Museum of Freemasonry - Masonic Library
The pinpricks of the stars have presented man with two cardinal questions to answer: where are the stars and what are they? In the last four decades after centuries of effort, man has finally learned the answer to both these questions. The stars are tremendous thermonuclear reactors organized by gravity out of gas and arranged in space in inconceivably large systems called galaxies. The sun and the other 7,000 odd stars that can be seen by the unaided eye are simply a small part of our galaxy, the Milky Way.

The story of a star begins with its birth, an event little different from the birth of our sun. A cloud of dust and gas, whirled into pockets of high density, begins to contract around one or more of its gravitational centres. Many centres in one tight cloud can result in a single star plus planets, a multiple star, or a multiple star plus planets. The finished product depends on the density and size of the original cloud and on the degree of rough and tumble in its movements. Astronomers believe that they may see unlit protostars in the very act of contracting in the nearby clouds of the Milky Way’s spiral arms. They appear as dark globules against the less opaque regions of gas and dust around them.

When a protostar contracts, its central regions are warmed by the release of gravitational energy – the heat of in-falling atoms colliding with one another. Eventually the heat becomes so intense that the hydrogen of the core begins to fuse into helium. At first the nuclear fusions of single atoms are infrequent and release little energy but, as the star continues to contract under the weight of its accumulating outer layers, the atoms of the core are pressed closer together and fuse more and more frequently. Eventually they are producing exactly enough out-pushing energy to counteract the stars in-pulling gravitation. At that point the process is over and the star has arrived at a stable, mature state. If the star is a massive, highly gravitational one, its in-falling has taken place fast and forcefully, and its core is extremely compressed and hot, pouring out huge amounts of fusion energy to stave off further crushing and collapse. On the other hand, if the star is a slight one, its contraction has taken place gradually and gently, and its un-crowded inner atoms need to fuse only casually and occasionally in order to offset the squeeze of gravity.

Astronomers had the idea that they might be able to estimate a star’s distance by its apparent brightness. It seemed possible that all stars might have the same intrinsic brightness if they could only be seen from the same distance away. Working on this assumption, astronomers developed precise methods for measuring the visible brightness or dimness – the magnitude – of stars and hoped that these measurements could be translated someday into distances according to the simple formula: brighter equals closer, fainter equals farther. But when the parallactic distances to nearby stars began to be found, 1it was clear at once that faintness and brightness do not depend on distance alone, but that some stars are actually much brighter than others. To the naked eye, for instance, the two most luminous stars in the sky are Sirius in Canis Majoris, the Great Dog, and Canopus in Carina, the southern hemisphere’s constellation of the Keel. It looks as if Sirius is twice as bright as Canopus but it turns out from their parallaxes that Sirius is only 8.7 light years away, whereas Canopus is 100 light-years away. This means that Canopus really burns not more faintly than Sirius but 65 times as brightly.

The most straightforward way of finding a star’s distance is by measuring its parallax, its apparent annual shift in position against the background of more distant stars. Unhappily, this direct method works well only at fairly short range. Within a distance of 30 light-years, the stars can be positioned with better than 85% accuracy, but only a handful of stars – 170 of them – are so close. Beyond 30 light-years, direct parallax measurements become more difficult. Astronomers consider 400 light-years their limit.

Although the brightness yardstick would not work for all stars indiscriminately, astronomers still hoped that it might work for stars of any one kind. To see if it would, they first had to classify the stars near the sun, find their distances by parallax and then seek out faint duplicates of each species on the far horizons. This laborious undertaking, though still in progress, has already proved to be the key to the cosmos, opening the door of human understanding to the enormous distances that separate the stars of the Milky Way from the galaxies beyond. Altogether, many species of stars have been found that do reveal their distances according to the simple formula of brighter-nearer, fainter-further. One of the most important – because it can be spotted the furthest off – is the Cepheid variable, a kind of pulsating star that has the convenient quirk of growing brighter and dimmer in regular periods which depend on its true brilliance. The brighter a Cepheid is on the average, the longer it takes to pulsate. A Cepheid with a thirty day period averages 4,000 times as bright as the sun. One with a one day averages only 100 times as bright as the sun. After measuring the pulsation period in a Cepheid, modern astronomers believe they can calculate its average intrinsic brilliance- absolute magnitude –with 90% accuracy. By comparing the result with its average visible brightness – apparent magnitude – they can then, with equal accuracy, work out its distance. And they can do this whether the star is a mere 300 light-years away like Polaris, the nearest Cepheid, or over two million light-years like the Cepheids in the Andromeda nebula, an entirely separate galaxy outside the Milky Way.

Most of the other kinds of stars which serve as distance gauges are not as easily recognisable as Cepheids but they make admirable beacons for judging the remoteness of relatively nearby regions where Cepheids are scarce. In the middle distances of the Milky Way, for instance, astronomers often take advantage of RR Lyrae stars, a pulsating breed that waxes and wanes more rapidly and faintly than do Cepheids. Still other stars of predictable intrinsic brightness can be identified by their spectral lines and the colour of their light. One recently devised yardstick – good for a distance of some 2,000 light-years and applicable to common stars like the sun – takes advantage of the strange fact that two of the bright lines emitted by a star’s calcium atoms are always wider or narrower depending precisely on the star’s over-all brilliance.

Such sophisticated methods might not carry much conviction if it were not for a rough-and-ready way of checking on stellar distances through stellar velocities. Long before the astronomers knew that the stars are all circling the centre of the galaxy – in fact long before they had any inkling of what a galaxy was – they realized that all the stars that they could see were in motion. Under the circumstances nearby stars – like low flying aircraft, should seem to move rapidly and remote stars, like high-flying aircraft, should seem to creep along.

In using velocities to double check distances, astronomers have perfected careful methods for measuring the various movements of the stars relative to the sun and for subtracting all the movements caused by the earth’s own wending, whirling, and wobbling in its orbit. Simple star movements across the face of space are called proper motions and measured straightforwardly by small, angular shifts in the co-ordinates of stars. For some nearby stars it takes only a few years of watching for proper motions to become detectable; for other distant stars it takes centuries.

In addition to proper motions, 19th century astronomers found that they could measure radial velocities, the motions of stars directly towards or away from the sun. As it travels through space, a star cuts its own bow-wave of light, emitting the successive wave crests closer together than usual. In the same way, the light waves of its wake are slightly pulled apart by its motion away from them. As a result the bow waves become higher in frequency, shorter in wave length and bluer than they would be if the star were lying at celestial anchor. The wake waves become lower in frequency, longer in wave length and redder. The degree of compression or pulling apart is known as the Doppler shift and it is measured by the fact that emission and absorption lines are moved up or down the spectrum by amounts which depend exactly on the speed of the star towards or away from the earth.

From studying red wakes and blue bow waves, Cepheids and other star types, calcium and other emission or absorption lines, modern astronomers have put two and two together, combined the distances of stars with their motions and come up with a picture of the total breathtaking, dynamic system in which the sun is just one of 10,000 million orbiting participants. Visualizing the whole Milky Way has not been easy. The stars move in circular tracks around the galactic hub, and their real motions are mixtures of apparent motions parallel to the sun and other motions towards or away from it. Stars on the inside lanes can be either catching up with the sun or pulling ahead of it. Stars on the outside lanes can be either dropping back towards the sun or falling away behind it. To compound confusion, many stars travel in clusters, whirling around one another.

While charting the Milky Way and discovering where the stars are, astronomers have also learned what they are. The same observations about brightness which led to distance calculations also led to knowledge of star sizes and masses. The long studies with spectroscopes, filters, photoelectric cells and thermocouples which made it possible to find star species that would serve as beacons and yardsticks also led to an astonishing amount of detailed knowledge about stars – knowledge that revealed the seemingly monotonous multitudes of the heavens as a motley crew, distinguished by an infinite variety of unexpected conditions and situations.

To appreciate the infinite variety that the stars show, one must have some idea how astronomers can acquire information at long-distance, as they do. One might think, for example, that gassy structures like stars cannot differ much in their magnetic properties, or if they do, that astronomers could never find out about it anyway. But they do and astronomers can. The spectral lines of light emitted in magnetic fields are split into double or triple lines, separated by gaps which are broad or narrow, depending on the magnetic field strength. From measuring the gaps – the Zeeman splitting – hundreds of stars have been measured and have been found to vary from one or two gauss, like the sun, up to 34,000 gauss for a fast spinning star like HD 215441. The undoubtedly weird effects which such huge magnetic fields have on the flares and the sunspots of such stars have yet to be calculated, but if any of those stars has inhabited planets, the beings on them must be able to generate all the electricity they need simply by laying out coils of copper on the ground and letting planetary rotation do the rest.

Another extraordinary feat of the spectrograph is measuring how fast stars rotate. Even though the advancing and retreating edges of a star are merged in its infinitesimal light shift, the Doppler shift can still be gauged. Because of rotation the atoms of each element on the star’s surface are either advancing and showing blue, retreating and showing red, or keeping their distance. The net result of the combined reddening and bluing is smudged spectral lines, widened in a manner that tells exactly how fast the star is spinning.

At the equator, most small stars like the sun are moving at only one or two miles per second but many of the massive stars are found to be spinning dizzily at speeds of up to 200 miles per second. The reason probably is that some big stars, in their formative years, condense so quickly and start spinning so swiftly and abruptly that they are not slowed much by the elastic magnetic spokes they create around themselves in the gas clouds out of which they form. What happens to a fast-spinning star after its birth is exemplified by Pleione, one of the brightest of the Pleiades cluster. Pleione’s equator rotates at 190 miles per second, with the result that it constantly hurls hydrogen off into space, girdling its waist in a ring of gas that glows with excitement from Pleione’s intense ultraviolet rays. The fact that most small stars spin far more slowly than Pleione is thought to indicate that small stars are girdled by rings of planets, which helped, at their formation to slow them down.

The two work horses of stellar astronomy are temperature and brightness measurements. This is not because temperature and brightness are the two most valuable pieces of information about stars but because they are the only two pieces of information which can be had readily. Taking a star’s temperature can be done in several ways: it is simply a matter of finding out in what section of the spectrum the star shines most brightly. In general, if it is brightest in red light, it is a cool star; if it is brightest in yellow light, it is a warm star; and if it is brightest in blue light, it is a hot star. In similar fashion, the over-all brightness of a star can be ascertained through measuring the intensities of its light at many wave lengths and adding them all up.

Of all the stellar characteristics, one of the most important to know is mass. From the mass of a star – the amount of matter in it – modern astrophysicists can calculate roughly what all its other properties should be after it has been alight for any given number of years. By the same token, they can calculate how old a star is from the way it is shining – as long as they first know how much matter there is in it. Unfortunately the mass of a star is often the most elusive and indirect of its vital statistics.

The only kind of star in which mass can be measured in a straightforward way is a double star: a system of two stars revolving around one another in orbits shaped by their mutual gravitation. From the length of time they take to revolve and the distance they keep between them, their masses can be figured out easily by Newton’s laws of gravitation. By happy circumstance, 75% of the stars do have one or more companions with which they dance as they go down the galactic track. Often they circle their orbiting mates so closely that they seem to be single stars when they are really pairs, triumvirates or gangs. Antares in Scorpio, the 16th most brilliant star in the sky, is actually two stars. Capella and Alpha Centauri are each three; Castor is six. Since 1889 the number of multi-component stars made visible by the telescope has been increased by an even larger number revealed through the spectroscope. Some of them, like UV Puppis, orbit so closely that they roll around one another’s multi-million mile equators in under two hours flat. Others like Beta Lyrae, swap star-stuff through the crests of huge tidal waves and are wrapped in turbulence. Of all the strange multiple stars disclosed by the telescope and spectroscope, only the simple double-stars reveal their masses. This is because the tempos and patterns of three star tangos, four star fandangos and many-star mazurkas are often too complicated even for modern mathematics. Luckily, however, many multiple stars are binaries, and it is from these examples that astronomers know how much matter there is in stars in general. From each item of such knowledge flows a great deal of other knowledge. Star UW Canis Majoris in the Great Dog, for instance, is a double star with a total mass 36 times that of the sun. From this and the fact that this UW pair is 10,000 times as bright as the sun, astronomers can calculate that the pair will burn out and die in a mere 300,000 year moment of eternity. Moreover they can be reasonably sure that a single star like Rigel in Orion, which is similar to UW Canis Majoris in other respects, must have a similar mass and a similar future.

Through virtuoso use of instruments – uncovering tremendous truths in tiny fractions and nuances – astronomers have sorted out the many-complexioned stars of the Milky Way by their masses, brightness, temperatures, composition, spin and magnetic strengths and have found that they fall into two principal groups: normal stars and abnormal stars. The normal stars are normal for two reasons: they are in the majority, especially in the regions of the Milky Way near the sun, and they burn in the manner astrophysicists expect stars to burn. Given fusion, astrophysicists can calculate how stars made of hydrogen ought to shine. Massive stars, in which the force of gravity jams the fuel most quickly and forcefully towards the centre, ought to burn far more rapidly than lightweight stars, in which the central hydrogen fuel is packed less densely. Because of their gravitational stoking and corresponding temperature, big stars generate more energy than small stars do. In terms of what can be seen, they must burn brightly, blue and hot, while medium-sized stars must burn moderately warm and yellow and small stars must burn dimly cool and red.

This exact hierarchy of brightness and colour, as calculated by astrophysicists, was actually observed by astronomers long before anyone knew a fission from a fusion. It was discovered by plotting the brilliance of stars on a graph against their spectral types. It was realised that each spectral type frequents a range of colour and temperature. Massive, brilliant O-stars at one end of the spectrum are hot and blue and range from 50,000 down to 25,000 degrees C in surface temperature. They are so hot that most of their energy is emitted in invisible ultra violet rays. Lightweight, dim M-stars, at the other end of the spectrum, are cool and red and range from 3,300 down to 1,600 degrees C. They are so cool that most of their energy is invisible infra-red heat rays. Mild, yellow middleweight G-stars like the sun fall at the centre of the spectrum. They range in temperature from 5,500 down to 4,900 degrees C and emit almost all their energy in the visible fraction of the spectrum.

When the various kinds of normal stars are set out on a graph – brightness plotted against spectral type – they fall on a line sloping downwards from hot blue O-stars in the upper left to cool red M-stars in the lower right. G-stars like the sun occupy a satisfying, average sort of position near the centre of the graph. The line on which normal stars plot out on the graph has come to be known as the ‘main sequence’. This splendid agreement between astrophysical theory and astronomical observation as to what should be and what actually is scarcely filled either party with jubilation because, from the start, there were all sorts of abnormal stars which did not fall on the main-sequence line in the colour-brightness graph and did not satisfy the thermonuclear requirements of early atomic theory. Most of these abnormal stars were overbright for their spectral type and thus plotted out above the main-sequence line. At one end of the spectrum there were over-bright blue super-giants like Rigel in Orion which is 800 light years away but maintains status as the seventh brightest star in the sky by pouring out energy at the astonishing rate of 40,000 suns. At the other end of the spectrum from blue super-giants the roster of abnormal stars included red giants like Arcturus, in Bootes, No 4 star in the heavens, and red super-giants like Betelgeuse, in Orion, the ninth brightest star. In between these two extremes there were over-bright white, yellow and orange giants and super-giants – and also a puzzling assortment of pulsating and exploding stars: brilliant orange and yellow Cepheids, less brilliant white RR Lyrae stars and bluish exploding stars of fantastic million-sun brightness that are known as supernovae.

Just how peculiar some of the abnormal over-bright stars are is illustrated by Betelgeuse, the red super-giant in Orion. In spectral type, Betelgeuse is only a red M-star, shedding its ruddy light from a surface half as hot as the sun’s. Normal M-stars are ten times smaller in diameter and 1,000 times dimmer in light than the sun. But Betelgeuse equals 500 suns in diameter and 17,000 suns in brightness. At the outer edge of its dark substance, huge currents of billowing gas are rising and falling more quickly than the whole globe of the star is rotating. And in these convection currents the atoms are more loosely packed than in the most perfect vacuum man can create on earth.

As well as the over-bright abnormal stars, there are also under-bright ones that plot out below the main-sequence line on the colour-brightness graph. Erupting stars called novae are normally dim for their colour but grow periodically over-bright during flare-ups and hurl off celestial smoke rings of gas and dust into space around them. Still further downwards in the colour-brightness graph fall the extremely under-bright stars called ‘white dwarfs’. Though dim and small, these dwarfs each contain about as much matter as the sun but cram it densely into volumes as small as the planet Mercury’s and weighing anywhere from one to twenty or more tons per cubic inch. Presumably the reason that the matter in white dwarfs does not explode with new nuclear transformations under such fantastically tight packing is that all of it has already been converted into nuclear ash – atoms incapable of any more reactions.

The fact that white dwarfs seem to be dying stars and that most of the other abnormal stars are actively unstable – or at least bloated in a way that augers ill for their future stability – convinces astronomers that abnormal stars are suffering the maladies of old age. Yet it is important to realise that abnormal dying stars are a tiny minority of all stars. Most varieties of abnormal stars – revealed by examples found in double star combinations – are from one to thirty times as massive as the sun. Because they are big they are short lived. Stars of the sun’s mass and smaller are long-lived and have not yet had time to become abnormal. And they are overwhelmingly numerous in comparison to the sick heavy stars.

For every ultraviolet Rigel, 30 times as massive, 40,000 times as bright and probably 100,000 times as short-lived as the sun, there exist 200,000 yellow suns and several million faint red M-stars smaller than the sun. The true nature of the Milky Way’s average members can be glimpsed best in the sun’s own cosmic surroundings. Within sixteen light-years of the sun there are fifty stars: 28 singles, eight doubles and two triples. In addition there are five unseen companions, either miniscule stars or enormous planets which cannot be seen but only detected by the kinks they put in the motions of the stars with which they are associated. Of the fifty bona-fide stars in the sun’s neighbourhood, four are white dwarfs, already burned out, two are fast-living, ultra-bright A-stars, one is a brilliant yellow-white F-star, two are mild yellow G-stars like the sun, seven are small orange K-stars, and 34 are tiny common-as-dust M-stars.

The crisis that overtakes a star when it has consumed a goodly percentage of the hydrogen arises from the accumulating helium ash in its core. As the ash piles up in the centre, fusion continues in a bright skin around it. The ash has no internal energy source, and so it contracts under its own growing weight. In the contraction its atomic nuclei are pressed in on one another, its electrons are crushed out of their orbits and gravitational energy is released. This energy raises the temperature of the core and extra heat steps up the tempo of the fusion reactions taking place in the skin around it. The primary proton-proton reaction, important in the sun, is not much affected by the added heat, but the secondary carbon-cycle reactions quickens rapidly, becoming dominant and is soon spending the star’s patrimony in a prodigal outpouring of energy.

During the past few years another remarkable feature has been discovered in the Crab Nebula. It contains one of the very small, rapidly-rotating radio sources known as pulsars, now believed to be neutron stars in which even the nuclei of atoms are crushed together to make material of incredible density – far surpassing even that of a white dwarf. The pulsar in the Crab has been identified with a very faint flashing object, and was the first pulsar to be linked with something which can actually be seen. Inevitably it has led to the suggestion that all pulsars are the end-products of supernovae, and this may well be the case, though it is too early to be sure. At any rate the Crab pulsar is an amazing object. A cupful of its material would weigh millions of tons.

If black holes really exist, they are the most bizarre objects known to us. Inside the boundary of the ’hole’ (known as the ‘event horizon’), all the ordinary laws of physics break down, and it has even be suggested that the collapsed star may crush itself out of existence altogether! All kinds of exotic theories have been proposed in connection with ‘black holes’, but our studies of them are still in a very elementary stage, and there is as yet no absolutely conclusive proof of their reality.

Yet the evidence, so far as it goes, is in favour of ‘black holes’; this may be the fate of a really massive star – though there is no chance that the sun will end its career in such a way. A star’s evolution depends largely upon its initial mass, and the sun is by no means exceptional. Meantime, we have to admit that the past few decades have provided many surprises. Quasars – pulsars – and now ‘black holes’, all of which were both unknown and unsuspected as recently as 1960.

If you would pursue further knowledge of stars and astronomy in general there are many more recent books than those that I have accessed, also the internet with so many web sites, such as the Hubble Telescope, devoted to the most recent finds that will maintain your interest.

VW Bro Robert Taylor