The universe around us

The process of carving out the universe which we considered in the last chapter ends normally with a simple star, although special accidents may have other consequences. As the result of close approaches with other stars, a tiny fraction of the total number of the stars, perhaps about one star in 100,000 (p. 341 below), may be attended by a retinue of planets. Another fraction, still small, although far greater than the foregoing, appears to have broken up as the result of excessive rotation, and formed binary or perchance multiple systems. But the destiny of the majority of stars is to pursue their paths solitary through space, neither breaking up of themselves nor being broken up by other stars. The only contact such stars have with the outer universe is that they are incessantly pouring away radiation into space. This outpouring of radiation is almost entirely a one-way process, any radiation a star may receive from other stars being quite inappreciable in comparison with the amount it is itself emitting. The radiation is accompanied by a loss of weight, and this again is all give and no take, the weight of any stray matter the star may sweep up out of space, like that of any radiation it receives, being quite inappreciable in comparison with the weight it loses by radiation. Without unduly straining the facts, the normal object in the sky may be idealised as a solitary body, alone in endless space, which continually pours out radiation and receives nothing in return.

In the present chapter we shall consider the sequence of changes which such a star may be expected to experience during the course of its life. Having already discussed the mechanical accidents to which stars are liable, namely, fission through rotation and break-up through the tidal action of a passing star, we now turn to consider the life of a normal star which escapes all accidents until it finally becomes extinct through mere old age.

It will be necessary in the first place to describe the physical states of the various types of stars observed in the sky, and as a preliminary to this we must explain how the observations of the astronomer are translated into a form which gives us direct information as to the condition of the star.

SURFACE-TEMPERATURE. In Chapter II (p. 140) we saw how each colour of light or wave-length of radiation has a special temperature associated with it, light of this colour predominating when a body is heated up to the temperature in question. For instance, a body raised to what we call a red-heat emits more red light than light of any other colour, and so looks red to the eye.

Thus if a star looks red, it is legitimate to infer that its surface is at the temperature we describe as a red-heat. If another star has the colour of the carbon of an arc-light, we may conclude that its surface is at about the same temperature as the arc. In this way we can estimate the temperatures of the surfaces of the stars.

In practice the procedure is not so crude as the foregoing description might seem to imply. The astronomer passes the light from a star through a spectroscope, thus analysing it into its different colours. By a process of exact measurement, he then determines the proportions in which the different colours of light occur. This shews at once which colour of light is most plentiful in the spectrum of the star. Either from this or from the general distribution of colours, he can deduce the temperature of the star’s surface.

We have already seen (p. 123) how Planck discovered the law according to which the radiation emitted by a full radiator is distributed amongst the different colours or wave-lengths of the spectrum. The four curves shewn in fig. 15 represent the theoretical distribution for the radiation emitted by surfaces at the four temperatures 3000, 4000, 5000 and 6000 degrees respectively. The different wave-lengths of light are represented by points on the horizontal axis, the marked wave-lengths being measured in the unit of a hundred-millionth part of a centimetre, which is usually called an Angstrom. The height of the curve above such a point represents the abundance of radiation of the wave-length in question.

The two methods of determining stellar temperature will be easily understood by reference to these curves. The 6000 degrees curve reaches its greatest height at a wave-length of 4800 Angstroms, so that if light of wave-length 4800 Angstroms proves to be most abundant in the spectrum of any star, we know that the star’s surface has a temperature of 6000 degrees. The second method consists merely in examining to which of the theoretical curves shewn in fig. 15 the observed curve can be fitted most closely.

Either of these methods indicates that the temperature of the sun’s surface is about 6000 degrees absolute, which is nearly twice the temperature of the hottest part of the electric arc. The total amount of light and heat received on earth from the sun shews that the sun’s radiation must be very nearly, although not quite, the “full temperature radiation” (p. 123) of a body at this temperature. This is also shewn by the sun’s radiation being distributed among the various colours in a way which conforms very closely to the theoretical curve for a full radiator at 6000 degrees shewn in fig. 15.

The surface-temperature of a star can also be estimated from its spectral type. Many of the lines in stellar spectra are emitted by atoms from which one or more electrons have been torn off by the heat of the star’s atmosphere. We know the temperatures at which the electrons in question are first stripped off their atoms, and so can deduce the star’s temperature.

The temperatures which correspond to the different types of stellar spectra as shewn in Plate VIII (p. 51), are approximately as follows:

The last three entries in the table refer only to normal stars having diameters comparable with that of the sun. We shall find (p. 276) that a second class of stars (giants) exist, whose diameters are enormously greater than the sun’s. These have the substantially lower temperatures shewn below:

In studying stellar structure and mechanism, we are less concerned with the heat of the star’s surface as measured by its temperature, than with the amount of radiation it pours out per square inch.

This of course depends on the temperature; the hotter a surface, the more radiation it emits. But the temperature does not measure the quantity of radiation emitted. If we double the temperature of a surface it emits 16 times, not twice, its previous amount of radiation; the radiation from each square inch of surface varies as the fourth power of the temperature. As a consequence, a star with a surface-temperature of 3000 degrees, or half that of the sun, emits only a sixteenth part as much radiation per square inch as the sun[23]. The radiation of each star is a compound of light, heat and ultra-violet radiation, and the proportions of these are not the same in different stars; the cooler a star’s surface the greater the fraction of its radiation which is emitted as heat. Thus the star at 3000 degrees will emit nothing like as much as a sixteenth of the sun’s light per square inch, but will emit more than a sixteenth of the sun’s heat.

This shews that the total emission of radiation of a star cannot be estimated from its visual brightness alone; a substantial allowance must always be made for invisible radiations, both for the invisible heat at the red end of the spectrum and for the invisible ultra-violet radiation at the other end. The importance of these corrections is shewn in fig. 16. The four thick curves are identical with those already given in fig. 15, and shew how the radiation from a star of given surface-temperature is distributed over the different wave-lengths. The total radiation emitted at any temperature is of course represented by the whole area enclosed between the corresponding curve and the horizontal axis. The eye is only sensitive to radiation of wave-lengths lying between 3750 and 7500 Angstroms, so that of all this radiation only that part in the shaded strip is visible, all the rest representing invisible radiation.

We see at once that a fair proportion of the radiation emitted by a star at 6000 degrees comes within the range of visibility, but only a small fraction of that emitted by a star at 3000 degrees. Taking the stars as a whole, star-light forms only a small part of the total radiation of the stars.

If our eyes were suddenly to become sensitive to all kinds of radiation, and not to visual light alone, the appearance of the sky would undergo a strange metamorphosis. The red stars Betelgeux and Antares, which are at present only 12th and 16th in order of brightness, would flash out as the two brightest stars in the sky, while Sirius, at present the brightest of all, would sink to third place. A star in the very undistinguished constellation of Hercules would be seen as the sixth brightest star in the sky. It is the star α Herculis, at present outshone by about 250 stars. As a consequence of its extremely low temperature of 2650 degrees, this star emits its radiation almost entirely in the form of invisible heat. For instance it emits 60 times as much heat as the blue star η Aurigae, whose temperature is about 20,000 degrees, but only four-fifths as much light.

Allowances for invisible radiation have been made in all the calculations referred to in the present book, although it has not been thought necessary continually to restate this.

STELLAR DIAMETERS. It is easy to measure the diameter of a planet, because this appears in the telescope as a disc of finite size. But the stars are too remote for their diameters to be measured in the same way. No star appears larger in the sky than a pin-head held at a distance of six miles, and no telescope yet built can shew an object of this size as a disc. All stars, even the nearest and largest, appear as mere points of light[24], so that their diameters can only be measured by roundabout methods.

When a star’s distance is known, we can tell its luminosity from its apparent brightness. From this, after allowing for invisible radiation, we can deduce the star’s total outpouring of energy—so many million million million million horse-power. We also know its outpouring of energy per square inch of surface, because this depends only on its surface-temperature which we deduce directly from spectroscopic observation. Knowing these two data, it is a mere matter of simple division to calculate the number of square inches which make up the star’s surface, and this immediately tells us the diameter of the star.

The diameters of exceptionally large stars may be measured more directly by an instrument known as the interferometer. When we focus a telescope on a star we do not, strictly speaking, see only a point of light, but a point of light surrounded by a rather elaborate system of rings of alternating light and darkness, called a diffraction pattern. It might be thought that the size of these rings would tell us the size of the star, but the two have nothing to do with one another. The rings represent a mere instrumental defect, their size depending solely on the size and optical arrangement of the telescope. Following a method suggested by Fizeau in 1868, Professor Michelson has shewn how even this defect can be turned to useful ends, and by its aid has produced what is perhaps the most ingenious and sensational instrument in the service of modern astronomy—the interferometer. In effect, this instrument superposes two separate diffraction patterns of the same star, and sets one off against the other in such a way as to disclose the size of star producing them. The diameters of a few of the largest stars have been measured in this way, so that we may say that we know their sizes from direct observation. In every case the directly measured diameter agrees fairly well, although not perfectly, with that calculated indirectly in the way already explained. The discrepancies, which are not serious, appear to result from red stars not being accurate “full radiators” in the sense explained on p. 123.

The interferometer method is only available for the largest stars, but at the extreme other end of the scale the theory of relativity has come to the rescue. Einstein shewed it to be a necessary consequence of his theory of relativity that the spectrum of a star should be shifted towards the red end by an amount depending on both the weight and the diameter of the star. If, then, a star’s weight is known, the observed spectral shift ought immediately to tell us its diameter. This spectral shift has recently been observed in the light received from the companion of Sirius, and measurements of its amount lead to a value for the star’s diameter which agrees exactly with that calculated from its luminosity. Thus at both ends of the scale, for the very largest as well as for the very smallest of stars, direct observation confirms the values calculated for the diameters of the stars.

We may accordingly feel every confidence in the calculated diameters of all stars, even when these cannot be checked by direct measurement. Indeed a discrepancy between the true and calculated diameters could only arise in one way. The diameters are calculated on the assumption that the stars emit their full temperature-radiation. If the stars had been partially transparent like the nebulae, or solid bodies like the moon, this assumption would have been false, and its falsity would at once have been shewn by discordances between the calculated and measured diameters of the stars. The fact that no large discordances appear suggests that the stars emit nearly full temperature-radiation throughout the whole range of size from the largest to the smallest.

THE VARIETY OF STARS

Observation shews that the physical characteristics of the stars vary enormously, so that it is easy, as we shall soon see, to tell a sensational story by contrasting extremes, setting the brightest against the dimmest, the biggest against the smallest, and so on. This would, however, give a very unfair impression of the inhabitants of the sky; it would be like judging a nation from the giants and dwarfs, the strong men and the fasting men, seen inside the showman’s tent.

We shall obtain a more balanced impression of the actual degree of diversity shewn by the stars as a whole if we consider the physical states of those stars which are nearest the sun. By taking these precisely in the order in which they come, we avoid any suspicion of going out of our way to introduce stars merely because they are bizarre or exceptional. The small group of stars obtained in this way may be expected to form a fair sample of the stars in the sky, although of course it will not be a large enough sample to include extremes. We need not discuss the sun itself in detail because it will figure as our standard star, with reference to which all comparisons are made.

The System of α Centauri. This system consists of three constituent stars, which are believed to be our three nearest neighbours in space.

The brightest, α Centauri A, is very similar to the sun. It is of the same colour and spectral type, but weighs 14 per cent. more and is about 12 per cent. more luminous. Being of the same colour as the sun, it emits the same amount of radiation per square inch. Thus its 12 per cent. greater luminosity shews that it must have a surface 12 per cent. greater, and therefore a diameter 6 per cent. greater, than the sun.

The second constituent, α Centauri B, is considerably redder than the sun, its surface-temperature being only about 4400 degrees against the sun’s 6000 degrees or so. It has 97 per cent. of the sun’s weight, but only about a third of its luminosity. Yet, as a consequence of its low temperature, it needs 50 per cent. more area than the sun to discharge a third of the sun’s radiation; this makes its diameter 22 per cent. greater than that of the sun. α Centauri A and α Centauri B together form a visual binary, the two components revolving about one another in a period of 79 years.

Neither of these two constituents is very dissimilar from the sun, but the third star of the system, Proxima Centauri, is of an altogether different type. It is red in colour, with a surface-temperature of only about 3000 degrees. It is exceedingly dim, emitting only a ten-thousandth part as much light as the sun, and has only a fourteenth part of the sun’s diameter. Its weight is unknown.

The sizes of the three stars of this system, with that of the sun for comparison, are shewn in fig. 17.

Munich 15040. This is a single faint star about which little is known. Its surface is red, with a temperature probably little above 2500 degrees, and it emits only ¹/₂₅₀₀th of the light of the sun.

Wolf 359. This is the faintest star yet discovered, but beyond this very little is known about it. It is red in colour and emits only about 1/50,000th of the light of the sun.

Lalande 21185. Another faint red star, emitting ¹/₂₀₀th of the light of the sun.

The System of Sirius. This consists of two very dissimilar stars, there being some suspicion that a third also may exist.

The principal star, Sirius A, which appears as the brightest star in the sky (the Dog-star), is white in colour and has a surface-temperature of about 11,000 degrees. As this is nearly twice the sun’s temperature, Sirius A emits nearly 16 times as much radiation per square inch as the sun. Its luminosity is about 26 times that of the sun, and this requires the star’s diameter to be 58 per cent. greater than that of the sun. It has nearly four times the sun’s volume, but only 2·45 times its weight, so that matter is not as closely packed in Sirius A as in the sun. An average cubic metre contains 1·42 ton in the sun, but only 0·93 ton in Sirius A.

The faint companion Sirius B is one of the most interesting stars in the sky. It is of nearly the same colour and spectral type as Sirius A, but emits only a ten-thousandth part as much light. After allowing for the slight difference in surface-temperature, we find that its surface is only ¹/₂₅₀₀th, and its diameter ¹/₅₀th of that of Sirius A. Yet Sirius A weighs only three times as much as Sirius B, although having 125,000 times its volume. It is not Sirius A but Sirius B that is remarkable; the average density of matter in the latter is about 60,000 times that of water, the average cubic inch containing nearly a ton of matter. Fig. 18 shews the sizes of the two components of Sirius drawn to the same scale as fig. 17.

B.D. 12° 4523 and Innes 11 h. 12 m., 57·2°. Two stars, as to the physical state of which nothing is known, except that they are very faint, emitting ¹/₁₄₀₀th and 1/10,000th of the sun’s light respectively.

Cordoba 5 h. 343 and τ Ceti. Two faint stars, both of reddish colour, emitting ¹/₆₀₀th and a third of the sun’s light respectively.

The System of Procyon. This is a binary system, similar in many respects to Sirius. The main star, Procyon A, is of the same general type as the sun, but weighs 24 per cent. more, and emits 5½ times as much light. Its surface-temperature is about 7000 degrees, and its diameter is 1·80 times that of the sun.

The faint companion, Procyon B, is so faint that nothing is known as to its physical condition except that it emits only 1/30,000th of the light of the sun. Its weight is 39 per cent. of the sun’s weight.

Fig. 19 shews the sizes of the two components of Procyon on the same scale as before.

Next in order, as we recede from the sun, come eight very undistinguished stars, every one of which is redder and fainter than the sun, none of them having a surface-temperature higher than 5000 degrees, and none of them emitting more than a quarter of the sun’s light. After these we come to:

The System of Kruger 60. This is a binary system in which both components are small, red and dim.

The brighter component, Kruger 60 A, has a surface-temperature of 3200 degrees, and emits ¹/₄₀₀th of the light of the sun. Its diameter is a third, and its weight a quarter of the sun’s; so that its substance must be packed about 7 times as closely as that of the sun.

The fainter component, Kruger 60 B, has a similar surface-temperature but emits only 1/14,000th of the sun’s light. Its diameter is a sixth, and its weight a fifth of the sun’s; so that its substance must be packed about 40 times as closely as that of the sun. The system is illustrated in fig. 20.

van Maanen’s star. Another very faint star, which has the high surface-temperature of 7000 degrees. Notwithstanding this, it only emits ¹/₆₀₀₀th of the sun’s light. Consequently its diameter is only about ¹/₁₁₀th of the sun’s, the star being if anything smaller than the earth. Its weight is unknown, but its substance is in all probability packed even more closely than in Sirius B.

The discussion of this sample of stars suggests that the majority of stars in space are smaller, cooler and fainter than the sun. Stars exist which are far brighter than the sun, but they are exceptional, the average star in the sky being a small dull dim affair in comparison with our sun.

With this sample of the average population of the sky before us, we may proceed to discuss the various characteristics of stars in a systematic way, without fearing to mention extremes. Let us begin with their weights.

STELLAR WEIGHTS. The two stars of smallest known weight in the whole sky are the faint constituent of Kruger 60, just discussed, and the faintest constituent of the triple system ο₂ Eridani, each of which has a fifth of the sun’s weight. But the stars whose weights are known are so few that there can be no justification for supposing these to be the smallest weights which occur in the whole universe of stars. A general survey of the situation, on lines to be indicated later (p. 281), suggests that there may be many stars of still smaller weight, but that very few are likely to have weights which are enormously smaller. Probably very few stars weigh as little as a tenth of the sun’s weight.

The vast majority of stars have weights intermediate between this and ten times the sun’s weight. Stars which weigh even three times as much as the sun are rare, those which weigh ten times as much are very rare, probably only about one star in 100,000 having ten times the weight of the sun. Even higher weights undoubtedly occur—we have already mentioned Plaskett’s star, whose two constituents have more than 75 and 63 times the sun’s weight respectively, and the quadruple system 27 Canis Majoris which to all appearances weighs 940 times as much as the sun—but such instances are very, very unusual. We may say that as a general rule the weights of the stars lie within the range of from a tenth to ten times the sun’s weight, and we shall find that stars differ less in their weights than in most of their other physical characteristics.

LUMINOSITY. A far greater range is shewn, for instance, in the luminosities of the stars—in their candle-powers measured in terms of the sun’s candle-power as unity. The most luminous star known is S Doradus, already mentioned, with 300,000 times the luminosity of the sun, while the least luminous is Wolf 359 with only a fifty-thousandth part of the luminosity of the sun. The range of stellar luminosities, as of stellar weights, extends about equally on the two sides of the sun, so that the sun is rather a medium star in respect both of weight and luminosity. It is medium in the sense of being about half-way between extremes, but we have seen that there are many more stars below than above it.

In comparison with the very moderate range of stellar weights, the range of luminosity is enormous; S Doradus is 15,000,000,000 times as luminous as Wolf 359. If S Doradus is a lighthouse, Wolf 359 is something less than a firefly, the sun being an ordinary candle. If the sun suddenly started to emit as much light and heat as S Doradus, the temperature of the earth and everything on it would run up to about 7000 degrees, so that both we and the solid earth would disappear into a cloud of vapour. On the other hand, if the sun’s emission of light and heat were suddenly to sink to that of Wolf 359, people at the earth’s equator would find that their new sun only gave as much light and heat at mid-day as a coal fire a mile away; we should all be frozen solid, while the earth’s atmosphere would surround us in the form of an ocean of liquid air. So far as we know, there is no possibility of the sun suddenly beginning to behave like S Doradus, but we shall see later that the possibility of its behaving like Wolf 359 is not altogether a visionary dream.

SURFACE-TEMPERATURE AND RADIATION. Sirius has been found to have the highest surface-temperature of all the stars near the sun; it is about 11,000 degrees, or nearly double that of the sun. Going further afield, we find many stars with far higher surface-temperatures. For instance, Plaskett’s star is credited with a temperature of 28,000 degrees, although it must be admitted that a substantial element of uncertainty enters into all estimates of very high stellar temperatures.

At the other extreme, stellar temperatures ranging down to about 2500 degrees are comparatively common. The lowest temperatures of all are confined to variable stars of a very special type (long period variables) in which the light-variation is accompanied by, and indeed mainly arises from, a variation in the temperature of the star’s surface. The temperature of these stars when at the lowest, ranges down to 1650 degrees, which is but little above the temperature of an ordinary coal fire. In many of them, the temperature varies through a large range, but it never sinks so low that the star becomes completely invisible. Thus there is a range of temperature below about 2500 degrees which no star is known to occupy, except for the long-period variables which only enter it at intervals. This would seem to suggest that the number of absolutely dark stars in the sky is relatively small. Other lines of evidence lead to the same conclusion. If a star ceased to shine, its gravitational pull would still betray its existence. Although we could not detect a single dark star in this way, we could detect a multitude. If a great proportion of stars were dark, we should probably suspect the existence of the dark stars from their effects on the motions of the remainder, so that general gravitational considerations preclude the possibility of there being a great number of dark stars.

So far as our present knowledge goes, the temperature of stellar surfaces ranges, in the main, from about 30,000 degrees down to about 2500, the lower limit being extended to about 1650 for long-period variables at their lowest temperatures.

Apart from the long-period variables, this is only a 12 to 1 range, so that the temperatures of the stars are more uniform than either their luminosities or their weights. We must, however, remember that a star’s radiation per square inch is far more fundamental than its surface-temperature, and that a 12 to 1 range in the latter involves a range of over 20,000 to 1 in the former. If we include the long-period variables, there is a range of about 110,000 to 1 in the emission of radiation per square inch.

In terms of horse-power, the sun emits energy at the rate of 50 horse-power per square inch, a star with a surface-temperature of 1650 degrees emits only 0·35 horse-power per square inch, while Plaskett’s star, with a surface-temperature of 28,000 degrees, emits about 28,000 horse-power per square inch. In plain English, each square inch of this last star pours out enough energy to keep an Atlantic liner going at full speed, hour after hour, and century after century. And the energy emitted per square inch by the surfaces of various stars covers the whole range from the power of a liner to that of a man in a row-boat.

SIZE. The four stars of largest known diameter are the following:

All these diameters have been measured directly by the interferometer. On the scale used in figs. 17 to 20, in which the sun is about the size of a sixpence, the circle necessary to represent ο Ceti would be as large as the floor of a good-sized room, while the second star of the system (for ο Ceti is binary) would be the size of a grain of sand. We may obtain some idea of the immense size of these stars by noticing that every one of their diameters is larger than the diameter of the earth’s orbit, so that if the sun were to expand to the size of any one of them we should find ourselves inside it.

These stars must be exceedingly tenuous. Antares, for instance, occupies 90,000,000 times as much space as the sun, so that if its substance were as closely packed, it would weigh 90,000,000 times as much as the sun. Yet, in actual fact, it probably has only about 40 or 50 times the sun’s weight, the difference between this number and 90,000,000 arising from the difference between the densities of Antares and the sun. On the average a ton of matter in the sun occupies considerably less than a cubic yard; in Antares it occupies rather more space than the interior of Saint Paul’s Cathedral. Yet a detailed study of stellar interiors shews that we can attach but little meaning to an average of this sort. It is quite likely that matter at the centre of Antares is packed nearly (but not quite) as closely as matter at the centre of the sun (p. 291 below). The huge size of Antares is probably due mainly to an enormously extended atmosphere of very tenuous gas, and there is not much point in striking an average between this and the compact matter at the centre of the star.

The mysterious objects known as planetary nebulae, of which examples are shewn in Plate II (p. 28), ought perhaps to be regarded as stars of still larger diameter. At the centre of each of these the telescope discloses a comparatively faint star with an extremely high surface-temperature. Surrounding this is the nebulosity from which these objects derive their somewhat unfortunate name. This is in all probability merely an atmosphere of even greater extent than that surrounding the four stars of our table. Van Maanen estimates the diameter of the nebulosity of the Ring Nebula in Lyra (fig. 2 of Plate II) to be 570 times that of the earth’s orbit, or about 106,000,000,000 miles. This nebulosity, however, differs from the atmosphere of an ordinary star in being very nearly transparent; we can see through 106,000,000,000 miles of the Ring Nebula but can only see a few tens or hundreds of miles into an ordinary star.

At the other extreme of size, the smallest known star, van Maanen’s star (p. 268) is just about as large as the earth; over a million such stars could be packed inside the sun and still leave room to spare. And yet its weight is in all probability comparable, not with that of the earth, but with that of the sun; at a guess it may have about a fifth of the sun’s weight. To pack a fifth of the sun’s substance inside a globe of the size of the earth, the average ton of matter must be packed into a space of about the size of a small cherry—ten tons or so to the cubic inch. The solidity of the earth suggests that its atoms must be packed pretty closely together, but the atoms in van Maanen’s star must be packed 66,000 times more closely.

How is it done? As we shall shortly see, there is only one possible answer. The atom consists mostly of emptiness—we compared the carbon atom to six wasps buzzing about in Waterloo Station. Let us break the atom up into its constituent parts, pack these together as closely as they will go, and we see the way in which matter is packed in van Maanen’s star. Six wasps which can roam throughout the whole of Waterloo Station can nevertheless be packed inside a very small box.

GIANTS AND DWARFS. There is a continuous series of stars between the limits of weight we have mentioned, and the same is true of the limits of temperature (and so also of colour) and of size.

Within these specified limits, I can find you a star of any weight or of any colour or of any size you like. But this does not mean that you may specify the weight and colour and size of the star you want, and that I will undertake to find it for you; if the weight is right the colour may be wrong, and so on. For instance, if you ask for a red star I can find you a very heavy one or a very light one, but it is no good your asking for one of intermediate weight. So far as we know, red stars of intermediate weight simply do not exist. The same is true as regards size—there are no red stars of intermediate size. Hertzsprung noticed in 1905 that the red stars could be divided sharply into two distinct classes characterised by large and small size—he called them Giants and Dwarfs. Russell, studying the question further in 1913, confirmed Hertzsprung’s earlier conclusions, and shewed that the giant-dwarf division extended to stars of other colours than red.

Imagine that we have a series of coloured ladders, one for each colour of star—red, orange, etc. Take all the red stars and stand them (in imagination) on the different rungs of the red ladder. Do not merely place them on at random; arrange them in order of their luminosities, placing those of highest luminosity upper-most. Further let several stars stand on the same rung if their luminosities are about equal. To make the arrangement definite, let each rung of the ladder represent 5 times higher luminosity than the rung immediately below it, so that each rung has a definite luminosity associated with it[25].

With this agreement we are now ready to proceed. We take our red stars and place each on the appropriate rung of the red ladder, and so on for each other colour. The result is shewn diagrammatically in fig. 21, the different stars being represented by crosses.

The red stars will be found to lie as on the right of the diagram, Hertzsprung’s division into giants and dwarfs being very clearly marked. The orange stars lie as on the next ladder to the left; as Russell found, the division again appears, but is less marked.

THE RUSSELL DIAGRAM. Let us make ladder diagrams of this kind for each colour of star, and put them side by side in their proper order, so as to represent stars of all possible colours. We obtain a diagram of the kind shewn in fig. 22. This type of diagram was introduced by Russell in 1913, and is now generally known as a Russell diagram.

The letters at the top of the diagram represent spectral types of stars, because these provide a better and more exact working classification than the names of colours. The colours which approximately correspond to the various spectral types are indicated at the bottom of the diagram.

Only a very few sample stars are shewn, but all known stars are found to be concentrated around the positions of these few typical stars. Broadly speaking, there are two distinct and disconnected regions which are occupied by stars. First, and most important, is a region shaped rather like a reversed γ: the central line of this region is marked in by a continuous thick line, following a determination of its position by Redman. Second, there is a smaller region near the left-hand bottom corner of the diagram. The stars which occupy this region are very faint, and have far higher surface-temperatures than other stars of similar luminosity.

We have already seen how a star’s diameter can be calculated from its surface-temperature and luminosity. This amounts to the same thing as saying that two stars which occupy the same position in the Russell diagram must have the same diameter. Thus there is a definite diameter associated with each point in the diagram, and we can map out stellar diameters in the diagram, just as we can map out heights above sea-level on a geographical map, by a system of “contour lines.” In the present case the “contour lines” prove to be a system of almost parallel curves. These lie roughly as shewn by the broken lines in fig. 22, all stars lying on any one line having the same diameter.

This diagram throws a flood of light on the general question of stellar diameters. We see at once that stars of the biggest diameters—100 times the sun’s diameter or more—must necessarily be red stars of high luminosity. And in actual fact the stars of large diameter shewn in the table on p. 272 are all red and have very high luminosities; they are red giants.

The majority of the stars in the sky lie in the belt which runs across the diagram of fig. 22 from top left-hand to bottom right-hand. This is known as the “main-sequence.” The position of this band with reference to the “contour lines” of diameters shews that main-sequence stars are of moderate diameters. The brightest of all may have twenty times the diameter of the sun, while the faintest may have only about a twentieth of the sun’s diameter, but they all have diameters which are at least comparable with that of the sun. The sample of stars from near the sun, which we have already discussed, provides many instances of main-sequence stars; we have, in order of decreasing luminosity:

This table shews clearly how stellar luminosity and diameter decrease together as we pass down the main-sequence.

The remaining group of stars in fig. 22, those in the bottom left-hand corner, are generally known as “white dwarfs.” Their position in the diagram shews that their diameters must be excessively small. The vicinity of the sun provides three examples of this class of star, as shewn in the following table:

In addition to these, the faint companion of ο Ceti is certainly a white dwarf, while Procyon B may be. These are the only known examples of white dwarfs, but the extreme faintness of these stars makes them very difficult of detection, so that it is quite likely that they are fairly frequent objects in space.

In the table on p. 279, the main-sequence stars were intended to be arranged in the order of luminosity, but this happens also to be the order of weights. The weights of three of the stars are unknown; those of the remainder are as follows:

Like the luminosities, the weights fall off steadily as we pass down the main-sequence, although, as already remarked, weight falls far less rapidly than luminosity.

The only stars whose weights can be measured directly are the components of binary systems, and these are relatively few in number. Seares found, however, that the weights of binary systems conformed to the law of equipartition of energy already explained in Chapter III, so that it is highly probable that other stars which are not binary also conform, for it is difficult to imagine any reason why binary systems should attain to a state of equipartition sooner than other stars. It will be remembered that this state is defined by a purely statistical law connecting the weights and speeds of motion of stars, so that the fact that a system of stars has attained this state can give no information as to the weight of an individual star whose speed is known, but it makes it possible to determine the average weight of any group of stars in terms of their average speeds of motion. In this way Seares has determined the average weights of stars of different assigned luminosities and spectral types—in other words, the average weights of the stars represented at the various points in the diagram of fig. 22. The results he obtained are shewn by the thick curved lines in fig. 23. The arrangement of these curves confirms the inference we have drawn from a few selected stars; the weight of main-sequence stars falls off steadily as we pass down the sequence from high luminosity to low.

These curved lines specify the average weight of the stars represented at each point in the Russell diagram, and the diameters are already known from fig. 22. From these two data the mean density of the star can of course be calculated. The mean densities as calculated by Seares are shewn by the broken lines in fig. 23.