Postulated over 60 years ago, neutron stars have more recently come to be observed in the form of pulsars. Dr. Norman Glendenning of the Lawrence Berkeley National Laboratory in Berkeley, California traces the story of these remarkable objects and shows how their observation may in fact give us crucial information about the state of matter in the earliest moments of our universe.

"I bow low. I have observed the apparition of a guest star....Its color was an iridescent yellow." So wrote the astonished court astronomer of the Sung dynasty in 1054 when he witnessed the sudden appearance of an object so bright that it was clearly visible in daylight and for weeks thereafter. We now know that it had the brightness of 10 billion suns. Such sudden flare-ups occur in our own galaxy once every hundred years or so and can be seen even if they occur in distant galaxies because of their intrinsic brightness. They came to be called supernovae.

Nine hundred years later in Pasadena, California, the German astronomer Walter Baade and Swiss theoretician Fritz Zwicky puzzled over these rare but extremely bright outbursts. In 1934 they advanced the proposition that a star much more massive than the sun ends its life in a cataclysmic explosiongiving rise to what is observed as a supernova and leaves behind the core of the original star, now very much shrunk in size a neutron star.


Walter Baade	Fritz Zwicky

It is easy to follow their reasoning. Material objects are held together by some force or othernucleons in a nucleus by the nuclear force, electrons of an atom by the electric force, cellulose molecules of wood by the atomic and molecular forces, and the material of stars by the gravitational force. The amount of energy that would be required to take apart objects held together by their own attractive forces is called the binding energy. Because of the conservation of energy, it is also the energy that is released or given up by an object when assembled from its constituents by its own forces.

For exactly that reason, Baade and Zwicky understood that, even if only the thousand-kilometer core of a large star were collapsed by its own gravity into an object of "closely packed neutrons" with a diameter of ten kilometers, it would release more than enough energy to blow off the rest of the star. The energy released by the formation of a neutron star is so great that the explosion can hurl most of the original star, whose weight is 10 suns or more, into space at a velocity of 10,000 kilometers a second. A thousand years after such an explosion the one seen by the Chinese astronomer we see its remains as a diffuse and beautiful object 15 light years across and still expandingthe Crab nebula (Figure 1). How the energy released by the collapse of the star's core was converted into a spectacular explosion belongs to our story of the neutrino.

Figure 1: The Crab nebula, produced by the supernova explosion observed in 1054. Left: the nebula observed at the Palomar Observatory in 1996 by J. Hester and P. Scowen, Arizona State University. Right: Detail showing the intense activity in the nebula caused by emission from the rotating pulsar, as observed by the Hubble Space Telescope.

Neutrinos (see "Cosmic Phantoms" by R. L. Hahn, Science Spectra No.1, p.48, 1995) are subatomic particles that interact so weakly with matter that most often a neutrino will pass through the Earth without leaving any trace of its passage. Theorists were convinced that most of the energy released by the collapse of a star's core to form a neutron star would create neutrinos in huge numbers, more than one for each neutron in the neutron star. They would carry with them much more energy than is actually needed to light the heavens and hurl most of the star into space to create the enormous nebula we now see. But because of their weak interaction, only a small fraction of neutrinos would actually share their energy with the rest of the star and expel it in the supernova explosion. The remainder of the neutrinos, by far the largest number, would escape into space without effect on the star. They would carry with them ten times more energy than the living star had produced in its entire lifetime.

In 1987 the explosion of a star in a neighboring minor galaxy called the Large Magellanic cloud was seen. As fast as light can travel from there to Earth, recoiling protons resulting from neutrino interactions were observed in giant detectors in Japan and in the USA in just the right number to confirm in broad outline the theory of death and transfiguration of stars in supernovae. Neutrinos were the messengers from the heart of the collapsed star, announcing the birth of a neutron star. Years later, rings of gas expelled by the explosion are seen around that "dead" star (Figure 2).

Figure 2: Supernova SN1987A. This Hubble Space Telescope picture taken in 1994 shows three rings. The small, bright ring lies in the plane of the supernova and presumably represents material ejected by it; the other rings lie behind and in front of it and their origin is not known. SN1987A lies in the Large Magellanic Cloud, a dwarf galaxy 169,000 light years away from Earth.

The great Cambridge astronomer, Sir Arthur Eddington, correctly guessed in the 1920s that a star shines because, under the enormous pressure of its own weight, the core is heated to such high temperatures that hydrogen is burned to form helium. He realized that it will take 15 billion years for our sun to consume all its primordial hydrogen and that it will shine as we see it now until close to the end of its life. Thermal and radiant pressure produced by the fire resists the attraction of gravity and forestalls the ultimate collapse of the star.

Some stars are more than ten times as massive as our sun. Their greater weight causes their nuclear fuel to burn more rapidly than it does in our sun. These are the stars that end their lives in supernova explosions. Instead of shining for billions of years, such stars burn out in something like 10 million years. Six or seven generations of such stars have lived and died since the extinction of the dinosaurs on Earth. And their greater weight and size causes a long chain of nuclear burning processes to take place. What it means for such a star to burn out involves the combined ideas of several scientists working on seemingly unrelated aspects of the lives of stars.

White dwarfs were discovered in 1910. It was known that they were enormously dense stars and were essentially dead they produced no new energy but simply radiated what was left from some earlier incarnation. In 1931, the young Indian physicist S. Chandrasekhar was on his way to study with Eddington at Cambridge when he realized, on the boat from India, that a burned-out star like a white dwarf could not support much more weight than the sunotherwise it would collapse.

S.Chandrasekhar

In a classic 1957 paper, G. R. Burbidge, E. M. Burbidge, W. A. Fowler and F. Hoyle solved the mystery of how the universe, beginning with mostly hydrogen and several very light elements, manufactured the elements of which we ourselves and everything around us are made. A star heavier than our sun will burn ever hotter by consuming a succession of elements, the ashes of one being the fuel for the next stage. The evolving star will develop an onion-shell-like structure, each shell toward the center containing heavier elements, the product of burning in the outer shells. Burbidge et al. also realized that the nuclear fuel that keeps a star alive would run out when thermonuclear fusion reactions reached the end of the chain and produced iron. As iron is the most tightly bound of all nuclei, nuclear burning stops with that element no energy can be gained by fusing heavier elements from lighter ones beyond iron. Therefore, a growing core of iron is produced until its mass reaches the limit calculated by Chandrasekhar. At that point, the core collapses to a neutron star as envisaged by Baade and Zwicky. It remained for S. A. Colgate and R. H. White in Los Alamos (1965), and many others working to this day, to elucidate all the processes by which a fraction of the binding energy released by the collapsed neutron star, most of it carried by the weakly interacting neutrinos, could expel the rest of the star in a supernova explosion instead of the whole star falling into a black hole, which no doubt sometimes happens.

A neutron star, then, is the collapsed iron core of a very massive star. It is so small in comparison with its original size that there is insufficient room for all the nuclei that were contained in the core. The nuclei are destroyed during the collapse and reduced to their elementary constituents the neutrons, protons and electrons. As the collapse continues, most of the electrons are captured by protons to yield neutrons and neutrinos. The neutrinos have the velocity of light because they have no (or very little) mass; therefore they escape, leaving behind a star made mostly of neutrons.

Of what relevance are neutron stars to us as human beings? Without them we would not be! Many generations of evolving stars have spent their lives manufacturing the elements of our Earth and our bodies. These elements were cycled back into the vast spaces of our universe by supernova explosions powered by the birth of neutron stars. For generations of stars these elements wandered in immense diffuse clouds of gas, eventually being caught up in compact pockets of interstellar gas where new protostars are born to repeat the cycle (Figure 3). By this slow enrichment with heavier elements, conditions for the creation of the planets and life were eventually attained. Without the explosive energy provided by the formation of neutron stars, none of this would have come to be. We are made of the stuff of stars.

Figure 3: Star-forming region in the Eagle nebula (also called M16) 7,000 light-years away from the Earth in the constellation Serpens. This picture, taken with the Wide Field and Planetary Camera 2 on the Hubble Space Telescope, shows enormous pillars of cold gas and dust, light years long. Inside these columns are regions where the gas is dense enough to collapse under its own gravity to form stars.

Neutron stars, though postulated in 1934, and studied as theoretical objects in 1939 by J. R. Oppenheimer and G. Volkoff in Berkeley and R. C. Tolman in Pasadena, were for many decades not searched for by astronomers, even though the notion of Baade and Zwicky was quite convincing. No one knew what to look for. Such a star, the collapsed core of a once living star, would be quite deadit could produce no energy of its own and, being very small, would be hard to see by the visible light that it could emit from the store of heat left from its earlier life as part of a large living star.

Robert Oppenheimer

The first discovery of a neutron star came quite by accident. Anthony Hewish of Cambridge had designed a large radio antenna of wires strung out on poles in a five acre field for the purpose of detecting signals from very distant objects called quasars. However, soon after the antenna was put into operation, his graduate student, Jocelyn Bell, detected a mysterious signal of a single note that persisted day after day. At times the signal was stronger, at times weaker, sometimes fading but always returning and always the same note. Bell and Hewish determined that the signal came from outside the solar system. And they suspected, even before announcing their discovery to the world in a paper published in Nature, that they were observing periodic signals from a neutron star.

Coincidentally, F. Pacini, an Italian working then at Cornell, had published a seminal paper earlier in the same year. He reasoned from one of the conservation laws of physics that neutron stars would have enormous magnetic fields, and if rotating, would emit a signal along the direction of the magnet that would be seen once every rotation by an observer who happened to be located in the direction swept out by the beam (Figure 4). The beamed radio signal, rotating with the star just like the beacon of a lighthouse, would appear as a pulsing star just as was detected by Hewish and Bell.

Figure 4: Charged particles are accelerated in the magnetic field of a rotating pulsar. The motion of the particles focuses radio emission in a narrow cone around the magnetic axis. An observer located on the cone swept out by the radiation "sees" the radio emission once every rotation, hence the pulses of the pulsar.

The scientific world was electrified. One of the great discoveries in astronomy had been made, confirming earlier ideas about the source of the energy that powered supernovae and opening a new chapter in observational astronomy. It would lead, among other things, to the confirmation of Einstein's theory of gravity in what is called the strong-field regime of his General Theory the theory that, unlike Newton's, can describe gravity in the region of neutron stars and black holes.

Neutron stars that are detected by means of their beamed radiation, seen once every rotation, are called pulsars. Soon others were detected through observations using large radio telescopes, including one within the remnant of the star that had exploded in 1054. Since the discovery of the first neutron star in 1967, some 800 others have been found.

Some neutron stars rotate only once or twice a second. Even this is very rapid considering that our sun rotates only once every 25 days. It is another conservation law, that of angular momentum, that assures the spin-up of the collapsing core of a slowly rotating star, just as an ice skater can spin up by drawing in his outstretched arms. The young Crab pulsar, the very neutron star whose formation exploded the supernova of 1054, spins 30 times a second. A star the mass of the sun spinning at this rate has an enormous store of energy. It is known from observations made on the Crab nebula that the pulsar within it is converting its rotational energy into radiation radio waves, gamma rays, electron - antielectron pairs at a power equal to that of 100,000 suns. This energy lights the Crab nebula, 15 light years in diameter, making it luminous in radio, optical and X-rays, and accelerates wisps of gas in it to half the speed of light (Figure 1).

The nebula, consisting of the 10 solar masses of debris from the exploded star, will continue to expand, becoming more diffuse and dimmer. Perhaps in 50,000 years it will disappear, while the pulsar within, only somewhat reduced in spin, will join other isolated pulsars. It will continue its outpouring of energy for another 10 million years, but at a decreasing rate as its rotation slows. Finally it will disappear from the radio sky and will join a growing number of silent, unseen neutron stars.

Though neutron stars are usually detected through their very weak pulsed radio signal, occasionally one makes a spectacular appearance in the heavens that can be seen in telescopes because of the bow shock created in the interstellar hydrogen by its high velocity passage (as illustrated in Figure 5).

Figure 5: Bow shock produced by a neutron star moving with a velocity of several hundred km/s. The shock front is exhibited by the hydrogen alpha line. The neutron star itself is not visible, but it has a white dwarf companion, the yellow dot about 1 cm inside the front of the bow. The other dots are background stars. (Image courtesy of Andrew Fruchter.)

"Absolute space.....[and time] always remains similar and unmovable," wrote Isaac Newton in The Principia. Newton's laws of mechanics and gravity took on their simple form as he wrote them, only if space and time had a meaning independent of anything or anyone. For 200 years his theory met with one success after another.

But by the early 1900s problems began to stir in a few minds. Maxwell's theory of electricity and magnetism described many verifiable phenomena. It also predicted that the velocity of light in vacuum was a constant of nature. But this seemed incompatible with Newton's absolute space and time; light velocity ought to depend also on the speed of the source. Albert Einstein solved the dilemma by fusing the meaning of space and time into a single fabric that we call spacetime. In this fused spacetime there could be no absolutes. Thus was born the Special Theory of Relativity (1905).

Einstein's new laws found almost immediate acceptance and they are daily confirmed as a matter of routine in the world's large particle accelerators. The pion, an important subatomic particle that is partly responsible for the nuclear force, lives for only 1/100 millionth of a second if it is measured by a person at rest with the pion. Yet its lifetime can be stretched almost infinitely with respect to the same person, if the pion is accelerated to a high velocity close to the speed of light. The new laws do not contradict our everyday experience. For it is only when relative velocities are near the speed of light that differences between relative spacetime and absolute space and time show up.

However, Einstein's crowning achievement came a decade later with the discovery of his theory of gravity that is often called General Relativity. His way was beset by many difficulties, but years later in his Princeton lectures he was able to say precisely what bothered him about the Special Theory. "... it is contrary to the mode of thinking in science to conceive of a thing which acts, but cannot be acted upon." Therefore if objects and events were affected by motion in spacetime, as was predicted by his Special Theory and abundantly confirmed, they must in turn act upon spacetime. This insight was realized in his formulation of what most scientists regard as the most beautiful of physical theories.

Einstein's notion that spacetime must be acted upon by mass-energy, just as mass-energy is shaped and moved by spacetime was given precise expression in the symbolic equation

Einstein's theory of gravity transforms seamlessly into Newton's theory when gravity is weak as it is on Earth and in the solar system. It is especially remarkable in this connection that when gravity is weak the gravitational force is proportional to the inverse square of the distanceprecisely. Newton postulated the inverse square because the theory worked well with the inverse square dependence, and perhaps because he was partial to integers. The inverse of distance raised to the 1.999 or 2.001 power would have worked just about as well for the solar system dynamics. There was nothing about Newton's theory that absolutely demanded the integer power 2. In Einstein's theory it could be nothing else.

Although the equation is beautiful in the simplicity of its form and directness of its statement, it is so pregnant with meaning and implication that to this day it has not been fathomed to its depth. Neither Einstein, nor anyone else, foresaw all the wonders that flow from his theory. Chandrasekhar was the first to hint at one of its unexpected properties. He found that a star of the class known as white dwarfs could not exceed the mass of the sun by more than a factor 1.5. Eddington, who had made many marvelous discoveries of his own, refused to accept Chandrasekhar's idea. He probably saw in it another "absurd" prediction that any star more massive than a certain limit would eventually collapse to a black hole. He was such a towering presence in astronomy that Chandrasekhar's idea was not accepted for some time and is now understood to apply more to the cores of massive stars near their death than to white dwarfs.

It remained for Oppenheimer and Volkoff in 1939 to discover the true nature of gravity's grasp on the mass of dead relativistic stars. They studied the prediction of Einstein's equations for a spherical star that could produce no energy because, in the language of physics, its matter was in a degenerate state the state of lowest energy at whatever density of the matter. They invented a simple model of neutron stars almost 30 years before the first neutron star was discovered. And they showed, as a consequence of the warpage of spacetime predicted by General Relativity, that a dead star's mass cannot be greater than several times the sun's mass.

Oppenheimer and his student, Hartland Snyder, took a step further in their study of the "absurd" notion implied by a mass limit for dead stars, that of continued gravitational collapseforeverinto a black hole if the mass exceeds the limit. Even though black holes are a logical consequence of Einstein's equations, the possible existence of such objects was not at first accepted even by such an expert and visionary as John Wheeler. At a 1958 conference in Brussels, he concluded a brilliant lecture on the theorems and discoveries of his group at Princeton concerning the two families of dead stars, white dwarfs and neutron stars, by arguing that some physical process would intervene to prevent continued collapse. Oppenheimer politely demurred, saying "I believe....in....General Relativity." Not long afterward, Wheeler accepted the logical imperative, and it was he who in fact coined the name "black hole."

In a curious footnote to history, the notion of a star "whose light could not arrive at us" was conceived much earlier by a certain Reverend John Michell in a letter to John Cavendish in 1783 and published in the Philosophical Transactions of the Royal Society in the following year. He reasoned that Newton's law of gravity would act on light, just as it does on mass. In this case he calculated the condition that light could not escape from stars having a certain relation between their mass and size. Curiously, the relation he derived, albeit by incorrect reasoning, is precisely the one that follows from Einstein's theory, known as the Schwarzschild limit after the German astrophysicist Karl Schwarzschild (1873-1916). Michell thought that light would be slowed down in its flight from a star, like a stone thrown into the sky, though we now know this to be untrue. Rather, the warpage of spacetime inside a black hole must be so severe that it is not possible for light to travel in any direction other than inward. So light does in fact not leave. Michell also devised the only means we have of detecting a black hole "yet, if any other luminous bodies should happen to revolve about them we might...from the motion of these revolving bodies infer the existence of the central ones." The world was not ready for these ideas in the 18th century. Michell's prescient notion was not uncovered again until long after the modern theory of gravity and black holes had been formulated.

Neutron stars were first conceived of as being just thatstars made of closely packed neutrons. We now believe, based on several lines of evidence, that neutron stars are in fact populated by a veritable zoo of particle types.

Still there are many uncertainties regarding the nature of superdense matter. The immense densities found in the interior of neutron stars are nothing like anything we will ever know on Earth except possibly in the fleeting moment following the collision of high-energy nuclei in the world's largest accelerators. Never-theless, we can use established laws and principles to guide us in the investigation of possible states of superdense matter in the interior of neutron stars, being always alert to what observable effect they might have. In this way we are offered the possibility of discovering properties of superdense matter that are not known from laboratory experimentsmatter that can never exist on Earth. And in so doing, we can elucidate and extend the laws of nature and the range of known phenomena.

Thus the laws of physics including Einstein's theory of gravity and the well-substantiated theory of the underlying quark structure of nucleons known as quantum chromodynamics allow us to investigate a range of possible phenomena that may occur in superdense matter. Only in its simplest conception can neutron star matter be thought of as a uniform medium of closely spaced nucleons. So-called phase transitions may occur at successively higher densities and can fundamentally change the nature of dense matter. The concept of phase transitions is familiar to all of us in its simpler forms, for example in such phenomena as the transition of water to ice or steam. In other systems, particularly in substances that have a richer composition to begin with, phase transitions can introduce quite unexpected new structure to the substancea lattice of quite marvelous nature. Neutron star matter belongs to the second category (Figure 6).

Figure 6: Cutaway schematic of a hypothetical neutron star showing its crust of ordinary iron (and other neighboring elements), the "quantum liquid" of nuclear matter (mostly neutrons) and, at the center, a region occupied by a mixture of nuclear matter and quark matter and (not shown) near the very center, pure quark matter.

From the rotation rate of millisecond pulsars, such as the one discovered by Berkeley astronomer Donald Backer in 1982 that rotates 600 times a second, we can estimate the range of densities of matter that occur in neutron stars. The estimate is made by comparing the centrifugal force on a particle at the surface of a star rotating at 600 times a second with the gravitational attraction of the rest of the star. Gravity must win or the star would fly apart at the equator. By such a comparison we learn that the central density must be a few times nuclear density. From laboratory experiments we know the size of nucleons. At the central density of neutron stars, the nucleons would overlap. Therefore, just as nuclei themselves dissolve into matter composed of its nucleon constituents, so too we expect that at higher density nucleons will dissolve into their constituentsthe quarks.

Quarks have a peculiar property compared to the constituents of matter at all other known scales. Molecules can be taken apart and their constituents, the atoms, can be studied. Atoms can likewise be taken apart and the central nucleus as well as the electrons surrounding it can be studied. The nucleus too can be separated into its nucleons, and such nuclear reactions in all their complexity have been investigated. But it is apparently a law of nature that the quarks of an individual nucleon cannot be removed and isolated for study. Nevertheless, it is a prediction of the theory that if nucleons are crushed together, the quarks will lose their association with their previous hosts so that matter dissolves into a quark gas. The individual quarks still cannot be separated from such a crushed dense state of matter. But this new state of matter is among the most fascinating we can imagine. It is called quark matter and it must have pervaded the universe in its very earliest instants when it was immensely hot and dense, and before the universe, expanding from the Big Bang, cooled, and thus made it possible for quarks to combine into individual nucleons such as the neutrons and protons that make up the atoms in our bodies.

The state of matter quark matter which existed in the fiery furnace at the beginning of time may exist now in much the same form deep within the interior of neutron stars. How might it be possible to learn if indeed this primordial state of matter is being recreated in some neutron stars?

Amazingly, we here on Earth may learn what is happening in the heart of a neutron star in a very direct way. The same law of physics used by ice skaters when they spin up from a slow twirl to a dazzling whirl provides the signal. The law is the conservation of angular momentum, or spin as we will call it for brevity. As we shall see, something analogous to what happens to the ice skater will happen to a rotating neutron star if its center converts to quark matter.

Imagine a rapidly rotating star. It will be somewhat flattened because of the centrifugal force, i.e. it will bulge at the equator. It has a huge magnetic field embedded in it along which radio waves are beamed like a lighthouse beacon (Figure 4). The radio waves and other radiation carry off rotational energy and therefore the star very slowly loses spin. The star's loss of spin does not violate the law of the conservation of angular momentum because what the star loses, the outside world gains. Part of this gain is what powers the very radio antennae by which we can "see" the spinning pulsar.

As the star slowly loses its spin, the centrifugal force weakens and the star becomes less pancake-shaped, more spherical. Its mass becomes more centrally concentrated and its central density increases. This process continues for millions of years while the slow relaxation of the centrifugal force occasioned by the radiation emitted by the star paces its loss of spin.

When the density has increased to the critical value such that individual nucleons cannot exist, their quarks break free into the state of matter written of earlier quark matter. This state is far less resistant to compression than the nuclear matter that formerly occupied that region of the star. Therefore, the rest of the star, weighing down on it, compresses and reduces the size of the star.

Just like the ice skater when he concentrates his weight closer to his center spins faster so as to conserve angular momentum, the star, by converting nuclear matter to quark matter, concentrates its weight closer to its center and spins faster. Just as the ice skater's performance is quite stunning, so too would be such a performance by a star. I call it stunning, because the natural state of affairs when a star or anything else loses or radiates spin is that it spins slower not faster.

Moreover, whether a pulsar's rate of rotation is increasing or decreasing would be quite "visible" to us because of the beam of radio waves that is sent toward us each time the pulsar turns. And what is also important, if any particular pulsar is converting ordinary nuclear matter to quark matter, the epoch of spinning ever faster should last for 10 million years according to our calculations (N. K. Glendenning, S. Pei and W. Weber (1997). Any given millisecond pulsar will be presently in this phase of its evolution for 1/100th of its billion-year lifetime. While that gives us only a small chance for observing a given pulsar in the act of increasing its spin during its lifetime, it also means that one in a hundred pulsars, on average, will be in this phase of its life. So far, radio astronomers have discovered only about 25 isolated millisecond pulsars that are candidates for the peculiar spin-up we have described as a signal of a phase transition to quark matter. Millisecond pulsarsthose that rotate more than 100 times a second are harder to detect than ordinary, more slowly rotating ones. But as the sensitivity (or size) of radio telescope arrays increases and the computers that analyze the incoming data become faster, we can anticipate new additions to our inventory of neutron stars of this important class.

We thus have a reasonable chance of hearing, from deep within the heart of a neutron star, the signal of the slow conversion of matter as we know it to matter as we believe it once was. Such a discoveryif madewould confirm one of our central ideas of what existed in the fiery furnace that was our universe near the beginning of time.

Thorne, Kip S. Black Holes and Time Warps, W.W. Norton & Co., New York (1994).

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