Download white dwarfs, neutron stars, black hole

INTRODUCTION
At the end of its evolution an ordinary star forms a compact stellar object. It may
be a white dwarf, a neutron star or a black hole. This text is an introduction to the
physics of white dwarfs and neutron stars, remnants left behind by ordinary stars after
they have ceased nuclear fusion.
These objects support themselves against gravitational collapse by physical
mechanisms other than the pressure of hot gas (the heat being generated by nuclear
fusion at the core). A white dwarf is stabilized ultimately by the “degeneracy
pressure” of electrons arising from the Exclusion Principle. A neutron star is
stabilized mainly by repulsive strong interactions between the neutrons out of which
it is (primarily) composed. In this thesis we concentrate on neutron stars, which
typically are assumed to be almost entirely composed of neutrons.
To emphasize that the matter inside them can be in the decanted state, we call
them compact stars. Their masses are at least of the order of the solar mass M = 1, 98
1030 kg and their radii of the order of 10km. It follows that the average density in
compact stars is at least of the order of that of the baryon number saturation density.
Compact stars are of special interest because they are the only places in nature where
cold nuclear matter can reach densities above that of a single nucleus. To understand
this and to introduce the underlying physical aspects, we will attest talk about them in
their own right.
The physics involved is extremely rich, involving gravitational physics (including
general relativity in the case of neutron stars), thermodynamics, quantum mechanics,
and nuclear and particle physics. The equilibrium structure of these objects is
naturally described by a set of coupled ordinary differential equations, which we
solved numerically with program Wolfram Mathematica 9. An overview of the
relevant computational techniques is also presented.
We used set of parameterizations that has been found to be a good description of
matter at nuclear densities to model static white dwarf and neutron stars and
compared resulting with observations, which published in the astrophysical journal
The results obtained in modelling structure of the not rotating neutron stars and a
white dwarf was applied to improve estimates of mass, radius and densities for star
objects.
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1 The life cycle of a star
1.1 The main - sequence stars
The structure of stars, their evolution from birth to death, and the remnants they
leave behind are central problems in astrophysics. The basics of star formation are
well described in a number of introductory astronomy texts, and the reader may wish
to consult one of these to “set the stage”.
Imagine an enormous cloud of gas and dust many light-years across. Gravity, as
it always does, tries to pull the materials together. A few grains of dust collect a few
more, then a few more, then more still. Eventually, enough gas and dust has been
collected into a giant ball that, at the center of the ball, the temperature (from all the
gas and dust bumping into each other under the great pressure of the surrounding
material) reaches 15 million degrees or so.
A wondrous event occurs, nuclear fusion begins and the ball of gas and dust
starts to glow. A new star has begun its life in our Universe. As the contraction of the
gas and dust progresses and the temperature reaches 15 million degrees or so, the
pressure at the center of the ball becomes enormous. The electrons are stripped off of
their parent atoms, creating plasma. The contraction continues and the nuclei in the
plasma start moving faster and faster.
Eventually, they approach each other so fast that they overcome the electrical
repulsion that exists between their protons. The nuclei crash into each other so hard
that they stick together, or fuse. In doing so, they give off a great deal of energy. This
energy from fusion pours out from the core, setting up an outward pressure in the gas
around it that balances the inward pull of gravity. When the released energy reaches
the outer layers of the ball of gas and dust, it moves off into space in the form of
electromagnetic radiation. The ball, now a star, begins to shine.
New stars come in a variety of sizes and colors. They range from blue to red,
from less than half the size of our Sun to over 20 times the Sun’s size. It all depends
on how much gas and dust is collected during the star’s formation. The color of the
star depends on the surface temperature of the star. And its temperature depends,
again, on how much gas and dust were accumulated during formation. The more
mass a star starts out with, the brighter and hotter it will be. For a star, everything
depends on its mass.
Throughout their lives, stars fight the inward pull of the force of gravity. It is
only the outward pressure created by the nuclear reactions pushing away from the
star's core that keeps the star “intact”. But these nuclear reactions require fuel, in
particular hydrogen. Eventually the supply of hydrogen runs out and the star begins
its demise.
After millions to billions of years, depending on their initial masses, stars run
out of their main fuel - hydrogen. Once the ready supply of hydrogen in the core is
gone, nuclear processes occurring there cease. Without the outward pressure
generated from these reactions to counteract the force of gravity, the outer layers of
the star begin to collapse inward toward the core. Just as during formation, when the
material contracts, the temperature and pressure 1 increase. This newly generated
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heat temporarily counteracts the force of gravity, and the outer layers of the star are
now pushed outward.
The star expands to larger than it ever was during its lifetime -- a few to about a
hundred times bigger. The star has become a red giant. What happens next in the life
of a star depends on its initial mass. Whether it was a “massive” star (some 5 or more
times the mass of our Sun) or whether it was a “low or medium mass” star (about 0.4
to 3.4 times the mass of our Sun), the next steps after the red giant phase are very,
very different.
The Fate of Sun-Sized Stars: Black Dwarfs Once a medium size star (such as
our Sun) has reached the red giant phase, its outer layers continue to expand, the core
contracts inward, and helium atoms in the core fuse together to form carbon. This
fusion releases energy and the star gets a temporary reprieve. However, in a Sunsized star, this process might only take a few minutes. The atomic structure of carbon
is too strong to be further compressed by the mass of the surrounding material. The
core is stabilized and the end is near. The star will now begin to shed its outer layers
as a diffuse cloud called a planetary nebula.
Eventually, only about 20% of the star’s initial mass remains and the star
spends the rest of its days cooling and shrinking until it is only a few thousand miles
in diameter. It has become a white dwarf. White dwarfs are stable because the inward
pull of gravity is balanced by the electrons in the core of the star repulsing each other.
With no fuel left to burn, the hot star radiates its remaining heat into the coldness of
space for many billions of years. In the end, it will just sit in space as a cold dark
mass sometimes referred to as a black dwarf.
Figure 1.1.1- The life cycle of a star
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The Fate of Massive Stars: Supernovae. Fate has something very different,
and very dramatic, in store for stars which are some 5 or more times as massive as
our Sun. After the outer layers of the star have swollen into a red supergiant (i.e., a
very big red giant), the core begins to yield to gravity and starts to shrink. As it
shrinks, it grows hotter and denser, and a new series of nuclear reactions begin to
occur, temporarily halting the collapse of the core.
However, when the core becomes essentially just iron, it has nothing left to
fuse (because of iron's nuclear structure, it does not permit its atoms to fuse into
heavier elements) and fusion ceases. In less than a second, the star begins the final
phase of its gravitational collapse. The core temperature rises to over 100 billion
degrees as the iron atoms are crushed together.
The repulsive force between the nuclei overcomes the force of gravity, and the
core recoils out from the heart of the star in an explosive shock wave. As the shock
encounters material in the star's outer layers, the material is heated, fusing to form
new elements and radioactive isotopes. In one of the most spectacular events in the
Universe, the shock propels the material away from the star in a tremendous
explosion called a supernova. The material spews off into interstellar space - perhaps
to collide with other cosmic debris and form new stars, perhaps to form planets and
moons, perhaps to act as the seeds for an infinite variety of living things.
Unlike in smaller stars, where the core becomes essentially all carbon and
stable, the intense pressure inside the supergiant causes the electrons to be forced
inside of (or combined with) the protons, forming neutrons. In fact, the whole core of
the star becomes nothing but a dense ball of neutrons. It is possible that this core will
remain intact after the supernova, and be called a neutron star. However, if the
original star was very massive (say 15 or more times the mass of our Sun), even the
neutrons will not be able to survive the core collapse and a black hole will form.
In the early 1900’s two astronomers, Ejnar Hertzsprung and Henry Norris
Russell, independently discovered a relationship between the luminosity of a star and
its temperature. The Hertzsprung-Russell (H-R) diagram is a plot of the luminosity
(or absolute magnitude) against temperature (or spectral class) for a group of stars.
The H-R diagram is one of the most powerful analytic tools available to astronomers.
It can be used to estimate many characteristics of stars, such as size and mass.
Spectral class or temperature is plotted along the horizontal axis from the
highest temperatures on the left to the coolest temperatures on the right. Absolute
magnitude is plotted along the vertical scale. Luminosity is the total amount of
energy emitted by a star each second. A logarithmic luminosity scale can also be used
for the vertical axis. If luminosity is measured relative to the Sun’s luminosity, the
scale, for stars in our galaxy, ranges approximately from 10−4 to 106 .
Almost 90% of observed stars lie along a band that stretches from the upper left
to the lower right on the H-R diagram. This band is called the main sequence. “Hot”
main sequence stars are “bright” (left top of the diagram) and “cool” main sequence
stars are “dim” (right bottom of the diagram). The photosphere (surface) temperatures
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of stars on the main sequence range from about 3,000 K to about 30,000 K, which is
a factor of 10. However, luminosities stretch over ten powers of ten (1010 ).
It is now understood that all stars on the main sequence generate energy by the
same mechanism, namely by fusing hydrogen into helium. The scattering of stars
along the band of the main sequence is a consequence of their different initial masses.
For main sequence stars, there is a simple relationship between luminosity and mass.
Stellar masses and luminosities increase from the lower right of the main sequence to
the upper left. From this relationship, the mass of a main sequence star can be
estimated by its position on the H-R diagram. Unfortunately, there is no such rule
between luminosity and mass for the approximately 10% of stars that are not on the
main sequence.
Giant Stars and White Dwarfs The upper right corner of the H-R diagram is
populated with cool but high-luminosity giant stars. These stars are more luminous
than main sequence stars of the same temperature. Since the luminosity of a star
depends on both the temperature and the size of a star, giant stars must be larger than
main sequence stars of the same temperature. Small hot stars that present low
luminosities in spite of their high temperatures, are called white dwarfs. White dwarfs
fall to the left of the main sequence on the H-R diagram. Masses vary widely in these
regions off the main sequence.
Stars that are not on the main sequence have different mechanisms for generating
energy. Giant stars fuse hydrogen in a shell around the core (rather than fuse
hydrogen in the core) or fuse elements higher than hydrogen, which produces more
power than the fusion of hydrogen in the stellar core. White dwarfs are the cores of
Sun-like stars that have lost their outer layers. They no longer generate energy, but
shine by radiating away energy stored in them from their previous stages.
Stars fuse lower elements into higher elements and thus, slowly change their
compositions. This process is called stellar evolution. The rate of stellar evolution
varies with the star’s mass. A more massive star evolves faster than a less massive
star because of its stronger gravity. Stronger gravity compresses the core more,
increasing temperatures and pressures, which in turn increases the rate of nuclear
fusion.
Stars with the mass of the Sun typically remain on the main sequence for 10
billion years. Stars with less mass than the Sun remain on the main sequence longer.
Although lower mass stars have less hydrogen in their cores than the Sun, they also
have lower core temperatures and pressures. Consequently fuse their hydrogen more
slowly. A 0.75 solar mass (0.75Msun) star remains on the main sequence for some 20
billion years, while a five solar mass (5Msun) star spends only about 70 million years
on the main sequence. Stars much higher along the main sequence than the Sun must
be younger than the Sun, else they would have used up the hydrogen in their cores by
now and would have moved off the main sequence.
The various stages of a star’s cycle occupy different points on the H-R diagram.
As the star passes through these stages, it follows a path on the H-R diagram. A plot
of a star’s evolution on a HR diagram is called its evolutionary track. Astronomers
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can use the position of a star on the H-R diagram to place constraints on its age. A
one solar mass (1Msun) protostar takes about 30 million years to reach the main
sequence.
If a protostar does not have sufficient mass to generate high enough
temperatures to initiate nuclear fusion, the protostar will become a brown dwarf or
“failed star”. That is, since the brown dwarf does not generate energy through nuclear
fusion, it is not a star. To become a star a mass between 0.08 Msun and 150 Msun is
needed. If the mass of a protostar is less than 0.08 Msun it will become a brown
dwarf. Brown dwarfs radiate energy due to their temperatures, and as they do so they
cool down.
A brown dwarf does not shrink because of the balance between electron
degeneracy pressure and gravity. Electron degeneracy pressure does not depend on
temperature and thus the size of the brown dwarf will stay the same as it cools down.
Electron degeneracy pressure is a quantum mechanical effect that comes into play at
high densities. Just as electrons in an atom can only have specific energy levels,
quantum mechanics places constraints on how closely together electrons can be
packed in a gas.
On the other hand, stars with masses 150 times that of the Sun (150Msun) tend
to develop such high temperatures that pressure from rapid fusion quickly tears them
apart. Thus, main sequence stars can have masses only between about 0.08 and 150
solar masses. Evolutionary Track of our Sun: The Sun is expected to be on the main
sequence for a total time of about 1010 years, until it has fused most of the hydrogen
in its core to helium. The Sun has been on the main sequence for about 4.6×109
years. So, in about 5 billion years the Sun will leave the main sequence stage and
enter the red giant stage. In the red giant stage the core of the Sun will begin to shrink
and its photosphere will begin to expand. The material remaining in the core is
helium which requires a higher temperature to burn. In this stage nuclear fusion will
not be occurring in the Sun’s core, but it will occur in a hydrogen shell around the
helium core. In the red giant stage the total luminosity of the Sun will increase. That
is, the energy rate production of the hydrogen burning shell will be higher than that of
the hydrogen burning core of the Sun as it is now. The radius of the photosphere will
increase in this stage. As a consequence of this, the surface temperature will decrease
(and the Sun will go towards a color red). When the core of the Sun becomes hot
enough to burn helium, the Sun will leave the red giant stage and enter the helium
burning stage. The instant when helium begins to burn is called the “Helium Flash”.
During the helium burning stage the Sun will be burning helium into carbon in its
core and, additionally, there will also be a hydrogen burning shell around the core.
Due to the pressure generated by the nuclear burning of helium, the core will begin to
expand and the total luminosity of the Sun is reduced with respect to when it was in
the red giant stage. The Sun will also begin to shrink in size as well as increase its
surface temperature. When the core of the Sun consumes all the helium fuel, it will
leave the helium burning stage, and enter the double burning shell stage. In this stage
the Sun will be left with an inert carbon core. The lack of nuclear reaction in the
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Sun’s core will result in a shrinking of the core due to gravity and a helium burning
shell will be formed around the carbon core. In turn a hydrogen burning shell will
continue around the helium burning shell, thus the name of this stage. The luminosity
of the Sun will begin to increase again in this stage, its photosphere will expand, and
it surface temperature will begin to decrease (see path from position 10 to 11 in
Figure 1.1.2). The Sun does not have sufficient mass to generate the temperature
necessary to burn carbon. When the carbon core of the star stops shrinking due to
electron degeneracy pressure, energy sources for the Sun will have been consumed,
and the Sun will begin to eject or “blow away” its outer layers.
In astronomy, the main sequence is a continuous and distinctive band of stars that
appears on plots of stellar color versus brightness. These color-magnitude plots are
known as Hertzsprung–Russell diagrams (Fig.1.1.2) after their co-developers, Ejnar
Hertzsprung and Henry Norris Russell. Stars on this band are known as mainsequence stars or "dwarf" stars.
After a star has formed, it generates thermal energy in the dense core region
through the nuclear fusion of hydrogen atoms into helium. During this stage of the
star's lifetime, it is located along the main sequence at a position determined
primarily by its mass, but also based upon its chemical composition and other factors.
All main-sequence stars are in hydrostatic equilibrium, where outward thermal
pressure from the hot core is balanced by the inward pressure of gravitational
collapse from the overlying layers. The strong dependence of the rate of energy
generation in the core on the temperature and pressure helps to sustain this balance.
Energy generated at the core makes its way to the surface and is radiated away at
the photosphere. The energy is carried by either radiation or convection, with the
latter occurring in regions with steeper temperature gradients, higher opacity or both.
Figure 1.1.2 - Hertzsprung–Russell diagram
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The main sequence is sometimes divided into upper and lower parts, based
on the dominant process that a star uses to generate energy. Stars below about 1.5
times the mass of the Sun (or 1.5 solar masses (M☉)) primarily fuse hydrogen atoms
together in a series of stages to form helium, a sequence called the proton–proton
chain. Above this mass, in the upper main sequence, the nuclear fusion process
mainly uses atoms of carbon, nitrogen and oxygen as intermediaries in the CNO
cycle that produces helium from hydrogen atoms. Main-sequence stars with more
than two solar masses undergo convection in their core regions, which acts to stir up
the newly created helium and maintain the proportion of fuel needed for fusion to
occur. Below this mass, stars have cores that are entirely radiative with convective
zones near the surface. With decreasing stellar mass, the proportion of the star
forming a convective envelope steadily increases, while main-sequence stars below
0.4 M☉ undergo convection throughout their mass. When core convection does not
occur, a helium-rich core develops surrounded by an outer layer of hydrogen.
1.2 Compact objects: white dwarfs, neutron stars, black hole
Compact objects are an important class of astronomical objects in current
research. Supermassive black holes play an important role in the understanding of the
formation of galaxies in the early Universe. Old white dwarfs are nowadays used to
calibrate the age of the Universe. Mergers of neutron stars and black holes are the
sources of intense gravitational waves which will be measured in the next ten years
by gravitational wave detectors.
The helium nuclei are harder to involve in fusion reactions than protons: they
have a greater electric charge and thus experience greater repulsion from other nuclei
in their vicinity. However, if the star is sufficiently massive, so that the inward
pressure of gravity is high enough, this barrier can be overcome and the helium made
to fuse into heavier nuclei, with additional energy release. And so, given a
sufficiently large star, it works its way up the periodic table, creating heavier and
heavier nuclei so long as the core pressure and temperature can rise high enough.
But at some point the nuclear reactions will cease. This can happen for a couple
of reasons, depending ultimately on the total mass of the star. First, the star may not
be big enough to continue driving fusion reactions past some point; in this case, a
non-burning “ash" of the last nucleus produced will build up in the core of the star.
The details of what happens next are complicated, but essentially the fusion shuts
down and the star is unable to produce the energy it needs to resist gravitational
collapse. It therefore collapses, and the question is whether some other force or
mechanism can intervene to halt this collapse.
A second possibility arises if the star is very large, large enough to drive the
fusion all the way to 56Fe. In this case nuclear physics intervenes, for further fusion
does not produce energy at all, but rather absorbs it. The effect is thus to act as a sort
of “fire extinguisher”, cooling the core and eventually shutting of further nuclear
reactions. The end result is the same as above: the star can no longer support itself
against gravitational collapse.
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At this stage the star is composed of a variety of nuclei, i.e. protons and neutrons,
as well as a number of electrons equal to the total number of protons. It is collapsing.
If there is not a non-thermal source of pressure that can stabilize it, it will collapse to
a very small size, becoming a black hole. Black holes are often described loosely as
being objects so massive that not even light can escape, but it is perhaps more
accurate to say that they warp space-time so severely in their vicinity that they create
a sort of «knot», in which there is simply no direction you (or a light ray) can travel
that takes you away from it.
This is the inevitable fate of stars that are sufficiently large, but for low- to midrange stars there are two other basic possibilities, again depending on the mass. If the
mass is not too large, then the “degeneracy pressure" of the electrons can stabilize it
against further collapse; the result is known as a white dwarf. This is an effect of the
Pauli Exclusion Principle, which states that no two electrons (or other fermions) can
be in the same quantum state. The result is that, roughly speaking, the electrons
cannot get too close to each other, and there is effectively a sort of pressure that
resists further compression of the electrons.
A white dwarf, also called a degenerate dwarf, is a stellar remnant composed
mostly of electron-degenerate matter. They are very dense; a white dwarf's mass is
comparable to that of the Sun, and its volume is comparable to that of the Earth. Its
faint luminosity comes from the emission of stored thermal energy. The nearest
known white dwarf is Sirius B, 8.6 light years away, the smaller component of the
Sirius binary star. There are currently thought to be eight white dwarfs among the
hundred star systems nearest the Sun. The unusual faintness of white dwarfs was first
recognized in 1910 by Henry Norris Russell, Edward Charles Pickering,
and Williamina Fleming.
White dwarfs are thought to be the final evolutionary state of all stars (including
our Sun) whose mass is not high enough to become a neutron—over 97% of the stars
in the Milky Way. After the hydrogen–fusing lifetime of a main-sequence star of low
or
medium
mass
ends,
it
will
expand
to
a red
giant which
fuses helium to carbon and oxygen in its core by the triple-alpha process. If a red
giant has insufficient mass to generate the core temperatures required to fuse carbon,
around 1 billion K, an inert mass of carbon and oxygen will build up at its center.
After shedding its outer layers to form a planetary nebula, it will leave behind this
core, which forms the remnant white dwarf. Usually, therefore, white dwarfs are
composed of carbon and oxygen. If the mass of the progenitor is between 8 and
10.5solar masses (M☉), the core temperature is sufficient to fuse carbon but not neon,
in which case an oxygen-neon–magnesium white dwarf may be formed. Also,
some helium white dwarfs appear to have been formed by mass loss in binary
systems.
The material in a white dwarf no longer undergoes fusion reactions, so the star
has no source of energy, nor is it supported by the heat generated by fusion
against gravitational collapse. It is supported only by electron degeneracy pressure,
causing it to be extremely dense. The physics of degeneracy yields a maximum mass
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for a non-rotating white dwarf, the Chandrasekhar limit—approximately 1.4 M☉—
beyond which it cannot be supported by electron degeneracy pressure. A carbonoxygen white dwarf that approaches this mass limit, typically by mass transfer from a
companion star, may explode as a Type Ia supernova via a process known as carbon
detonation.
A white dwarf is very hot when it is formed, but since it has no source of energy,
it will gradually radiate away its energy and cool. This means that its radiation, which
initially has a high color temperature, will lessen and redden with time. Over a very
long time, a white dwarf will cool to temperatures at which it will no longer emit
significant heat or light, and it will become a cold black dwarf .However, the length
of time it takes for a white dwarf to reach this state is calculated to be longer than the
current age of the universe, and since no white dwarf can be older than the age of the
universe, it is thought that no black dwarfs yet exist. The oldest white dwarfs still
radiate at temperatures of a few thousand kelvins.
Figure 1.2.1 - White dwarf
However, if the mass is sufficiently large then this electron degeneracy pressure
is unable to support the star and the collapse continues. Eventually the protons and
electrons are so close together that they undergo inverse beta decay, combining to
produce neutrons (and neutrinos, which quickly escape the star). The star becomes
composed almost entirely of neutrons. At this point the strong nuclear force can
perhaps stabilize the star, for there is ultimately a strong repulsive force between
neutrons this close together. If this occurs the result is known as a neutron star.
A neutron star is a type of stellar remnant that can result from the gravitational
collapse of a massive star after a supernova. Neutron stars are the densest and
smallest stars known to exist in the universe; with a radius of only about 12–13 km
(7 mi), they can have a mass of about two times that of the Sun.
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Neutron stars are composed almost entirely of neutrons, which are subatomic
particles without net electrical charge and with slightly larger mass than protons.
Neutron stars are very hot and are supported against further collapse by quantum
degeneracy pressure due to the phenomenon described by the Pauli exclusion
principle, which states that no two neutrons (or any other fermionic particles) can
occupy the same place and quantum state simultaneously.
A typical neutron star has a mass between ~1.4 and about 3 solar masses (M☉)
with a surface temperature of ~6×105 K. Neutron stars have overall densities
of 3.7×1017 to 5.9×1017 kg/m3 (2.6×1014 to 4.1×1014 times the density of the
Sun), which is comparable to the approximate density of an atomic
nucleus of 3×1017 kg/m3. The neutron star's density varies from below 1×109 kg/m3 in
the crust – increasing with depth – to above 6×1017 or 8×1017 kg/m3 deeper inside
(denser than an atomic nucleus). A normal-sized matchbox containing neutron star
material would have a mass of approximately 5 billion tonnes or ~1 km3 of Earth
rock.
In general, compact stars of less than 1.44 M☉ (the Chandrasekhar limit)
are white dwarfs while compact stars weighing between that and 3 M☉ (the Tolman–
Oppenheimer–Volkoff limit) should be neutron stars. The maximum observed mass
of neutron stars is about 2 M☉. Compact stars with more than 10 M☉ will overcome
the neutron degeneracy pressure and gravitational collapse will usually occur to
produce a black hole. The smallest observed mass of a black hole is about 5 M☉.
Between
these,
hypothetical
intermediate-mass
stars
such
as quark
stars and electroweak stars have been proposed, but none have been shown to exist.
The equations of state of matter at such high densities are not precisely known
because of the theoretical and empirical difficulties.
Some neutron stars rotate very rapidly (up to 716 times a second, or
approximately 43,000 revolutions per minute) and emit beams of electromagnetic
radiation as pulsars. Indeed, the discovery of pulsars in 1967 first suggested that
neutron stars exist.Gamma-ray bursts may be produced from rapidly rotating, highmass stars that collapse to form a neutron star, or from the merger of binary neutron
stars. There are thought to be on the order of 108 neutron stars in the galaxy, but they
can only be easily detected in certain instances, such as if they are a pulsar or part of
a binary system. Non-rotating and non-accreting neutron stars are virtually
undetectable; however, the Hubble Space Telescope has observed one thermally
radiating neutron star, called RX J185635-3754.
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