White Dwarfs, Neutron Stars, And Black Holes

 01 sep 99
 greg goebel (gvgoebel@yahoo.com)
 public domain

While stars seem unchanging in comparison with a person's lifetime, they are in fact evolving objects that are born, mature, age, and die.

After death, they leave behind stellar "fossils" as gravestones of their existence. The most evident of these fossils, the small stars known as white dwarfs, have been known for over a century. In recent decades, however, research has shown that such fossils can be more remarkable objects, known as neutron stars, or possibly can even be "singularities", collapsing forever and folding space around themselves to form "black holes".

This document provides a survey of white dwarfs, neutron stars, and black holes.

Contents List













Between the years 1834 and 1844, the German astronomer Friedrich W. Bessel performed a series of careful observations of Sirius, the brightest star in our sky. Sirius, sometimes called the Dog Star, is about twice as massive as our own Sun, 25 times brighter, and is about nine light years away in the constellation Canis Major.

Bessel's careful observations revealed a wobble in the motion of Sirius across the sky, indicating the presence of a hidden companion. However, nobody was able to locate the hidden companion until 1862, when the telescope maker Alvan Graham Clark spotted it while he was testing out a new large refracting telescope. The companion became known as Sirius B, or just the Pup, while the Dog Star itself became technically known as Sirius A.

Sirius B proved to be a very puzzling object.

The temperature of a glowing body approximates a curve known as a "black body spectrum". The peak of the black body curve gives the temperature of the body, and the hotter the body, the higher the frequency of the peak of the curve and the more intense the radiation. Observations of the spectrum of Sirius B indicated that it was very hot, with a temperature of about 30,000 degrees Kelvin (K). This high temperature meant that Sirius B was radiating a great deal of energy per unit of surface area.

However, Sirius B was about 10,000 times fainter than Sirius A. Since it was very bright per unit of surface area, the Pup had to be much smaller than Sirius A, with roughly the diameter of the Earth.

The faintness, of course, was one of the reasons that Sirius B took decades to find, even though astronomers knew roughly where to look. Sirius A was so much brighter than Sirius B that looking for the Pup was like looking for a lit match next to a searchlight beam. In fact, one of the main reasons the Sirius B was discovered in 1862 was because it had moved in its mutual orbit with Sirius A so that its angular separation as seen from Earth was over three times greater than it had been when the search began in 1844.

The mass of stars in a binary system can be easily determined. The orbital velocity of the visible companion can be determined by the Doppler shift of its light, and given the orbital velocity and the period of the orbit, the size of the orbit can be determined. A simple calculation of the gravitational forces involved gives the masses of the two stars.

Analysis of the orbit of the Sirius star system showed that the mass of the Pup was almost the same as that of our oun Sun. This implied that Sirius B was thousands of times more dense than lead. As more white dwarfs were found, astronomers began to discover that although the Pup might be bizarre, it was hardly unique. White dwarfs are common in our Galaxy.


In the 1920s, led by the brilliant Sir Arthur Stanley Eddington, astronomers began to understand the processes of stellar evolution. Eddington's landmark 1926 book on the interiors of stars laid down basic concepts that evolved into our current understanding of stars.

Eddington suggested that the high densities of white dwarfs were due to the complete ionization of the atoms in their interiors. With all the electrons stripped from all the nuclei, the nuclei could pack much more closely together, resulting in the extraordinary densities observed. However, the energetics involved in this process were puzzling and contradictory, at least by the rules of the physics Eddington had available to him.

Fortunately, another branch of physics that was evolving in parallel, quantum mechanics, came to the rescue. In July 1930, the 19 year old Indian astrophysicist Subraymanyan Chandrasekhar was on a sea voyage from Madras, India, to Southampton, England, and tinkered with physics to hold off boredom. Following work done by astrophysicist Ralph J. Fowler in 1926, Chandrasekhar applied quantum mechanics to the interior of a white dwarf star and determined how it could have such enormous densities.

While a star is performing fusion reactions in its core, the outward pressure of the thermal motion of the particles in the star keeps it from collapse. When the star is depleted of materials that can support fusion reactions, it collapses.

In the case of big stars, this collapse leads to a catastrophic supernova explosion, while the collapse of smaller stars is much less violent. In either case, the star falls in on itself until halted by some obstacle.

As the exhausted star can no longer produce fusion reactions, the only obstacle to collapse is "quantum-mechanical electron degeneracy". This is due to the Pauli exclusion principle, a rule of quantum mechanics that dictates that no two electrons in the same system can have the same energy level. As the star shrinks into itself, the electrons arrange themselves in a fully occupied range of base level energy states that can accommodate no more electrons. This creates an "electron degeneracy pressure", completely independent of the electrical repulsion between electrons, that resists further contraction.

Once the white dwarf is stabilized by electron degeneracy into a "fully degenerate" state, it can no longer contract. As it cannot sustain fusion reactions, the white dwarf's energy is only due to the gravitational collapse that formed it. Chandrasekhar's insight into degeneracy pressure finally explained how white dwarfs could exist. He would later win the Nobel Prize for his work.


Chandrasekhar's theoretical studies led to a better understanding of some of the characteristics of white dwarfs.

The degenerate free electrons that permeate the white dwarf make the object an excellent thermal conductor, so the white dwarf is almost "isothermal" -- that is, its temperature almost uniform throughout its entire volume. The bare nuclei in this sea of electrons act as a close approximation of an ideal gas, providing a deep reservoir of kinetic energy in their random motions.

The material on the surface of the white dwarf is not degenerate. Although this layer is only about 50 kilometers (30 miles) thick and only constitutes about 0.01% of the mass of the white dwarf, it nevertheless acts as an effective insulating layer. While the temperature at the bottom of the surface layer is about 10 million K, it is only about 10,000 K at the surface, with the energy flow throttled by the diffusion of radiation through the surface layer, and the vertical flow of heated material by convection through that layer.

A white dwarf star, then, has a large supply of internal energy and an insulating surface layer to keep the energy from radiating away rapidly. The result is that white dwarfs cool off very slowly through most of their lifetime.

When the 5.1 meter (200 inch) Hale telescope on Palomar Mountain, California, went into operation in 1948, astronomers were finally able to perform reasonable spectroscopic observations of white dwarfs. The result was another surprise: 80 percent of them showed an absorption spectrum of pure hydrogen, while most of the rest showed an absorption spectrum of pure helium.

The white dwarfs exhibiting pure hydrogen absorption spectra were designated type DA, while those exhibiting pure helium absorption spectra were designated type DB. In both cases, the surface layer was homogeneous to 1 part in 100,000. A small remainder had more complicated spectra and were designated type DC, while a tiny handful had unclassifiable spectra.

The puzzling thing was that the stars the white dwarfs were derived from had no such purity of composition. The key to the puzzle was the intense gravity of the white dwarf, about 200,000 times that of Earth, which left light atoms on the surface while heavier atoms sank. A DA white dwarf still retains some hydrogen, and so has a surface layer of hydrogen with a sublayer of helium above the degenerate core. A DB white dwarf has lost most of its hydrogen and so has a surface layer of helium.

The majority of white dwarfs that have been observed are isolated (or "field") stars, rather than white dwarfs in binary systems. These isolated white dwarfs can be found by searching the sky for a faint blue star with a large rate of motion across the sky. The blue color says that the object is hot, the fast motion hints that the object is nearby, and given these two facts the faintness suggests the object is small.

White dwarfs are also found in multiple star systems. In many of these systems, the white dwarf is draining mass off an active stellar companion, a process that leads to explosive outbursts, known as "novas. The subject of such "cataclysmic variables" will be discussed in detail in another document.

The mechanisms of stellar evolution that lead to the creation of a white dwarf are broadly understood. A star begins its life as a collapsing cloud of hydrogen and traces of other elements. As the mass falls in on itself, the temperature at its core rises until eventually fusion reactions start, converting hydrogen to helium and lighting up the star.

In time, the star runs out of hydrogen in its core, and hydrogen fusion then proceeds in an expanding shell around the pure helium core. The star swells in size and cools, becoming a "red giant".

With further age, fusion reactions begin in the core helium, converting it into carbon and oxygen. For a star with a mass between 2 and 8 Suns, helium burning goes on in a quiet fashion, with a helium burning core surrounded by the hydrogen burning shell.

When the core is then exhausted of helium, a helium burning shell then begins to expand outward from the center of the star in the path of the hydrogen burning shell. The star swells even more, becoming a "red supergiant".

As the star evolves into a red supergiant, its outer shell becomes increasingly tenuous, and in fact begins to evaporate into space. The star becomes unstable, "flashing" with rapid changes of luminosity.

The result is that within a few tens of thousands of years, most of the star's mass is lost into space, creating a spherical gaseous shell, or "planetary nebula", around the remainder of the star, now reduced to about 20% of its original mass. By the way, this shell is known as a "planetary nebula" because early astronomers tended to mistake them for planets, and these nebulas have nothing else to do with planets.

The mass loss may end before all the outer hydrogen envelope is lost, and the the ultimate result is a DA white dwarf. If all the hydrogen envelope is lost, the result is a DB white dwarf.

The white dwarf precursor forming at the center of the planetary nebula is known as a "planetary nebula nucleus", or PNN. A PNN with a mass of 0.6 Suns will evolve into a white dwarf in about 10,000 years, as the planetary nebula fades into space and all fusion reactions die out.

At first, the white dwarf is very hot, with a surface temperature of more than 100,000 K, and much hotter in its interior. It is so hot that any trace of hydrogen left in its interior is quickly fused into helium, and helium is converted to carbon and oxygen. The interior of a typical white dwarf is mostly composed of carbon and oxygen nuclei, though white dwarfs formed by smaller stars may be mostly helium and those formed by bigger stars may be formed of oxygen, neon, and magnesium.

In the early phase of their existence, the internal processes of a white dwarf generate large numbers of neutrinos. Neutrinos hardly interact with matter and flood out of the interior of the white dwarf, draining it of energy and allowing it to cool rapidly.

About 10 million years after its formation, the interior of a white dwarf cools to about 30,000 K and the star no longer radiates neutrinos. Cooling slows down dramatically. At first, most of the white dwarf's energy is lost by radiation, but as the white dwarf cools further, convection processes come into play, mixing the surface hydrogen layer with the lower helium layer. Eventually, helium may predominate, turning a DA white dwarf into a DB white dwarf.

A white dwarf loses most of its energy a billion years after its formation. During the long cooling period, the degenerate core continues to grow at the expense of the outer layer. Once the energy has effectively been dissipated, the white dwarf then starts to crystallize. The bare nuclei in the core of the object link up into a symmetrical crystalline lattice, and the crystallization then expands outward.

The transformation from a fluid to a crystal releases energy and slows down the cooling for a short time. Once the interior becomes heavily crystallized, however, the white dwarf's cooling proceeds more rapidly. The white dwarf becomes a dim, fading cinder, the only remnant of a once brilliant star.


One of the reasons astronomers find white dwarf stars interesting is that they are a key to understanding the age of the Universe. As already described, a white dwarf is the fossil remnant of a star that has exhausted its nuclear fuel, lost most of its mass in a planetary nebula, and cooled down to a dim cinder.

A plot of all the observed white dwarfs by their temperatures shows that as white dwarfs grow cooler, their numbers increase until the temperature of 3,500 K is reached. Below that temperature, there are none.

The reason for this is because the Galaxy is not old enough to have allowed even the oldest white dwarfs to cool off any more than that. This means that if we know how long it takes a white dwarf to cool off, we can use that knowledge to estimate the age of our Galaxy, which in turn would be a clue to the age of the Universe itself.

The primary way of estimating the age of the Universe is through measurements of its expansion rate, derived from the redshifts of distant galaxies and various means of determining the distance to nearby galaxies galaxies for calibration. Using the cooling rate of white dwarfs as a stepping stone to the age of the Universe is an entirely independent approach, and is useful as a reality check.

Theoretical studies of the cooling processes in white dwarfs gives an estimate of an age of about 9.5 billion years for the oldest white dwarfs in our Galaxy. Factoring in the time required for galaxies to form after the Big Bang and for stars to become white dwarfs gives an age for the Universe of 11 billion years. This indicates a substantially younger Universe than given by estimates provided by mainstream techniques, though not by an order of magnitude.

This estimate is based entirely on theory, but better estimates based on detailed observations are becoming available. As a white dwarf cools, vibrations can arise with a period from 100 seconds to several hours, due to spasmodic releases of energy through the dwarf's outer layer that cause the entire star to oscillate.

These vibrations, which appear as small variations in brightness, give clues to the internal processes of the dwarf, just as seismic waves give clues to the internal structure of the Earth. Understanding the internal structure of a white dwarf means obtaining a better estimate for its cooling rate.

The patterns of oscillation can be complicated, with different oscillatory modes and frequencies overlaying each other. Fourier analysis can be used to break the composite oscillation down into its spectrum, or graph of individual frequency components, but mapping the composite oscillation can take a day or more.

This task requires extended observations from a set of networked telescopes around the world. The Whole Earth Telescope, as it is known, has been developed through the 1990s and now can provide effectively continuous observations for extended periods of time, with data collected at a central location using electronic mail.

The process of studying white dwarfs through "asteroseismology", as the study of stellar vibrations of such dense objects has become known, is still evolving, but practitioners feel assured that they will be able to obtain much more precise data on the structure and evolution of white dwarfs.


When Chandrasekhar published his analysis of the underlying mechanisms of white dwarfs in 1930, there was an implication that disturbed many of his contemporaries.

Chadrasekhar determined that if a white dwarf has a mass of more than 1.4 Suns, electron degeneracy pressure would not be able to halt its collapse. This was not a problem in itself. What was troublesome was that once the "Chandrasekhar limit" was exceeded, "nothing" could halt stellar collapse, and the collapse would never end.

Eddington found this result distasteful and strongly attacked Chandrasekhar's work. Chandrasekhar was young and impressionable and the attacks were painful, but he was encouraged by others such as the Danish physicist Niels Bohr to stand his ground. Nonetheless, nobody knew exactly what to make of the idea that a star could collapse forever.

A hint was available, however. Einstein's theory of General Relativity, published in 1919, stated that mass distorted space and time in its vicinity. The German astronomer Karl Schwarzchild used the equations of General Relativity to perform an analysis of how a star distorts space and time in its vicinity, and while doing so had discovered something odd.

Schwarzchild found that for any given mass, there was a certain radius where time was compressed down to zero while the spatial dimensions stretched to infinity. This radius, now known as the "Schwarzchild radius", is very small, about three kilometers for a star with the mass of our Sun.

Schwarzchild felt that the matter was irrelevant. Chandrasekhar's analysis of white dwarfs lay in the future, and by the physics available Schwarzchild could see no way a star could become so compressed.

Albert Einstein was more uncomfortable with the Schwarzchild radius and its implications, but the matter still did not seem very important. Einstein didn't get around to dealing with it until 1939, when he published a paper in the physics press where he attempted to prove that a mass could not be compressed to its Schwarzchild radius.

In the meantime, however, other studies had been and were being performed on superdense objects and their properties. In 1932, physicist James Chadwick discovered the neutron, a nuclear particle similar to the proton but with no charge. Physicists began to tinker with the possibilities offered by the neutron, and a few astrophysicists, particularly Fritz Zwicky of the California Institute of Technology and Soviet physicist Lev D. Landau, speculated that they could be the key to stellar fossils far more dense than white dwarfs.

If a collapsing star were put under extreme pressure, they suggested, electrons could be forced into protons to form neutrons, creating a densely packed sphere a few kilometers across but with stellar mass. Zwicky and Walter Baade very astutely suggested further this pressure could be caused by supernova explosions.

Such a "neutron star" was a theoretical toy at the time, but physicists like to toy with ideas. The prominent American physicist J. Robert Oppenheimer and several of his students, most prominently Hartland S. Snyder, wrote a series of papers in 1938 and 1939 investigating the theoretical properties of neutron stars.

One of the interesting questions they considered was a mass limit for neutron stars, similar to the Chandrasekhar limit for white dwarfs, above which they would collapse. Snyder, working from suggestions by Oppenheimer, performed an analysis based on General Relativity of what would happen if the neutron star collapsed and fell through its Schwarzchild radius.

The mass would tend to collapse without limit, forming a "singularity". If an observer was watching a clock on the surface of the collapsing star that emitted a pulse of light at regular intervals, the pulses would become redder and the pulse interval would become longer, as time would slow down in the increasing gravity field. At the Schwarzchild radius, the pulse interval of the clock would become infinite, as would the wavelength of the redshifted light.

In other terms, once the clock reached the Schwarzchild radius, light could no longer escape from it. Oppenheimer and Snyder concluded that a singularity "tends to close itself off from any communication with a distant observer; only its gravitational field persists."

The concept of a singularity, a superdense object from which no light could escape, was a theoretical curiosity at the time. Global war put the matter on the back burner for decades. Oppenheimer went on to the Manhattan Project to help develop the atomic bomb. In 1947, he became director of the Institute of Advanced Studies at Princeton University, where Albert Einstein was a professor. There is no record of any discussions between them of the fate of collapsing stars.

In the postwar period, astronomers did search for neutron stars. A target of particular interest was the Crab Nebula, site of a supernova explosion that was observed on Earth by Chinese astronomers in 1054 AD. Although optical astronomers found a compact object at the core of the nebula, there was no way at the time for them to determine exactly what it was.


In 1967, a graduate student at Cambridge University in the UK named Jocelyn Bell discovered an interesting radio source in the constellation Vulpecula that emitted a sharp, intense pulse of radio energy on a period of every 1.33728 seconds. The period was extremely precise, with a variation of no more than 1 part in 10 million.

The initial reaction in the astronomy community was one of surprise, since no such regular sources had ever been discovered before. Some speculated that the sources might actually be beacons set up by a distant civilizations, and so the sources were initially known in some circles as "LGMs", for "Little Green Men".

However, the radio bursts were over a broad range of frequencies, which would have made the emitter an inefficient artificial beacon, and before long three more such sources were found in widely separated regions of the sky. The sources clearly seemed to be of natural origin, and were named "pulsars".

Bell's academic advisor, Anthony Hewish, wrote a careful analysis of pulsars. The sharpness of the radio pulses emitted by the pulsars suggested very small objects, maybe about 15 kilometers in diameter. If the object were larger, radio waves emitted from more distant regions of the object would arrive after those emitted from nearer regions, spreading out the pulse.

The pulse period indicated that the object was spinning rapidly, with radio "hot spots" coming into view with each spin. The rate of rotation implied an object of stellar mass, as anything lighter would simply tear itself apart. The only thing that could meet such constraints was a neutron star. Hewish later won the Nobel Prize for this discovery.

Once astronomers knew what to look for, they studied the Crab Nebula again and found a pulsar at its center, emitting bursts of radio energy at a rate of about 30 times per second. Precise measurements of the rotation rate of this pulsar showed that it was slowing down ever so slightly as it radiated away energy.

Another pulsar was found in a much closer supernova remnant in the constellation Vela. The Vela supernova occurred a few thousand years ago and this pulsar has lost much of its energy and slowed down, emitting radio bursts about 12 times a second. Over a thousand pulsars have now been identified, with periods ranging from ten seconds to a peculiar family of pulsars with periods on the order of a millisecond.


As had been suggested decades before and was clearly indicated by the Crab Nebula and Vela pulsars, a neutron star is the remnant of a supernova explosion, specifically from the collapse of a star with a mass of from 8 to 15 Suns.

The neutron star that results from such a catastrophe has a number of interesting characteristics. First, conservation of angular momentum as it collapses means that the young neutron star spins very fast, at a rate of about 50 times a second. (This does not come close to the period of the millisecond pulsars, but that will be discussed later.)

Second, for reasons not clearly understood the supernova explosion often does not occur symmetrically, giving the neutron star a "kick" that sends it out of its birthplace at velocities of more than 1,000 kilometers a second, fast enough in some cases to eject it from the Galaxy entirely. This is why some clearly young pulsars are not directly associated with supernova remnants.

Third, the young neutron star is also very hot, up to a 100,000 or a million K. The surface area of the neutron star is very small relative to its mass, and so the energy trapped during its formation can radiate away only very slowly.

Fourth, the young neutron star has an extraordinarily intense magnetic field. Since a moving magnetic field generates an electric current through a conductor, and since a young neutron star is a big powerful magnet spinning very fast, it sets up an immense flow of electrons, positrons, and ions over its surface and scatters them into space. This flow of charged particles is known as the "pulsar wind", analogous to the "Solar wind" emitted by our Sun.

The intense magnetic field and the flow of charged particles accounts for the radio pulses as well. The particles trapped in the magnetic field are focused by poorly-understood processes into focused floods of radiation from these two "hot spots". The magnetic poles are not necessarily aligned with the spin axis of the neutron star, and since the star is spinning rapidly the hot spots swing past like the searchlight beam on a lighthouse.

The pulse beams of young neutron stars, like the Crab Nebula or Vela pulsars, radiate energy all along the electromagnetic spectrum, from radio waves to gamma rays. As the pulsar ages and loses energy, however, the neutron star cools off and only radio emission occurs.

The rate at which the spin of a pulsar slows down indicates its rate of energy emission, and even though the beams are intense they only account for a small fraction of the energy emission of the pulsar. Most of the rest of the energy emission is likely in the form of the pulsar wind and other unseen radiation.

After about ten million years, the pulsar slows down and no longer has enough energy to emit pulses. The pulsar now becomes invisible to Earth observation, unless it is part of a star system and can be detected by its gravitational effects.

As the conditions in a neutron star are very difficult to duplicate on Earth, nobody is exactly sure just how big a neutron star can be. One indirect argument is based on the fact that as a neutron star becomes more massive, it must become stiffer to maintain itself, and the speed of sound through the star increases accordingly. Above six solar masses, the speed of sound exceeds that of light, which is ruled out by Einstein's theory of relativity.

Six solar masses is only an upper bound on the size of a neutron star. More practical calculations estimate the upper limit as three solar masses. No objects confirmed as neutron stars are known that are larger than two solar masses.


Neutron stars are often found in close binary systems with large normal stars. This might seem implausible, since neutron stars are born in supernova explosions that would tear apart a companion star. In fact, such companions often can survive the explosion.

The companion star swells as it ages, and for a close binary system the companion may eventually start losing mass to the neutron star. The mass spirals down to the neutron star in an orbiting disk of hot plasma, or "accretion disk", that can in some circumstances radiate brightly in the X-ray spectrum.

The mass spiraling into the surface of the neutron star can also "spin it up", increasing the star's rotation rate and restarting pulsar action. This mechanism is the origin of the otherwise baffling millisecond pulsars, the fastest of which spins at a rate of 667 times per second.

In a few rare cases the companion star itself evolves into a neutron star, and the result is a binary neutron star system. Such close neutron star binaries are of particular interest to physicists interested in gravity waves, as they are potentially strong sources of gravitational wave radiation.

Some also speculate that the mysterious "gamma ray bursts" that are detected on an intermittent basis may be due to the infall and collision of the members of a binary neutron star system.

The millisecond pulsars are not the only unusual types of neutron stars. There are also a handful of young pulsars that have intense magnetic fields, even by pulsar standards, and pulse mostly in the X-ray region of the spectrum. These objects are known as "anomalous X-ray pulsars", or AXPs.

There are also a small number of similar pulsars that occasionally generate intense bursts of low-energy ("soft") gamma rays, and are known as "soft gamma-ray repeaters", or SGRs. The gamma ray bursts appear to be caused by abrupt dislocations in the surface layers of the neutron star. Some astronomers lump AXPs and SGRs together as "magnetars", but these peculiar objects remain poorly understood.


Once neutron stars were discovered, astronomers began to wonder if singularities could exist as well. If they existed they would be very hard to detect, since Oppenheimer and Snyder had shown that no radiation could escape from them. Modern theorists described the result as a "black hole" in space.

Detecting such a black hole was a difficult prospect. They would be necessarily small, and could emit no detectable radiation by themselves. The only possible way to find one was through the observation of its effects on visible matter in its vicinity.

Astronomers have discovered phenomena in the cosmos that suggest that black holes do in fact exist. One is the existence of violent events associated with binary star systems and galactic cores. Such events require huge amounts of energy, and one of the most efficient ways to generate this energy is through matter falling into a black hole.

Another is the existence of binary star systems where a bright star is losing mass to a hidden companion, with the lost mass generating intense energy into the X-ray wavelengths. Analyses of some of these X-ray binary systems show that the hidden companion has a mass and size that could only be accounted for by a black hole.

One of the first bright X-ray sources in the sky, known as Cygnus X-1 and discovered in the early 1970s, appears to be a blue supergiant star losing mass to a hidden companion of about ten solar masses. This hidden companion is strongly believed to be a black hole due to its large mass and small size.

Similarly, observations of the cores of galaxies often show that there are objects hidden there with masses of thousands of millions of Suns but only the size of a planetary system. The only object known in theory that could have such great mass and compact dimensions is a black hole.

However, all that is known in these two scenarios is that there is a dense body involved whose specific characteristics are unknown, except for bounds on size and mass. These bounds can suggest the presence of a black hole, but the physics of black holes lie on the limits of physical theory, and although theoretical calculations can be surprisingly accurate, they have also in many cases proved dead wrong. Although the size and mass limits might imply a black hole in theory, nature might have other ideas.

Even if black holes exist, neutron stars are also clearly involved in energetic events in some binary systems, and telling the difference between a binary system interacting with a neutron star and one interacting with a black hole is difficult.

Black holes are in principle extremely efficient at converting infalling mass into energy. As objects are drawn toward the boundary of no escape, or "event horizon", they are accelerated to near the speed of light, and acquire tremendous kinetic energy, much of which is released in collisions.

The amount of energy conversion increases if the black hole is spinning, and can reach a theoretical maximum of 42%. The turbulent plasma falling into a black hole generates high-energy radiation in the form of X-rays. X-ray binaries such as Cygnus X-1 demonstrate intense emission consistent with such processes.

The distribution of the radiation emitted by X-ray binaries is in the form of a continuous black body spectrum. The black-body spectrum of an X-ray binary reveals a source temperature of about 10^7 K, which corresponds to the temperatures expected for matter falling into a black hole. The amount of energy released corresponds to the absorption of 10^-9 to 10^-8 solar mass per year, which matches the rate at which mass is being lost by the visible star.

That is not enough to prove that the X-ray emitting object is a black hole. A neutron star can generate a great flow of X-rays as well, by accelerating infalling matter to up to half the speed of light at impact. Conversion efficiencies are about 10% of the infalling mass, which is similar to that expected for a typical black hole.

In some cases, the hidden companion is clearly a neutron star. This is the case for pulsars, since they generate pulses from their hot spots. As a black hole has no surface, it cannot have a fixed hot spot. However, the lack of pulse activity does not necessarily prove the hidden object is a black hole.

The most significant hint that a hidden companion is a black hole is its mass. There is no known limit on the mass of a black hole. This is not the case for white dwarfs, which have a limit of 1.4 solar masses, and neutron stars, which have a limit of about 3 solar masses. This implies that any hidden companion in a binary system that is larger than 3 solar masses is a black hole.

Seven X-ray binaries have been found where the mass of the hidden companion is larger than three solar masses, with the measured mass of the hidden companions actually ranging from 4 to 12 solar masses.

Still, as mentioned, theory may be wrong, and we need to know more. The absolutely distinguishing feature of a black hole is its lack of a solid surface. All it has is an event horizon into which matter falls, never to be seen again.

One of the interesting implications of the lack of a solid surface is to consider what happens if hot plasma falls through a black hole's event horizon before the plasma can radiate away its energy. In this case, the energy simply vanishes, being manifested only as an increase in mass of the black hole. This process, known as "advection", can limit the energy conversion efficiency of a black hole.

In contrast, if hot plasma falls onto a neutron star, all its energy has to be radiated away, either from the plasma or from the surface of the neutron star. This means that if energy appears to be disappearing into a hidden companion, that companion is likely to be a black hole. Astronomers have been hunting for X-ray binaries with just such a characteristic.

Observations of some binary systems and galactic cores have strongly hinted that energy is disappearing without a trace in this way. Much work remains to be done, and though uncertainty remains, it is yet another piece of evidence that encourages astrophysicists to believe they are in fact on the right track.


As an interesting footnote to the story of black holes, the well-known British physicist Stephen Hawking has suggested that in the creation of the Universe there could have been regions where pressures and densities were so high that very small black holes, even with masses of far less than a kilogram, could have been created.

Hawking also suggested that such "miniholes" could actually "evaporate". Modern field theory proposes that the entire fabric of the Universe is filled with "virtual particle pairs", consisting of an antiparticle and a particle, that are spontaneously being created and then recombining so fast that they cannot be directly detected.

Hawking proposed that if such a virtual pair, such as a positron and an electron, were created near the event horizon of a black hole, one of the particles might disappear into the black hole and be lost forever, and the other would appear to have been emitted from the black hole.

Since energy conservation still remains an unviolated concept of physics, even quantum physics, the emitted particle has a certain amount of energy, and that energy can't simply appear out of nothing. Hawking's analysis showed that such a process would rob the black hole of energy to create the emitted particle.

For a large-scale black hole derived from stellar collapse, this process would have a negligible effect. As holes grow smaller and smaller, though, their rate of "evaporation" would increase. A minihole would exist for a certain time, leaking out particles at an ever increasing rate until it evaporated in a burst of gamma rays.

Hawking's miniholes remain an intriguiging speculation. Detecting large scale black holes is hard enough at present. Tracking down miniholes and the gamma ray bursts they emit when they evaporate is not practical for now.


This document is the first in a series on stars and stellar evolution. Eventually I hope to weld the series into a comprehensive document on the lives of stars.

Sources include :-
  1. "White Dwarfs: Fossil Stars", Steven D. Kawaler, SKY & TELESCOPE, August 1987, 132:135.
  2. "Taking The Pulse Of White Dwarfs", by Nather & Winget, SKY & TELESCOPE, April 1992, 374:378.
  3. "The Reluctant Father Of Black Holes", by Jeremy Bernstein, SCIENTIFIC AMERICAN, June 1996, 80:85
  4. "Unmasking Black Holes", by Jean-Pierre Lasota, SCIENTIFIC AMERICAN, May 1999, 40:47.
  5. "The Life Of A Neutron Star", by Joshua N. Winn, SKY & TELESCOPE, July 1999, 30:38.
Greg Goebel (gvgoebel@yahoo.com)

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