN. Many quasars, AGNs, and are 604 Appendix A

Salpeter IMF. no dust correction -1

., -I <.> ~ -1.5

-I 1-0 ~ o -~

o 1 2 3 4 5 redshifl FIGURE A.9. The rate at different epochs in the evolution ofthe Universe. At a red shift z == tü/).. = 4, the Universe was roughly one tenth its present age, not much older than 1.5 Gyr. The peak occurs around red shift 1.2, when the Universe was about one-third its present age. The plot makes no correction for potential absorption of radiation by dust at large red shifts. This might lead to an underestimate of the star formation rate at early times. Data for the most distant sources were derived from a deep search with the Rubble . (Courtesy ofP. Madau.)

also gamma-ray sources. Blazars, resemble quasars in most respects, except that their spectra are largely featureless. The term "" and "QSO" - for "quasi-stellar object" - are often used interchangeably. However, some reserve "quasar" for those QSOs that emit strongly at radio frequencies, and use "QSO" to denote both radio and powerful radio emitters - that is, the whole class ofthese compact objects. As we look to increasing distances across the Universe and are able to detect quasars and galaxies at large red shifts, their colors and luminosities begin to tell us the numbers of stars that are shining there and the lengths oftheir life spans. From such surveys we are beginning to the star formation rates in the Universe A: 10 Gamma-Ray Bursts 605

from early times to the present. Figure A.9 provides an estimate for these rates. It shows that current star formation rates may be roughly a factor of ten lower than at their peak when the Universe had attained only one-third its present age.

A:I0 Gamma-Ray Bursts

Gamma-ray bursts are short outbursts of gamma rays, in the energy range from 50 ke V to 1 Me V, generally lasting from a fraction of a second to one hundred seconds. In other energy ranges the bursts have sometimes been observed to last longer. An outburst that occurred on February 17, 1994, was observed to emit gamma radiation at an energy of30 GeV, for about an hour and a half. An outburst on May 8, 1997, was observed to brighten at optical wavelengths over the following two days, before fading over the following three or four days (Dj97). It lies far out in the Universe, beyond a red shift z = 0.835 (Me97a). The more than one thousand bursts observed to date, appear to arrive from random directions in the sky (Fig. A.l 0). Because they do not show any tendency to cluster along the Galactic plane, they have been thought to be extragalactic. If the optical identification of the May 5, 1997, burst is correct, the burst came from a remote galaxy and must have corresponded to an enormous explosion at this distance (Me97a). of the order inferred suggest that bursts may originate in the merger of two neutron stars to form a or the capture of a neutron star by a black hole. Such mergers provide almost the only ways in which we can conceive of vast amounts of energy to be liberated rapidly. The potential energy that can be released in these mergers is of order M0 c2 ~ 1056 erg. This may be contrasted to the burst ofneutrino energy emitted in a supernova explosion, which amounts to roughly 3 x 1053 erg emitted in about 10 seconds. A small handful of sources are repeating bursters identified with neutron stars associated with supernova remnants. The first to be discovered lies in the Large

+ 90'

- 90' FIGURE A.l O. Distribution of gamma-ray bursts across the sky (Je96). 606 Appendix A

Magellanic Cloud, only 50 kpc distant. The others have been identified with Galactic supernova remnants. Their lurninosity is far lower.

A: 11 and Cosmic Ray Particles

The Earth, the Solar System, and the Galaxy are all bathed in streams of photons and highly relativistic particles. Inside the Galaxy densities are higher than outside, since starlight and infrared emission make a strong contribution. Out side the Galaxy, there is a ubiquitous component that fills the Universe with the spectrum of a blackbody at 2.73 K (Fi96). Cosmic ray particles, highly energetic electrons and nucleons, constitute a denser energy bath in the Earth 's vieinity than starlight and microwave photons combined. We do not know how the particles are distributed in extragalactie space, but believe that lower-energy cosmie rays are trapped in the Galaxy's magnetic field, and are locally generated in supernova explosions. The highest-energy cosmic rays with energies of 1020 eV cannot be constrained by the Galaxy's magnetic field, and most probably are generated in violent explosions in quasars or active galaxies many megaparsecs away. Table A.7 shows the energy densities of some of these components. X-rays and gamma-rays, highly energetic photons, have far smaller energy densities than visible and microwave radiation (see also Fig. 12.2). The microwave component is partieularly interesting. As far as we can tell it is isotropie, except for a velocity component that we associate with the Galaxy's motion through the Universe. The radiation has a blackbody spectrurn at a temperature of2.73 K. Hot spots observed on various scales deviate from a uniform temperature by only a few parts in 105• We believe that the image obtained ofthe Universe through this radiation takes us back to a time when the was only a few hundred thousand years old. By then it had cooled down sufficiently for electrons to attach themselves to protons to form hydrogen atoms. This made the Universe transparent to light; before this it was opaque. The hot spots may provide us with clues to early phases of galaxy formation.

TABLE A.7. Energy and Number Densities ofPhotons and Cosmic Rays.

Cosmic Ray Visible Particles Light in Galaxy (ergs cm-3) 10-12 '" 2 X 10-13 '" 5 X 10-13 Extragalactic energy density (ergs cm-3) ? '" 2 X 10-14 '" 5 X 10- 13 Number density in Galaxy (cm-3) '" 10-9 '" 10-1 ~ 103 Extragalactic number density (cm-3) ? '" 10-2 '" 103 APPENDIX B Astrophysical Constants

B: 1 Physical Constants

Speed oflight c = 2,998 X 10 10 cm sec- I constant h = 6.626 X 10-27 erg sec G = 6.674 X 10-8 dyn cm2 g-2 Electron charge e = 4.803 x 10-10 esu Mass of electron me = 9.1094 x 10-28 g Mass of m p = 1.6726 x 10-24 g Mass ofhydrogen mH = 1.6735 x 10-24 g Mass of neutron mN = 1.6749 x 10-24 g Atomic mass unit amu = Cl/12) m12c = 1.6605 x 10-24 g Avogadro's number 6.0221 X 1023 k = 1.381 X 10-16 erg °K-1 Thomson (je = 6.652 X 10-25 cm2 Radiation density constant a = 7.566 x 10-15 erg cm-3 °K-4 Stefan-Boltzmann constant (j = 5.670 X 10-5 erg cm-2 °K-4 sec-1 Rydberg constant Roo = 2.1798 X 10-11 erg Fine structure constant Ci = 7.29735 X 10-3 608 Appendix B B:2 Astronomical Constants

Year 3.156 X 107 sec , AU 1.4960 x 10 13 cm Parsec, pc 3.086 x 10 18 cm 3.261 light years Solar mass, M0 1.989 x 1033 g , R0 6.960 X 10 10 cm Solar luminosity, L 0 3.827 x 1033 erg sec-I Luminosity of star with Mbol = 0 2.97 x 1035 erg sec-I Cosmic microwave temperature 2.73°K

B:3 Units

lEon 109 yr == 1 Gyr Angstf0m unit, A 10-8 cm Atmosphere, atm 1.01 x 106 dyn cm-2 = 760 torr Calorie 4.1841 x 107 erg Electron Volt, eV 1.602 x 10-12 erg , Hz 1 sec-I , Jy 10-26 W m-2 Hz-1 Megahertz, MHz 106 Hz Micron,f1,m 10-6 m = 10-4 cm List of References

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B.A.N.: Bulletin ofthe Astronomical Society ofthe Netherlands. I.A. U: International Astronomical Union. The organization issues symposium proceedings and a variety of other publications.

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Aberration oflight, 160-162 loss in star formation, 11,407-409 angle, 161 measured component of, 243 Accretion rate, 92, 547 of Solar System, 11,28 Action, 242 of stars, 30,407-409 Active Galactic Nuclei, AGN, 603 quantum mechanical conservation of, Adiabatic gradient, 295, 307-309 242 Adiabatic lapse rate, 295, 307-309 selection rules, 261-263 Adiabatic process, 138-139,308 total, 243 lEon, 4, 610 of matter, 469, 495, 507 Aerobes, 43, 564 annihilation , 495, 507 Alfven speed, 372 Antenna, 126--127 Alpha decay, 81, 320 beam width, 126 Alpha particle, 314-322 directional diagrarn, 126 Ambipolar diffusion, 400, 413 effective area, 126, 127 Amino acids, 562 gain,127 Amino group, 562 lobe pattern, 126--127 Ampere's law, 189 noise, 127, 127 modulation, 195 temperature, 126--127 Anaerobes, 42, 564 Antigalaxies, 469 Andromeda nebula, M31,35-38, 54, 61, , 77, 313,469,503 582 antibaryons, 313, 469 Angstr!llm unit, A, 610 antileptons, 313 Angular diameters of distant galaxies, antineutrinos, 313 447,450 Antipodal position, 445 Angular frequency, 195 Aphelion points of comets, 32, 578 Angular momentum, 11, 70, 166, Approach veiocity, 84 242-244,261-263 Archea,566 about galactic center, 553 Associations ofstars, 583 classical conservation of, 70 Asteroids, 33, 577, 578 636 Index

Asteroids (continued) entropy, 537 asteroidal belt, 577 primordial, 535 Astronomical unit, 49, 610 Blanketing effect, 362 Asymptotic giant branch, AGB, 19 Blazars, 603; see also BL Lacertae Atmosphere, 113-117 objects emission, 45 BL Lacertae objects, BL Lac, 353, 603 of Earth, 113, 564 Bode's law, 26 oxidizing, 33 Bohr atom, 244-245, 304 of planets, 34 radius, 244 reducing, 33 Bohr magneton, 250 stellar, 325-330 Bolometric correction, 587 unit of press ure, 610 Bolometric magnitude, 586 Atomic mass unit, 314, 609 Boltzmann constant, 110, 609 Attraction, 66 , 127 attracting force, 64 Boltzmann factor, 113 electrostatic, 142, 183, 314 Bose-Einstein statistics, 118, 135,313 gravitational, 63-95, 142 partieles, 118, 313 AU, Astronornical unit, 49, 610 see also Auger process, 329 Bosons, 118,313,498 borealis, 577 Bound-bound transitions, 279 Avogadro's number, 110,609 Bound-free interactions, 279, 304 ,5 Brackett spectral series, 247-248 Branching ratio, 473 Background radiation, see Cosmic , 172, 278, 379 background radiation Brightness temperature, 126 Bacteria, 43, 566 , 323 Balmer jump, 593 Bulging of space, 468 Balmer spectral series, 247-248 Barium stars, 328 C-shocks, 373 Barred spiral galaxies, 582 Calcium Hand K lines, 51-53 , 40, 313,402 Calorie, 610 Betadecay, 81, 314 Carbonaceous chondrite, 24, 25, 553, Biased galaxy formation, 546-549, 553 562; see also Meteorite Binary stars, 79, 210, 580, 581 Carbon cyele, 316, 325 elose binaries, 325 Carbon-nitrogen- cyele, 316, eelipsing, 79, 581 325 mass,79 Carbon-oxygen core, 20, 321-322 spectroscopic, 79, 581 Carbon stars, 23, 214, 327 visual, 79, 581 Carrier wave, 195 X-ray sources, 426, 599 Casimir effect, 123 Birkhoff's theorem, 410, 514, 519 Cavendish , 73 Bit rate, 570; see also Communication Celestial , 26, 63-73 in the universe Centaurs, 577 Blackbody radiation, 122,271 Center of charge, 205 microwave background, 48,166-169, , 68 442,491,606,610 Central force, 68 inhomogeneities, 524, 542 Centrifugal repulsion, 72, 91 Black holes, 2, 8, 20, 40--41, 177, 338, Cepheid variables, 14, 19, 344, 597 605 Chandrasekhar limit, 336 Index 637

Charge conjugation, 475 chemical composition, 31, 358 Charge exchange, 392,426, 539 dust tail, 358 Charge-to-mass ratio, 208 head,358 Chemical elements, 21-26, 241, ionized tail, 271, 358, 426 315-343,459 mother molecules, 31 comets,31 orbits, 578 cosmic rays, 27, 381 Communication channels, 3, 46 earth,33,43,325 Communication in the universe, 568 explosive synthesis, 331 Comoving features, 510, 528, 547 heavy element buildup, 316-343 Compact objects, 332-345,457 interior of stars, 279, 315-343 , 228-234, 353; see , 31 also Inverse Compton effect light elements, 1,25,315 Compton wavelength, 230, 497 formation, 505 Conductivity, 187 meteorites, 24, 25, 562 Conservation laws, 242, 313 sun, 21-26, 241 angular momentum, 242 surfaces of stars, 21-26, 241, baryons, 313 279-283,288 , 242, 313 universe, 459 energy,242 Cherenkov effect, 234-236, 379 leptons, 313 Chondrite, 27, 427 mass-energy, 78,162-164,313 carbonaceous, 24-26, 553,428, 562 momentum, 242 see also Meteorite particle-antiparticle, 313 , 35, 427 Constants ofNature, 464, 470-474 Chromosphere,576 , 23, 298, 307-309 Circumstellar clouds, 275 Convective energy transfer, 307-309 Civilizations, Cooling of protogalactic gases, 553 extraterrestrial, 44 Cooling of protostellar gases, 416-423 Clock hypothesis, 176 cooling time, 422 Clusters of galaxies, 35-38, 133, 142, Coordinate length, 176 168,584 , 176 mass, 89, 106, 525 Core, central of astar, 18, 318 CNO cycle, 23, 316, 325 Corona, solar, 134, 425, 576 COBE, Cosmic Background Explorer, Correspondence principle, 253 486 Cosmic background radiation, 166-169, Coherent radiation, 272 483,606 Collision frequency, 216 discrete sources of, 485 Collisions, 83-88,115,170, 187,381 microwave, 3°K, 48, 112, 166-169, distant, 83-88, 187 234,442,497-530,606,610 high energy, 170, 381 X-ray, 8, 353, 384, 383, 606 restituting, 115 Cosmic distance, 49-62, 449 spectralline broadening, 260 Cosmic expansion, 55, 89, 440, 443, Color-color diagram, 594 454 Color index, 587 Cosmic rays, 1,3,4,47, 149-182, Color-magnitude diagram, 13-19,587 187-192,226,234-236, , 124 379-383,606 Column density, 419 acceleration, 187-192 Comets, 31, 72, 83, 91, 254, 271, 357, age,381 358,386,402,578 air showers, 164, 170--172, 234-236 638 Index

Cosmic (continued) era, 491, 538, 545, 551 electron spectrum, 382 Degeneracy parameter, 305 energy losses, 379-380 Degenerate energy levels, 249 extragalactic, 129,606 , 120, 131 galactic, 129,226,379-383 in stars, 300, 305, 333-343 gamma-rays, 169-172,233-234,236 offreedom, 137 nuclear composition, 381 Density contrast, 553 origin of, 129, 187-192,606 Density parameter, 493, 522 particles, 129, 169-172,379-383 , 458, 461 proton and alpha particle spectrum, Detailed balancing, 115 383 Deuterium, 1,246,495,507 solar, 191 Diamagnetic materials, 193 Cosmological constant, 460, 489, 501, Dielectric constant, 183,215,217 535 complex, 215, 217 Cosmological models, 457-460; see DieIectric displacement, 184 also Universe Differential, exact, 136 , 441 , 83 perfect,442 in Galaxy, 83, 408 Coulomb barrier, 310 Dipole, 206, 208 Coulomb forces, 142, 183,314 electric, 206 Coulomb scattering, 219 magnetic, 208 Crab nebula, 6, 225, 343, 356, 599 radiation, 206 magnetic field, 358 Dirac monopoles, 192 polarization, 356 Directional diagram, antenna, 126 pulsar, 8, 236, 344,599,601 Dispersion measure, 200 supernova, 6, 343,600 Distance, cosmic, 49--62, 449 supernova remnant, 6, 20, 356, 373, Distance modulus, 54, 588 600 Distance parameter, cosrnic, 449 Critical density, 493 Divergence operator, 184 Curvature constant, 446 DNA (Deoxyribonucleic acid), 565 Curvature-dominated universes, 521 Domain walls, 501 Curvature of space, 443 , 164-165 Curve of growth, 280-283 broadening, 259 Cyclotron frequency, 186 shift, 50, 89, 247 Doppler peaks, 539-542 D-condition, 372 Doppler veIocity, 89 Dalton's law, 110 Dredge-up, 23 Damped oscillations, 194, 264 Dust grains, 111,358,383-387, Damping constant, 281 419--423,488,581 Damping force, 264 alignment in space, 394-400 Damping term, 216 circumstellar, 214, 388 Dark matter, 5, 39, 89, 106, 400, 533, comets, 357 542,554 dynamics, 87 hot and cold, 533-535 force on, 106, 112 de Broglie wavelength, 219 growth, 111,383-387 Debye shielding length, 145, 185, 199, heating and cooling by, 392-393 219 infrared emission, 388-391, 419-423 Decay products, nuclear, 31 interplanetary, 45,87, 166,213-215, , 453, 493 434,581 Index 639

interstellar, 213-215 Electro-weak forces, 498 interstellar reddening, 582 Embedding of spaces, 519 light polarization by, 394-400 Emission measure, 220 light scattering by, 213 Encounter, distant, 85-88 rotation, 137 Endergonic processes, 314, 317 temperature, 125,436 Energy, 71, 162 work function, 392 chemical, 291 zodiacal, 213-215, 579 conservation of, 78, 242, 313 Dwarf galaxies, 35, 91 density, 196 Dwarf stars, 591 generation in stars, 290-292 Dyson civilizations, 561 gravitational, 174--178,291 kinetic, 71, 163 Early main sequence stars, 345,591 loss in star formation, 11,407 Earth,32 mass energy, 78, 163 age, 32, 290, 320,473 nuclear, 291, 312 atmosphere, 33,43, 564 photon, 111 chemical abundance, 325 potential, 71 motion through universe, 168 rotational, 256-258 orbit, 34, 81 total, 71 orbital period, 29, 34 80 vibrational, 255 origins of life on, 42, 564 Enthalpy, 368 radioactive heating, 330 Entropy, 504, 560 rotation, 34, 80 Eötvös-Dicke experiment, 76 Ecliptic, 28, 579 Equation ofstate, 109,299,335 Eddington limit, 403 degenerate plasma, 300 Eddington universe, 459 for stellar interior, 299-301, 335 Einstein, 149-150,172 nondegenerate plasma, 299 coefficients, 272-274, 418 relativistic degenerate plasma, 335 relativity principle, 149-150 Equilibrium process, 319 universe, static, 458, 461 e-process, 319 Electric charge of elementary particles, Equipartition principle, 137 313 , 77, 93 Electric field, 183 , 280-283 Electromagnetic interaction, 472 , 59,152,443,519 Electromagnetic radiation, 3, 46, universe 443, 445 204-236,241-286 Eukarya, 566 absorption, 204--236, 241-286 , 465 absorption coefficient, 216 Event, 151 absorption cross section, 267-271, Evolving universe, 59, 81,441,466 274 Exclusion principle, 118, 243-245 emission, 204-236, 241-286 Exergonic processes, 310, 314 potential, 160, 205 Extinction of radiation, 213-215, speed of propagation, 150, 172, 196, 276-283 609 interstellar, 588 Electron, Extragalactic space, 351, 353, 358 cosmic ray, 169, 172 properties of, 313, 609 Falling body, 65-71 radius, classical, 231 Faraday rotation, 200-204, 352 Electron volt, eV, 610 Faraday's law, 188 640 Index

Fermi-Dirac, dwarf, 35, 35, 91, 582 particles, 118, 130-133, 313 elliptical, 105, 582, 583 assembly, 130 evolution of, 12,35-40,455,510 statistics, 130-133, 135 irregular, 584 Fermienerg~ 130-133,333 Local Group, 35-38 Fermi function, 130 mass of, 89, 92, 105 Fermions, 118, 130, 313, 498 molecular cIoud, 11 Fine structure, atomic, 250 nuclei,210 Fine structure constant, 270 0Id,441 Fischer-Tropsch reaction, 430 pairs of, 35, 105 Flare, solar, 191, 357, 577 random motions, 168,442 Flare stars, 598 red shift-magnitude relation, 55, 454 Flat space, 59, 152,443 rotation, 40 universe, 443 spiral, 40, 358, 582, 583 Flatness problem, 496 young,441 Fluctuations, 135-136 see also Angular diameter of distant Flux, radiation, 282 g.; Clusters of g.; Local Group Flux density, eIectromagnetic, 58, 197 of g.; Recession velocity; and Forced oscillation, 212 Seyfertg. Fourier theory, 264 Galaxy, Milky Way, 35, 129, 179, 189, Four-momentum, 160, 163 200,227,234,247,256,331, Four-vectors, 158-160, 162 376,391,393-400,484,552 Fraunhofer (absorption) line spectrum, age,554 281,358 center, 391, 415 , 410, 418 evolution of, 12,553 Free-free transitions, 215-222, 277, formation of, 552 278,303-307,355 gas content, 353, 358, in radio sources, 220-222 halo, 14, 15; 598 Frequency, electromagnetic wave, 195 , 83 angular, 195 magnetic field, 204, 358, 373, 415 Frequency space, 120 mass,36 Friedmann-Robertson-Walker, FRW, missing mass, 178 metric, 448, 518 plane, 14, 179,200,391 uni verse, 448, 518 Population I stars, 15,54,591 Friedmann uni verse, 460, 462 Population II stars, 15,54,591 Front, 367 spiral arms, 200, 358, 373 D-condition, 372 Galaxy formation, 38-40, 459, 510, ionization, 367 537,552,556 R-condition,371 chemical composition, 38 shock,367,408 in evolving universe, 552 Frozen-in ftow, hydromagnetic, 12, 186 in steady state universe, 547 Fundamentalobserver, 442, 518 Milky Way, 553 Fundamental particIe, 442 through mergers, 555 Galilean relativity principle, 150 Galactic clusters, 13, 583 Gamma-ray bursts, 46, 605 Galaxies, 35-40, 55, 108, 582 Gamma (y-) rays, 3, 4, 46,169-172, barred spiral, 582, 583 233-234,236,469,484 classification of, 581-584 background, 484 distance to, 49-62 in stellar nuclear processes, 314 Index 641

Gas clouds, interstellar, encounters with Halo, galactic, 14, 15,553 stars, 87; see also Interstellar Hanbury-Brown-Twiss Interferometer, space 120-121,124 Gas constant, 110 Harmonically bound charge, 212 Gas , 110 Harrison-Zel'dovich spectrum, 532 Gaunt factor, 305 , 15-16,315,323 Gauss's theorem, 184 , 137 Giant stars, 591 Heat content, 137 Gibbs free energy, 425 Heisenberg's , 118, Globular clusters, 14,38,87,91, 142, 242 331,582,583,583 Helium, 1, 25, 495 age,323 absorption and recombination chernicalabundances,22 coefficients, 362 stars, 323, 599 cosmic origin of, 332, 495, 507 Grains, see Dust Helium burning, 18,317-319 Grand unified theories, 498 shell buming, 19 Gravitational attraction, 39, 63, 142 Heliumcore, 18,317-319,323 strong fields, 174-178 , 18,319 Gravitational constant, G, 66, 73, 461, Helium stars, 23, 325 473,609 Hertz, Hz, 610 constancy of, 473 Hertzsprung gap, 14, 17 effective, 544-546 Hertzsprung-Russell (H-R) diagram, Gravitationallenses, 39,179-181,525 13-19,124,289,322-325,589 and the Hubble constant, 181 tum-off point, 17, 290, 323 Gravitational radiation, 3, 4, 47, see also Hertzsprung gap; Horizontal 209-210,258,263 branch stars; Main sequence; , 258, 263 and White dwarf sequence waves, 3, 4,47, 209-210 Higgs bosons, 503 Gravitational time delay, 178-179 Higgs era, 498 , 168 Higgs field, 463, 498 Ground state energy, 244 Homogeneous universe, 440 Grouping of objects, 583 inhomogeneities, 513 of galaxies, 583 Horizon,cosrnic,I64,465,527 of stars, 583 absolute, 465 Group velocity, 196, 199 event, 465 Gunn-Peterson effect, 352 particle, 465 helium, 352 Horizontal branch stars, 17,324,589 Gyro-frequency, 185 Hot bottom burning, 23 Gyro-radius, 185 H-R diagram, see Hertzsprung-Russell diagram Ha, 248-259, 362, 388; see also Balmer Hubble constant, 56, 181,461,489 spectral series Hubble Space Telescope, 39 HI (neutral hydrogen) region, 10-13, Hydrogen, 243-258, 362 111,358 absorption and recombination magnetic fields in, 253, 358 coefficients, 362 Hn (ionized hydrogen) region, 54, 111, atomic energy levels, 244-254 142-145,221,247,355,362, mass,609 388 molecular, 208, 254-258 Hadrons, 41, 341 negative ion, 255-254, 593 642 Index

Hydrogen (continued) magnetic fields, 185-192,398-399 positive ion, 253 moleeular cIoud, 11 21 cm (1420 MHz) line, 248 stability of medium, 139-141 Hydrogen burning, 17,316,345 IntervaI between events, 152 shell burning, 18,318,317,323,345 spaee like, 153 Hydromagnetics, 186,271,372; see time like, 153 also Invariant magnitude of four-vector, 160, shocks,372 162 , 293, 413 Inverse Compton effect, 228-234, 353 Hyperbolic space, 445, 462; see also energy loss, 380 Pseudosphericalspace see also Compton scattering Hyperbolic universe, 445, 462; see also Ionization front, 367, 415 Pseudospherical universe Ionization losses, 379 Hyperfine splitting, atomic, 248-260 Irreversible processes, 560 Hyperons, 41, 341 Isothermal gas, 112 Hypersphere, 444 IsothermaI processes, 138-139 Hypersurface, 444 , nucIear, 314 Hyperthermophiles, 566 Isotropie gas, 108 , 168, 440 Ideal gas law, 109-1ll of microwave background radiation, Impact parameter, 84 168 IncIination, 28 of uni verse, 440 of planetary orbits, 28, 34 Isotropy problem, 492 of solar , 28 Induced emission of radiation, 208, 266, J-shock, 373 271-283 Jansky, Jy, 610 Inertia, see Mass; Jeans eriterion, 410, 540 Inertial, coordinate system, 77, 149 Jeans mass, 412, 540 Inflationary universe, 39,441,499,527 Johnson noise, 127 inflationary era, 527 Jump conditions, 369 origin of structure, 531 Jupiter, 32, 34, 314, 577, 578 Information, 3-5,44-48, 196 Infrared radiation, 46, 233-234, 385, Kepler's laws, 65, 69-73 388-391 , 71, 163 association with cosmic masers, 276 Klein-Nishina formula, 231, 278 brightness, 124 Knock-on particIes, 171 galaxies, 354 Kpe, Kiloparsec, 36, 54; see also Parsee star formation, 10 Kramer's Law of Opacity, 305 Intensity, radiation, 125,207,266,282 bound-free transitions, 305 Intergalactic space, 351, 352, 358 free-free transitions, 305 Internal energy, 136, 389 Kuiper belt, 33, 577 Interplanetary space, 358 dust, 45 Ly-a, see Lyman radiation Interstellar spaee, 185, 213-232, particIe, 476 393-400 Laplacian operator, 194 dust, 213-215 Larmor frequency, 262 extinction, 588 Larmor radius, 185 gas, 187-192, 196-204,208, Late main sequenee stars, 345, 599 213-232,245-260 Lemaitre universes, 459, 549 Index 643

Length hypothesis, 176 interstellar generation, battery effect, Leptons, 313 375 Life, 559-570 dynamo, 377 chemical basis of, 565 of planets, 34 intellIigent, 568 ofstars, 251, 289, 373 origin of, 42--44, 559-570 ofsun, 241, 251, 373 Light cone, 153 origin,373 Line element, 153,444--447 seed fields, 375 Line shape, electromagnetic transition, shock fronts, 372,415 258-260 solar wind, 358 Lines of force, magnetic, 12, 186, 188 Magnetic , 189-192 Line trapping, 419 , 191 Line width, spectral, 52, 259 Magnetic monopoles, 5, 192, 503 Liouville's theorem, 91, 127-130 Magnetic permeability, 193 , origin, 507 Magnetic quantum number, 249 Local Group of galaxies, 36,45,91, Magnetic rigidity, 191 168,584 Magnetic storms, 577 Long period variable, 14; see also Mira Magnetographic method, 251 variable Magnetohydrodynamics, 186,271,372; Lorentz contraction, 157, 168 see also Hydromagnetics Lorentz force, 185 Magnetosphere, 187, 357, 577 Lorentz profile, spectrallines, 265 Magnitude, 585 Lorentz transformations, 154, 158-160 absolute, M, 588 Luminosity, 14, 19,293,294,301,588 apparent, m, 585 classes of stars, 591 bolometric, 586 of distant galaxies, 449, 452 infrared, 586 Luminosity profile, 293 photographic, 586 Lyman-a absorbers, 165,352,358 ultraviolet, 586 Lyman-a forest, 165,352 visual,586 Lyman limit, 253, 352 Main sequence, 13-21,323,589 Lyman radiation, 102,247,260,263, as distance indicator, 53 270,351,389 stars, 16-23 Lyman spectral series, 247-259, 270 zero-age, 323 oscillator strengths, 270 see also Hertzsprung-Russell diagram Mach's principle, 78,471 Maser, cosmic, 274-276 Mage1lanic clouds, 36, 58 pumping mechanisms, 275 Magnetic bottle, 129, 189-192 three-Ievel, 275 Magnetic dipole moment, 208 Mass, 75-77,164,313 Magnetic field, 129, 145, 185-192,204, elementary particles, 313 241,249-252,352,381 energy, 78, 163 acceleration of cosmic rays, 187-192 gravitational, 75-83 dynamo, 374, 377 inertial, 75-77 extragalactic, 352 Mass 10ss from stars, 23, 289, 367, 591 force-free, 189 Mass-Iuminosity relation, 292, 306, 403 interstellar, 12, 129, 185-192, Massive Compact Halo Object, 204,251-252,373,407--409, MACHO, 534 411--417,373,416 Matter-Antimatter asymmetry, 469, 503 interstellar dissipation, 12, 380 Matter-dominated era, 490 644 Index

Maxwell-Boltzmann statistics, sUrface sampIes, 383 132-133,134-136,260 Moons,34,579 distribution, 116-117 orbits of, 29 Maxwell Equations, 192, 204 Mpc, Megaparsec, see Parsec Mean deviation, 100 Multipole processes, 208 Mean values, 134-135 Muon, 172,470 Mesons, neutrino, 330 JL, 172,342 Mutation, 42, 564 7r, 118, 170, 172 element abundances, 21 Naturalline width, 259, 265 Meteorites, 27, 35, 83, 423, 426, 562, Neutrino, 3, 4, 20,47, 118, 132, 313, 579 329,470,506 abundance of chemical elements in, decay, 330 25 electron, 330 age,473 energy los ses from stars, 20, 316, 320 and cosmic rays, 383 muon, 330 , 35, 427 observations, 329 micrometeorites, 579 , 330 stony, 35, 427 Neutron, 118, 169-172,313,314,609 see also Carbonaceous chondrite; excess, 322 Chondrite Neutron stars, 20, 81, 192, 289, 320, Meteors, 92, 579 338,600 Metric of aspace, 175-176, 444-447 crystallattice, 342 Michelson, 150 density, 339 stellar interferometer, 120, 124 magnetic field, 289, 342 Micrometeorites, 579 mass, 341 Micron, 610 rotation, 343 Mikheyev-Smimov-Wolfenstein structure, 342 (MSW) effect, 330 superfluid, 342 !v1ilky Way, see Galaxy Neutronization, 20, 339 Minkowski diagram, 159, 174; see also Newtonian dynamics, 457 World diagram Novae, 14,54,344,387,591,597 Minkowski space, 152 dwarf,598 , 14-19,275,387,597; see recurrent, 597 also Long period variable NucJear processes in stars, 313-343 Mole, 110 alpha (a-) process, 318 Molar volume, 109 carbon buming, 321, 324 Molecules, interstellar, 256, 275, 387 carbon cycJe, 316, 325 formation, 387 CNO bi-cycJe, 316, 325 large organic, 214 equilibrium (e-) process, 319 Molecular cJoud, 358 oxygen buming, 322 Moment of inertia, 257, 399 p-process, 320 Momentum, 88, 106, 163, 164 proton-proton reaction, 316 conservation of, 242 rapid (r-) process, 320, 320 see also Four-momentum buming, 322 Momentum space, 120 slow (s-) process, 319 Monopoles, cosmic, 500 tripIe , 317, 325 Moon, 60, 117, 125,579 NucJear reaction rates, 310-313, formation of, 32 315-322,332 Index 645

in massive objects, 332 Pau1i exclusion principle, 118,243-245 in stars, 310-313, 315-322 pc, 50, 610; see also Parsec Nuciei, even-even, 314 Perfect cosmo1ogical principle, 442 Nucieons, 41, 245 Period of oscillation, 206 Nul1-geodesic.448 , 117-120,266 Number counts of galaxies, cell, 119,266 cosmological, 57-59, 450, 451, Phase velocity, 196, 199 454 Phonons, 391 Nyquist noise, 127 Photinos,5 Photodissociation regions, PDR, 372 Object,575 , 586 Olbers's paradox, 61, 463 Photovisual magnitude, 586 Opacity, 102,276--280,297,303-307 Photon absorption, 265-271 bound-bound absorption, 277 Photon drag see also Silk damping, 538 bound-free absorption, 277-280 Photons, 118, 243, 313 electron scattering, 277 angular momentum, 243, 409 free-free absorption, 277 Photosphere, 576 Kramer's law of, 305 Pions, 118, 172,469,470 Rosseland mean, 303 Pitch angle of electron trajectories in a stellar atmospheres, 305 magnetic field, 185 stellar interior, 297, 303-307 Planck length, 498 , 220; see also Opacity time, 498 Orbital angular momentum, 28 mass,497 quantum number, 249 P1anck's constant, 118, 131, 242, 609 Orbital period, 29 constancy of, 473 ofmoons,29 Planetary nebulae, 19, 141, 221, of planets, 29 325-327,355,358,399,403, of spectroscopic , 79 591 Orbits, 577 central stars, 14, 19, 591 direct,577 Planetary systems, 30 retrograde, 577 , 432 Organic acids, 562 P1anetoids, see Asteroids Oscillator strength, 269-271, 280 Planets, 26--35, 60, 61, 314, 577 atmospheres, 38 PAH, Polycyciic Aromatic chemica1 makeup, 31 Hyrdocarbons, 391 formation, 30, 109,434 Pair production, 169 giant,33 Paleochroic haloes, 473 mass,92 ,567 orbits, 28, 34,49, 60, 577 , stellar, 50 terrestrial, 33 spectroscopic, 50 Plasma, 87, 142-145, 198-204, trigonometric, 50 215-222,299-301,334 Paramagnetic , 399 drag,87 Paramagnetic substances, 193, 399 equation of state, 299-301 Parent nuciei, 31 Plasma frequency, 199 Parity operation, 475 Poisson-Boltzmann equation, 142-144 Parsec, 50, 610 Poisson's equation, 142,205 , 465 Polarization, 119, 266 Paschen spectral series, 247-259 circu1ar, 201 646 Index

Polarization (continued) , 32, 33, 146,434, Faraday rotation, 200-204 423 of cosmic masers, 276 Protostar, 10, 141,407-409,418 of e1ectrons, 119 Protostellar clouds, 11, 141,407-409 of scattered light, 211 Protostellar matter, 12, 141,407-409 of starlight, 394-400 Pseudospherical space, 445; see also of , 222, 356 Hyperbolic space of Zeeman split lines, 262-264 Pseudospherical universe, 445; see also plane, 202 Hyperbolic universe Polarization field, 184 Pulsar, 8, 20, 46,81,192,199-201,210, Polycyclic Aromatic Hydrocarbons, 343,422,599 PAH,391 binary,210 Population I stars, 15,54,591,599 Pulsating stars, see Vibration of stars Population II stars, 15, 54, 592, 599 Population III stars, 21, 331 Quadrupole radiation, 208-210 Population , 274 electromagnetic, 208, 208 Positron, 169, 172,313-316,470 gravitational, 209 cosmic ray component, 169, 172 moment, 208 Post-infiationary era, 503, 529 Quantum mechanical transition amplitude, 266 Potential, electromagnetic, matrix elements, 266 scalar,205 Quantum numbers, 246, 248, 249 vector,205 magnetic, 249 Potential, gravitational, 71, 79, 175 orbital angular momentum, 249 Potential energy, 71 principal, 246 Poynting-Robertson effect, 166,375 spin, 118 , 196 Quantum osciIlator, 121,273 Pressure, 108, 196-198,299-301 Quantum theory of radiation, 208, at shock front, 367 241-286 gas, 108 Quarks, 41, 341 in stellar interior, 294, 314, 299-301 Quasars, 8, 12,39,45,46, 165, 191, magnetic, 196-198 210,226,243-245,331,353, partial, 11 0 353,358,376,603 radiation, 111, 198, 271, 283 gravitationally lensed, 179-181 Primeval solar nebula, 24, 434 red shift-magnitude relation, 603 condensation temperatures, 426 Quasi stellar objects, QSO, see Quasars Primordial matter, 21-26 QSO, see Quasars Probability, 99, 103 absolute, 99 observations, 49,241,473 relative, 99 Radial velocity, 50-57, 82, 553 Properlength, 154, 157 Galactic differential rotation, 83 Proper motion of stars, 50, 598 of galaxies, 55-57, 105 Propertime, 154, 176,442,518 of stars, 50, 289, 553, 599 Protogalactic stage, 38; see also Galaxy Radiation, 111-1l2 formation density, 112,488 Protons, 118, 164, 169-172,313,476, gravitational defiection, 93 609 kinetics, 111-112 cosmic ray, 169-172 pressure, 111, 198,271,283,300 Proton-proton reaction, 316, 488 Radiation-dominated era, 490 Index 647

Radiative transfer, 102,280-283,297, for astar, 296 301-307,346 Rest-mass, 163 Radioactivity Riemann curvature constant, 446, 448, dating, 31, 320, 554 514 decay products, 31 RNA (Ribonuc1eic acid), 565 Radio observations, 125-127, 194, Robertson-Walker metric, 448 196,203,230-233,224-228, Rl/lmer,150 248-252,274-276,355,387, Root mean square deviation, 100 425 ROSAT (Röntgen Satellite), 8 of stars, 601 Rosseland mean opacity, 303 21 cm (1420 MHz), 248, 252 Rotation of stars, 29, 289, 597 Radius of curvature, cosmic, 445 RR Lyrae stars, 14,54,344,553,597, Random walk, 98-102 599 Rapid neutron (r-) process, 320, 554 Runaway stars, 92 Rayleigh-Jeans limit, 125,221 Rydberg constant, 609 , 213 R-condition,371 S stars, 23, 328 R Coronae Borealis stars, 598 Sachs-Wolfe effect, 526 Recession velocity of galaxies, 38, 440, Saha equation, 133-134, 304 443,454,585 Salpeter birthrate function, 292, 600 Recombination era, 495 Satellites of planets, 580 Recombination of ions and electrons, Saturn, 26-35 362,362,388,495 , 460, 489 coefficients for hydrogen and helium, Scale height of atmosphere, 114 362 Scale-invariant cosmic fluctuations, 532 Redgiant, Scattering,83-88 branch ofH-R diagram, 13-21,324, Coulomb, 83-88 589 dust grains, 213-215 second r.g. stage, 23 gravitational, 83-88 SUffS, 13-21,318,345,599 Klein-Nishina cross section, 231 Red shift, cosmological, 22, 55, 440, radiation, cross section, differential, 443,454,585 211 correction, 60, 452 Rayleigh,213 gravitational, 78-86 Thomson,211 parameter, z, 55, 449 total, 211 Reduced mass, 69 Schwarzschild line element, 176, 514 of an electron, 246 , 177,333,497 Re-entrant universe, 456 Scorpio XR-l, 7-8, 403 Rees-Sciama effect, 527 Seed galaxies, 547 , 214 Seed magnetic field, 375 Refractive index, 213, 215 Seeliger's theorem, 57 complex, 215 Selection rules, 208, 243, 261-263, 279 Relativity, 149-182 SETI (Search for Extra-Terrestrial Einstein's, 150 Intelligence),568 Galileo's, 150 Seyfert galaxies, 353, 603 general, 150, 174,448,457 Sheets of galaxies, 543 principle, 78, 149 Shell stars, 598 special, 149-182 Shock compression, 415 Relaxation time, 86, 296 triggering protostellar collapse, 415 648 Index

Shock frönt, 367, 408, 415 barred,582 Shooting star, see Meteor Spontaneous emission of radiation, 209, Signature of space, 153 266 Silk damping, 540 s-process, 319 Simply connected uni verse, 455 Sputtering,386 Simultaneity, 151 Star formation, 10-13, 139-141,323, Slow neutron (s-) process, 319 407-409,604 Slow roll, inflationary, 501 Stark effect, 273 Solar constant, 112, 124 Stars, see Associations of so; Barium so; Solar cycle, 576 Binary so; Black holes; Carbon Solar oscillations, 242 so; Cepheid variables; Chernical Solar System, 11,26,49,125,423-436, elements; Color-magnitude 484,577 diagram; Compact objects; abundance of chemical elements, 25 Core; Distance, Dwarf so; Early age,554 so; Energy generation in so; , 82 Equation of state for stellar formation of, 26-35 interior; Giant so; Globular origin, 109,434 cluster; Grouping of so; Helium primeval nebula, 27, 434 so; Hertsprung-Russell diagram; size,49 Horizontal branch so; Late Solar wind, 357, 358, 357, 367,403, so; Lithium so; Long period 425,576 variable; Mass loss from stars; , speed of, 366, 540 Mira variable; Neutron s; Source function, 282 Novae; Nuclear processes in so; Space trave1, 178, 568 Planetary nebulae; Population I Spallation products, 382 stars; Population II stars; Proper , 149-182 motion of So; Protostar; Pulsar; Spectral classification of stars, 589-591 Radial velocity of So; Spectral early types, 591 classification of So; S So; Star late types, 591 formation; Stellar atmospheres; Spectral index of radio sources, 226 Stellar diameters; Stellar Spectrallines, 258-274, 280-283 dynamics; Stellar evolution; collisional broadening, 260 Stellar opacity; Stellar structure; curve of growth, 280-283 Stellar winds; Subgiant So; Doppler broadening, 259 Supernova; Supergiant So; equivalent width, 52, 280-283 Variable So; Vibration of So; line shape, 259, 263-265 White dwarf; and X-ray sources naturalline width, 259, 265 Static field, 177 Spherical universe, 445, 462 Static metric, 519 Spin, 118,245,248-252,256,313 Stationary field, 177 of elementary particles, 313 Stationary non-equilibrium, 560 Spin period, 29 Statistical , 274, 498 ofplanets, 27, 34 Steady state universe, 441, 446, 547 of stars, 30 C-field, 463 ofsun, 27, 29 cosmology, 442, 460 Spin values, 118, 243, 313 matter creation, 463 Spiral density wave, 83 Stefan-Boltzmann constant, 123,609 Spiral galaxies, 582 Stellar atmospheres, 25, 280-283 arms, 83, 200, 582 Stellar diameters, 120, 124 Index 649

Stellar drag, 85 Swiss-cheese universe, 514-519, 550 Stellar dynamics, 85,142-145 Synchrotron radiation, 222-228, 353, Stellar evolution, 15-23,322-329,553 356 Stellar opacity, 276-280, 297, 303-307 energy los ses, 380 Stellar structure, 293 polarization, 356 Stellar surface composition, 12 self-absorption, 228 Stellar winds, 22, 357, 358, 367,423 of radiation, 266, Tachyons,172-174,570 271-283 Temperature, 109 Strange particles, 41 antenna, 127 Strings, cosmic 500 brightness, 126 Strömgren sphere, 360-365 color, 124 Strong interactions, 81, 472, 498 effective,124,595,596 Structure, cosmic, 513-556 of stellar surface, 124,287,288,595, Subdwarf stars, 591, 599 596 Subgiant, 14, 15 Texture, cosmic, 500 Subgiant branch, 14, 15 Thermal noise, 127 Subhorizon condensation, 542 , 130, 136-138 Substratum, 442 biological systems, 559 Sun, 241, 576 closed systems, 559 active, 191, 357 first law, 136 age,290,320 open systems, 559 atmosphere, radiative transport, 254 secondlaw,130,475,504 bolometric magnitude, 588 Thermonuclear reactions; see also chemical abundances, 325-330 Nuclear processes in stars corona, 576 Thomas-Kuhn sum rule, 271 distance, 49, 91, 610 , 211, 228, 278 evolution of, 323, 345 cross section, 211, 278, 488 gravitation al deftection of light, 179 opacity due to, 277, 303, 305,488 internal rotation, 242, 289 Tidal disruption, 37, 90 luminosity, 291, 323, 576, 588, 610 Time, 80-82,474-478 magnetic field measurements, 252 atomic,80 mass, 92, 290, 576, 610 for measuring, 80 radius, 296, 323, 576 direction of, 474-478 X-rays, 6, 289 , 80 see also Solar, , , nuclear,80 Sunspot, 576 pulsar, 81 number,576 universal, 80 Sunyaev-Zel'dovich effect, 232 , 157 Supergiant stars, 387, 591 gravitational, 82 Superhorizon condensation, 540 special relativistic, 157 Supernova, 1,6,20, 191,210,320,338, Time-reversal operation, 475 367,415,597 of the universe, 455 remnant, 6, 356, 391, 597, 600 Transfer, equation of, 282 Superparamagnetism, 400 Transition, atomic, 241-286 Suprathermal particles, 188 amplitude, 266-271 S urface brightness, 125 forbidden, 208, 273, 279 of a planet, 114 prob ability, 265-271 Surface integral, 184 selection mies, 273-276, 279 650 Index

Transition (continued) principle; Metric of aspace; two photon, 249 Number counts of galaxies; Travel in the universe, 568 Olbers's paradox; Proper time; Triple-alpha process, 317, 325 Pseudospherical universe; T-Tauri variables, 15, 16,596 Quasars; Radial velocity of Turbulence, 41-42, 374 galaxies; Radius of curvature; Turbulent motion, 374 Red shift; Re-entrant uni verse; Relativity; Riemann curvature U1traviolet radiation, 563 constant; Robertson-Walker brightness, 124, 360 metric; Schwarzschild radius, observations, 214, 455 Spherical universe; Steady state Uncertainty principle, 118, 120, 242 universe; Substratum Time; Universe, 132, 151, 168,439-478, Topology of the universe; World 483-510 map; World picture; and World age,446,491 time cIosed,446 Uranus, 27, 34 density, 463, 547 density-temperature history, 494, 524 Vacuum, false, 501 early history, 497-510 Vacuum mass density, 461 geometric properties, 443 Van Allen belts, 187 inhomogeneities, 513 Vapor pressure, 386, 427, 435 open, 446 Variable stars, 597 self-regenerating, 441, 463 extrinsic variables, 597 size, 38, 49-62 intrinsic variables, 597 stability, 459, 462 Velocities, composition (addition) of, see also B1ack holes; Chemical 156 elements; Constants of Nature; Vibrational energies, molecular, 255 Cosmic background radiation; Vibration of stars, 343 Cosmic distance; Cosmic Virial theorem, 88-90, 106, 140 expansion; Cosmological Visual magnitude, 586 constant; Cosmological models; Visual observations, 48-52, 52, 120, Cosmological principle; 124,161,214,237,233-234, Curvature of space; Deceleration 241-242,246,287,355-360, parameters; de Sitter universe; 454,606 Distance; Eddington universe; Voids, cosmic, 38, 584 Einstein universe; EucIidean space; Evolving universe; Flat vapor molecules, 275 space; Friedmann universe; Wave, electromagnetic, 194 Friedmann-Robertson-Walker carrier, 195 metric; Fundamental observer; damped,194 Galaxies; Galaxy formation; group velocity, 196, 199 Gravitational constant; phase velocity, 196, 199 Homogeneous universe; transverse, 195 Horizon; Hubble constant; Wave equation, 195 Hyperbolic universe; Isotropy, Wavelength,120 Klein-Alfven universe; Wave velocity, 196, 199 Lemaitre universe; Line group, 196, 199 element; Luminosity of phase, 196, 199 distant galaxies; Mach's Wave number, 195 Index 651

Weak interactions, 81, 472 points, 151 Weakly interacting massive particles, time, 442, 518 WIMPS, 5, 534 Worm holes, 569 White dwarf, 14, 19,324,333,591 W Virginis stars, 597 chemical composition, 362 companion, 426 X-ray sources, 5-9, 40, 230-234, 353, density, 339 422,599 H-R diagram, 14, 338, 589 background radiation, 8,384,484 rotation, 344 binary stars, 426, 601 structure, 333 galaxies, 8, 353 vibration, 344 observations, 5-9,46, 23J-234, 353, Wilson-Bappu effect, 51 384 WIMPS, see also Weakly interacting quasars, 353, 603 massive particles, 5 stars, 601 Wolf Rayet stars, 324, 591 Work,136 , YSO, 423 Work function, 392 World diagram, 153, 174; see also Zeeman effect, 250-252, 262 Minkowski diagram Zeeman splitting, 250-252, 262 World, Zero age main sequence, 323 line,151 Zodiacal dust, 35, 484, 579 map, Zodiacallight, 484, 579 picture, 442 [7\/\1 ASTRONOMY AND LIBRARY ASTROPHYSICS LIBRARY

Continued from page ii

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