Supernovae
(1981)

An observer watching the night sky with the unaided eye is presented with what seems to be a spectacle of unequalled serenity and changelessness. Indeed, the vast majority of the (so-called) “fixed” stares are extremely stable, producing a steady ourput of radiation over millions of years.

In marked contrast are the novae and supernovae: stars which spontaneously explode with a spectacular and rapid increas in brightness, and which, at their peak, may rival the brightest stars in the heavens, before fading into insignificance.

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The greatest of ancient astronomers, Hipparchus of Nicaea, observed such a spectacularly bright “new” star in 134 BC. (An event which, it is supposed, prompted him to prepare the first star map in order that other “visitors” be more easily recognised in the future.)

Many other spectacular stellar outbursts have been recorde in the centuries since. Most pre-Renaissance observations of “new” stars were made in the East: China, Japan and Korea. By contrast, there seems to have been very little interest in such events in ancient and mediaeval Europe and the Arab lands. Three “new” stars of noteworthy brightness and long duration were recorded in the orient in AD 1006, AD 1054 (in the constellation of Taurus) and in AD 1181.

A particularly bright “new” star appeared in November 1572 in the constellation of Cassiopeia, about which the Danish astronomer Tycho Brahe wrote a book: De nova stella (Concerning the new star). (From this title the expression nova came to be applied to temporary stars generally.) His more detailed inverstigation of the nature of the “new” star was recorded in Astronomica instaurate progymnasmata, published (posthumously) in 1602.

Thirty-two years after the appearanc of Tycho’s nova stella, the astronomer Johannes Kepler (who succeeded Tycho Brahe as Imperial Mathematician to the Holy Roman Emperor), made a careful study over twelve months of a remarkably bright “new” star in the constellation of Ophiuchus, his observations being recorded in De stella nova in pede serpentarii.

With the invention of the telescope in 1608, and its application to observational astronomy, it became clear that there aree uncounted millions of stars that are too faint to be seen with the naked eye. The notion arose that a “new” star or nova could be a star normally too dim to be seem without a telescope which (for some unspecified reason) grew much brighter – to the point of being visible to the unaided eye – for some time, and then faded to dimness below the level of ordinary vision again/ Hence, to the naked eye the nova would appear to have come from nowhere and returned to nowhere.

This notion was strengthened when, in 1848, the English astronomer John Russell Hind actually caught a nova “in the act”: He happened to be observing a star ordinarily invisible to the naked eye when it began to brighten. It reached a peak apparent magnitude of five (by which time it was visible as a adim star to naked-eye observers), then it faded.

WIth the inver=ntion of photography (and its application to observational astronomy) many more novae were detected. They did not prove to be as uncommon as had earlier been thought: It was now estimated that, on average, as many as thirty novae occur per year in our galaxy.

With the increased numbers of novae being studied it became apparent that such novae as those of Tycho and Kepler were exceptionally bright – the nova of 1054, for example, was visible in broad daylight for no fewer than twenty-three days. A seemingly reasonable explanation of this was that these novae were much nearer the Sun that the others, and hence appeared much brighter.

In 1885, however, a nova appeared in what was then known as the Andromeda Nebula, and supposed to lie within our own galaxy. The nova was not a particularly notable one, for it onl reached a maximum apparent magnitude of seven, and was never bright enough to be visible to the naked eye.

Close observation of the Andromeda Nebula over the following years saw numerous novae within its confines, It seemed unresonable to suppose that that many novae could occur in one particular areas in the sky, and so the notion grew that the Andromeda Nebula was a distant group of stars, too dim to be seen individually, except when one “went nova”. By the 1920s it was generally agreed that the Andromeda Nebula was, in fact, a galaxy in its own right and distinct from our own.

(In fact, this idea was not a new one: The German philosopher Immanual Kant had proposed the existence of island universes in 1755, after speculation by Thomas Wright, a British scientist, in 1750.)

All the novae observer in the Andromeda Galaxy after that of 1885 were exceedingly dim and (it was realised) were equivalent to the ordinary novae of our own galaxy. The nova of 1885 was of a completely different order: It had to be much brighter than the ordinary novae in either the Andromeda Galaxy or our own. It was so bright, in fact, that it had momentarily shone nearly as brightly as the Andromeda Galaxy itself: At its peak it was intrinsically ten billion times as bright as our Sun, and one hundred thousand times as bright as an ordinary nova. It became clear that the exceptionally bright novae of 1006, 1054, 1181, 1572 and 1604 were of the same ilk, and all were examples of what came to be called a supernova.

This century [the Twentieth] there have been many fruitful intergalactic supernova surveys. It is unfortunate that not one observable supernova has occured in our own galaxy since 1604, so that no such event has evern been investigated telescopically, at close range. In fact, in the four centuries since Kepler’s supernova occured, the Andromeda supernova of 1885 has been the closest to be observed.

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However, intergalactic observations have revealed much of interest. At least two types of supernova have been identified, these being differentiated primarily by their spectra and partly by their absolute luminoisties and light curves. (See Figures 2, 3 and 4.)

The so-called type-I supernovae typically have an absolute magniturde at maximum of -19, and, after an initial drop of about three magnitudes in twenty to thirty days, the light curve showas an approximately exponential decay. The spectra of type-I supernovae are extremely complex: Initially the spectrum is dominated by continuum, with several emission and absorbtion features common to type-II spectra also seen; the relative line strengths show that the abundance of various slement s relative to hydorgen is enhanced in comparison with the Sun; near maximum light the spectra are distinguished by a strong absorbtion line of ionized silicon.

The light curves of type-II supernovae are rather more individualistic, although a common feature is a “shoulder” after the maximum, followed by a rather rapid decline. The clear distinguishing feature of type-II supernovae is that their spectra show strong emission lines of hydrogen during the first few weeks following the maximum lightl; in addition, tehre are strong emission and absorbtion lines from ionized calscium and ionized sodium, magnesium and iron: The strength of the lines indicates that the relative abundance of these elements in type-II supernovae is not very different from their abundance in the Sun.

Type-I supernovae appear in both elliptical and spiral galaxies, while type-II supernovae occur only in spiral galaxies (preferentially in the arms): It may be inferred, therefore, that type-I supernovae belong to Population II stars, and type-II supernovae to Population I.

[Note: Population I stars, younger than Population II and with higher metalicity, tend to be found in only spiral galaxies. But we’re getting a little ahead of ourselves…]

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Before discussing the mechanisms by which supernov explosions are brought about, it will be useful to give a brief description of stellar evolution.

(This description will, in fact, lead directly into the discussion of such mechanisms.)

As a nascent star forms from a cloud of gas (mainly hydrogen) and dust collapsing under the action of its own gravity, the temperature of the interior increases as gravitational potential energy is partially transformed into kinetic (or thermal) energy (the remainder being radiated away, the emitted radiation being primarily in the infra-red). The contraction continues until the temperature at the core has risen sufficiently to initiate the fusion of hydrogen nuclei to form helium. (See Appendix.)

When such thermonuclear reactions proceed at a certain rate, a hydrostatic equilibrium between the gravitational contraction and the internal steallar pressure is established. At this time contraction stops altogether and the star is stable, and will remain so for millions of years (of the order of 10⁶ a for stars of spectral class O, and in excess of 10¹² a for class-M stars).

Eventually all the hydrogen in the core of the star is exhausted. As a result of gravitational contraction, material just beyond the core is pulled into a region of higher temperature and hydrogen “burning” starts in a shell surrounding the (primarily) helium core. Subsequently, as the star passes through the so-called Schönberg-Chandrasekhar limit, the core contracts much more rapidly, accelerating the energy generation in the shell, casuing the outer envelope to expand, with a corresponding cooling at the surface. The star has become a red giant.

In stars of low mass (of the order of 0,35 solar masses, or less), helium burning may not become appreciable because of low internal temperatures. Such a star will continue its gravitational collapse to become a white dwarf.

The compression is so great that the electrons in the steller material may occupy a limited number of energy states: The material has formed a “degenerate electron gas”. The nuclei themselves are tightly constrained such that they resemble a crystalline lattice, this state being referred to as a “quantum solid” (the state just prior to this being a “quantum liquid”).

The white dwarf remains stable due to an equilibrium between gravitational contraction and the pressure of the degenerate electron gas. Only stars of les than about 1,4 solar masses (the Chandrasekhar limit) can be stable white dwarfs because of limitations imposed by the hydrostatic equilibrium and the nature of the degenerate electron gas.

The contraction of the core in stars of slightly higher masses (of the order of one solar mass) may be such that the helium shell burning rates are accelerated, and the outer envelope expands and cools with such rapidity that tit becomes separated from the core as a transparent shell: This is a planetary nebula. The core remains as a white dwarf.

Temperatures in the interiors of massive stars (those with masses greater than 1,4 solar masses) rise due to core contraction such that, eventually the triple-α process (see Appendix) can begin at the star’s centre. Further contraction and increase in temperature allows the fusion of helium in the core. In very massive stars, helium burning may start well before the red giant phase. (It is at this stage in its life that a star may become a variable of the Cepheid or RR Lyrae type.)

The core temepratures easily become high enough for carbon burning to occur. Oxygen and neon are also involved in fusion reactions which give rise (eventually) to a core containing a variety of heavy nuclei, in particular an abundance of iron (Fe⁵⁶).

(The production of nuclei of various elements – nucleosynthesis – will be discussed in some detail later.)

At som stage this core will cool rapidly (possibly due to to a tremendous efflux of neutrinos) and collapses violently. This collapse brings lighter elements from outer shells to the extreme temperatures of the core, and this material undergoes nuclear reactions at a tremendous rate, generating an enormous flux of high-energy X-rays and γ-rays, which heats the matreial around the collapsed core.

The generation of enormous temperatures and pressures produces a shock wave, which will move outward to meet the collapsing envelope, with a resulting rapid compression and sharp increase in temperature, which (it is believed) initiates explosive nuclear reactions (such as the fusion of oxygen nuclei to form silicon) in the envelope. During the last moments of collapse further nucleosynthesis occurs to form very heavy nuclei. About eighty per cent of the star’s mass may be ejected into space, thus enriching the intersteller medium with heavy elements.

The cataclysmic demise of a massive star, as just outlined, is observed as a supernova.

In the explosion energy is effectively transferred to the star’s outer layers, which are heated and accelerated: The visible outer surface of the star (the “photosphere”) expands with nearly constant velocity. The initial increase in the emitting surface results in an increase in radiated light, although a subsequent falll in tempoerature with continuing expansion eventually produces a decrease. Theoretical considerations show that there would be a rapid decline in the light curve, as is seem in those for type-II supernovae.

Hence, it is reasonable to identify type-II supernovae with the collapse of “red supergiants”.

By contrast withw supernova, a nova is believed to be merely a “hiccup” in the normal evolutionary path of certain stars, and one which may, in fact, reccur at long intervals. In each nova explosion only a small amount of material is thought to be ejected, and some of this may fall back under gravity onto the star.

The most likely explanation of these sporadic outbursts is based on convincing observational evidence that a “prenova” is a close binary system, in which two stars orbit one another an are close enough for material to be transferred between them at certain times during the normal course of their evolution. Any binary system containing a white dwarf and a normal companion star is a potential nova candidate.

During an expansion phase of the companion star, material (mainly hydrogen) from the outer regions may come under the gravitational influence of the white dwarf and be drawn from the star to fall into the atmosphere of the white dwarf via an accretion disc, where it is compressed and heated such that hydrogen burning is initiated. Further thrmonuclear reactions at explosive rates produce the violent ejection of matter and radiation that is observed as a nova event.

The binary system is left (more or less) in its original condition. Theoretical considerations lead to the assumption that over repeated cyckles of this exchange of material between the stars followed by a nova outburst, the mass of the white dwarf gradually increases.

If the white dwarf captures sufficient matter that its mass exceeds the Chandrasekhar limit, the hydrostatic equilibrium is destroyed and the star collpses with the release of an enormous amount of energy and the explosive ejection of at least some material.

This is the probable cause of the events observed as type-I supernovae.

The slower decay of the light curves of type-I supernovae, accompanied by strong emission in lines in the spectrum, appears to require the continued input of energy. Possible post-supernova energy sources include: the supernova remnant (or which more later) itself; the decay of radioactive materials formed by nucleosynthesis; and a pulse of ultra-violet radiation causing continued fluorescence of helium atoms in the surrounding medium (this would explain, in particular, the strong emission lines). However, such theories remain, for the most part, speculative.

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Although the outer part of the star is ejected, the inner core continues to collapse with such violence that the pressure of the degenerate electron gas is insufficient to establish a stable equilibrium, and the matter is compressed far beyond that in a white dwarf. With the prodigious rise in density and pressure, the electrons are accelerated to speeds close to that of light, and tunnel into the nuclei to combine with nuclear protons, forming neutrons. At still higher pressure and density the individual nuclei disintegrate into their component neutrons and few remaining protons. At this point the material becomes virtually incompressable as a “degenerate neutron gas”: The supernova remnant is a neutron star, with a radius of fiveto fiftenn kilometres and a mass of the order of one to three solar masses. Such objects have been observed as variable micorwave sources of extremely short period.

The first of such microwave sources was discovered in 1967, in England: The microwaves originated from a point source and were emitted in bursts of approximately 0,05 seconds in duration, and at intervals of about 1,34 seconds. The astronomer Anthony Hewish (who was, in fact, in charge of the telescope which detected the signals) though that the source might be some form of “pulsating star”, a name which was shortened, almost at once, to pulsar, and by which such objects are now known.

Since 1967 many more pulsars have been discovered. All pulsars are characterised by extreme regularity of pulsation, with periods varying between 0,003 099 and 3,754 91 seconds.

Perhaps the best known (visible) supernova remnant is he Crab Nebula in the constellation of Taurus.

This nebula was first observed in 1731 by the English astronomer John Bevis, and later by the French comet-hunter Charles Messier (who at first mistook it for Halley’s comet) and the Irish astronomer William Parsons, Lord Rosse (whose sketch of the object inspired its name). High quality photographs of the Crab taken at different times have shown that the nebula is expanding at a rate of 1 300 km s^-1. Such measurements indicated that the expansion began about nine hundred years ago, which firmly identified the Crab Nebula as the remnant of the supernova of AD 1054 (an association which had previously been suggested due to the location, in Taurus, of the nebula and the supernova event).

The Austrian-born astronomer Thomas Gold was the first to suggest that pulsars are neutron stars: He pointed out that a neutron star is small enough and desnse enough to rotate on its axis in four seconds or less. Since neutron stars are (it is believed) formed in supernova explosions, the discovery in 1968 of a pulsar in the Crab Nebula (which was, incidentally, the first optical pulsar to be discovered) appeared to vindicate this hypothesis.

Pulsars are now generally regarded as being rotating, magnetic, neutron stars, with the axis of the (intense) magnetic field inclined to the axis of rotation. The pulses are intimately connected with the magnetic field: Most theories of their origin involve the behaviour of high-energy charged particles which interact with the field, perhaps with micorwaves (and posibly other radiation) being emitted in the region of the magnetic poles, as the particles lose energy.

The extraordinary stability of the pulse period is due to the rotation of the neutron star. The energy radiated by the pulsar derives from the energy of rotation, and hence leads to a slowing down of the rotation and a lengthening of the pulsar period: A phenomenon which has been observed for many pulsars.

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If a supernova explosion is one of sufficiently great violence, or if the mass of the collapsed core exceeds 3,2 solar masses such that the gravitational field is sufficiently intense, the pressure of the degenerate neutron gas will be unable to halt the collapse. No further force can arise to stop the contraction, which therefore must continued without limit: Hence, the volume of such a body diminishes, and the density and surface gravity increase, all also without limit.

Such a “supercollapsed” object has been referred to as a “collapsed star” or collapsar.

As it contracts, the collapsar passes through a point where its surface gravity is such that the escape velocity is equal to the velocity of light: The value of the radius of the body for which this is so is called the Schwartzschild radius. The point which contains the entire mass of the system is called the Schwartzschild singularity.

(Named after the German astronomer, Karl Schwartzschild, who first calculated such a value.)

Since no body with real rest mass can travel with a speed equal to or greater than that of light, any object which falls towards the collapsar past the event horizon (the surface of the sphere described by the Schwartzschild radius) can ever escape (baring quantum effects): It is as though the collapsar was an infinitely deep “hole” in space.

Since, also, light attempting to rise from such an infinitely deep gravitational well must loose all its energy and experience and infinite einsteinian red shift, no light (or, indeed, any other form of radiation) can emerge from this “hole” in space, which is, therefore, totally black.

Hence a collapsar is more commonly referred to as a black hole.

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The study – both theoretical and observational – of all types of supernova remnants is of considerable interest to modern astronomers and astrophysicists, the study of black holes being singularly interesting.

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The fusion of hydrogen nuclei at extreme temperatures to form helium is the principal energy source of a typical star for most of its life. This reaction might occur via the p-p chain or the CNO^– cycle. After the hydrogen burning phase the helium burning phase which follows results in the fusion of three helium nuclei to form a carbon nucleus (the triple-α process) The product of fusing two helium nuclei, a form of beryllium (₄Be⁸), is unstable and breaks up again into two helium nuclei.

Heavier elements can be formed by successive fusion of more helium nuclei, as occurs in the cores of massive stars. In this way, for example, oxygen, neon, magnesium, silicon and sulphur may be formed. It is believed that by subtle modifications of the α process, elements with mass increasing to that of iron, and whose mass number s are multiples of four, can be synthesised. At higher temperatures protons may be removed from individual nuclei, so triggering a whole series of new nuclear reactions creating the elements with intermediate mass numbers. Radioactive decay of fusion products may also be involved.

Element formation by the buildingup of nuclei of lighter elements, and related processes, can proceed only as far as the iron-group elements – iron, cobalt, nickel – as subsequent fusion requires the input of energy. Elements with greater mass numbers may be formed by the process of neutron capture: In the rapid r process, several neutrons are captured by a single nucleus before it has time to decay by β emission; by way of contrast, in the slow s process an unstable nucleus, newly created by neutron capture, has time to decay before teh next neutron. The mixtures of elements formed by the r and s processes differ: For example, gold and platinum are thought to be products of the r process, while copper and lead are thought to be produced by the s process.

Certain proton-risch heavy elements, such as molybdenum and samarium, cannot be the products of either the r or s process: For these elements a rare capture event known as the p process has been invoked, in which r and s process material is believed to be exposed to a flux of fast protons.

The s process takes place inside red giants, where element creation has advanced to the iron end-point. The r and p proceses occur only under extreme conditions, and so may take place only in the expanding envelopes of material ejected by supernovae.

Stellar nucleosynthesis, together with the r and p processes of supernova exposions, can account for the estimated cosmic abundances of nearly all the known elements: The existance of lithium, beryllium and boron (which are all rapidly destroyed in stellar interactions), for example, can be explained by spallation – the fission of atoms of interstellar materials by collisions with cosmic ray particles.

While playing only a mnor rôle in the creation of the elements, supernovae play a mojor rôle in their distribution: The interstellar medium, still mostly primordial hydrogen and helium, is enriched with heavier elements ejected into space by supernova outbursts.

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From the interstellar gas and dust (containing such elements as carbon, oxygen, aluminium and silicon) can form new stars, and planetary systems, such as our own.

It is a somewhat sobering thought that the bulk of the lements that form the organic compounds of our own bodies were forged in the hearts of giant stars, and blasted into space by the cataclysmic “death throes” of those stars.

We are stardust, we are golden,
We are billion-year-old carbon

― “Woodstock”, Joni Mitchell

Appendix: Thermonuclear Reactions

Two different processes lead to the conversion of hydrogen into helium: The proton-proton (p-p) chain and the carbon (CNO) cycle.

The p-p chain dominates at temperatures less than 2 . 10⁷ K, while the CNO cycle is prominent at higher temperatures. Hence, the p-p chain predominates in stars of spectral classes G to M, and the CNO cycle in the hotter stars of class O to F.

The proton-proton chain consists of the following reactions:

The carbon (CNO) cycle requires a carbon nucleus as catalyst:

The nuclei of elements heavier than helium, and with mass numbers which are multiples of four can be formed by successive fusion of helium nuclei.

Beryllium and carbon, for example, can be formed in the triple α process, viz.:

This process occurs only at very high temperatures, of the order of 10⁸ K.

Other reactions follow straightforwardly with the addition of further α particles, leading to the formation of ₈O¹⁶, ₁₀N²⁰, ₁₂Mg²⁴ and even heavier elements.

Nucleosynthesis: The Creation of the Elements

Bibliography

Isaac Asimov, The Collapsing Universe, ISBN 0552108847, Corgi (1978)

David H. Clark, Superstars, ISBN 0460043846, Dent (1979)

― and F. Richard Stephenson, The Historical Supernovae, ISBN 0080209149, Pergamon (1977)

Elske v. P. Smith and Kenneth C. Jacobs, Introductory Astronomy and Astrophysics, ISBN 0721683878, Saunders (1973)