01 sep 99
greg goebel (firstname.lastname@example.org)
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
dwarfs, have been known for over a century. In recent decades, however,
research has shown that such fossils can be more remarkable objects, known
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
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
our own Sun, 25 times brighter, and is about nine light years away in the
constellation Canis Major.
- THE DISCOVERY OF WHITE DWARFS
- WHITE DWARFS AND ELECTRON DEGENERACY
- THE STRUCTURE AND EVOLUTION OF WHITE DWARFS
- WHITE DWARFS AND THE AGE OF THE GALAXY
- BEYOND WHITE DWARFS?
- NEUTRON STARS DISCOVERED
- CHARACTERISTICS OF NEUTRON STARS
- MILLISECOND PULSARS AND OTHER UNUSUAL NEUTRON STARS
- BLACK HOLES DISCOVERED?
- COMMENTS, SOURCES, AND REVISION HISTORY
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
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
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
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
by the rules of the physics Eddington had available to him.
Fortunately, another branch of physics that was evolving in parallel,
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
and determined how it could have such enormous densities.
While a star is performing fusion reactions in its core, the outward
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
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
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
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
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
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.
result is that white dwarfs cool off very slowly through most of their
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
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
of the white dwarf, about 200,000 times that of Earth, which left light
on the surface while heavier atoms sank. A DA white dwarf still retains
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
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
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 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
will evolve into a white dwarf in about 10,000 years, as the planetary
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
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
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
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
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
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
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
the age of the Universe itself.
The primary way of estimating the age of the Universe is through
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
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
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
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
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
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
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
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
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
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
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
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
One of the interesting questions they considered was a mass limit for
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
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
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
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
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
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
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
However, the radio bursts were over a broad range of frequencies, which
have made the emitter an inefficient artificial beacon, and before long
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
The sharpness of the radio pulses emitted by the pulsars suggested very
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
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
Another pulsar was found in a much closer supernova remnant in the
constellation Vela. The Vela supernova occurred a few thousand years ago
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
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
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
Fourth, the young neutron star has an extraordinarily intense magnetic
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
The intense magnetic field and the flow of charged particles accounts for
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
hot spots swing past like the searchlight beam on a lighthouse.
The pulse beams of young neutron stars, like the Crab Nebula or Vela
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
After about ten million years, the pulsar slows down and no longer has
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
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
sound exceeds that of light, which is ruled out by Einstein's theory of
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
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
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
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"
Detecting such a black hole was a difficult prospect. They would be
necessarily small, and could emit no detectable radiation by themselves.
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
is through matter falling into a black hole.
Another is the existence of binary star systems where a bright star is
mass to a hidden companion, with the lost mass generating intense energy
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
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,
the physics of black holes lie on the limits of physical theory, and
theoretical calculations can be surprisingly accurate, they have also in
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
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
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
The distribution of the radiation emitted by X-ray binaries is in the form
a continuous black body spectrum. The black-body spectrum of an X-ray
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
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
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
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
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
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
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
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 :-
- "White Dwarfs: Fossil Stars", Steven D. Kawaler, SKY & TELESCOPE, August
- "Taking The Pulse Of White Dwarfs", by Nather & Winget, SKY & TELESCOPE,
April 1992, 374:378.
- "The Reluctant Father Of Black Holes", by Jeremy Bernstein, SCIENTIFIC
AMERICAN, June 1996, 80:85
- "Unmasking Black Holes", by Jean-Pierre Lasota, SCIENTIFIC AMERICAN, May
- "The Life Of A Neutron Star", by Joshua N. Winn, SKY & TELESCOPE, July
Greg Goebel (email@example.com)
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