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Compact stars
In astronomy, the term compact star (sometimes compact object) is used to refer collectively to
white dwarfs, neutron stars, other exotic dense stars, and black holes. Most compact stars are at
the endpoint of stellar evolution and thus are called stellar remnants; the form of the remnant
depends primarily on the mass of the star when it formed. These objects are all small for their
mass. The term compact star is often used when the exact nature of the star is not known, but
evidence suggests that it is very massive and has a small radius, thus implying one of the abovementioned possibilities. A compact star which is not a black hole may be called a degenerate
star.
Compact stars as the endpoint of stellar evolution
Compact stars form the endpoint of stellar evolution. A star shines and thus loses energy. The
loss from the radiating surface is compensated by the production of energy from nuclear fusion
in the interior of the star. When a star has exhausted all its energy and undergoes stellar death,
the gas pressure of the hot interior can no longer support the weight of the star and the star
collapses to a denser state: a compact star.
Lifetime
Although compact stars may radiate, and thus cool off and lose energy, they do not depend on
high temperatures to maintain their pressure. Barring external perturbation or baryon decay, they
will persist virtually forever, although black holes are generally believed to finally evaporate
from Hawking radiation. Eventually, given enough time (when we enter the so-called degenerate
era of the universe), all stars will have evolved into dark, compact stars.
A somewhat wider class of compact objects is sometimes defined to contain, as well as compact
stars, smaller solid objects such as planets, asteroids, and comets. These compact objects are the
only objects in the universe that could exist at low temperatures. There is a remarkable variety of
stars and other clumps of matter, but all dense matter in the universe must eventually end in one
of only five classes of compact objects.
1. Planets
At low density (planets and the like) the object is held up by electromagnetic forces. These
forces constrain electrons to occupy orbitals around nuclei, which give rise to chemical bonds
and thus allow stiff objects such as rocks to exist. These objects are so stiff that they do not
compress very much when mass is added. Adding more (cold) mass therefore makes the object
larger: radius increases with mass.
Eventually a point is reached where the central pressure is so great that all matter is ionized so
that the electrons are stripped from the nuclei and move freely. No chemical bonds now exist to
hold up the object. This point is reached at the center of the planet Jupiter. Add more mass to
Jupiter and the increase of pressure is smaller than the increase of gravity, so the radius will
decrease with increasing mass. The object will shrink.
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A planet such as Jupiter has about the largest volume possible for a cold mass. Add mass to
Jupiter and the planet's volume, somewhat counter-intuitively, becomes smaller. The central
density now is large enough that the free electrons become degenerate. This term means that the
electrons have fallen into the lowest-energy states available. Since electrons are fermions, they
obey the Pauli Exclusion Principle, and no two electrons can occupy the same state. The
electrons thus occupy a wide band of low-energy states. Compressing the mass forces this band
to widen, creating the quantum-mechanical force of electron degeneracy pressure which now
holds the center of the planet apart. (The ions present contribute almost no force.)
Questions:
1. If gravity is acting to pull all a planets material into the core of the planet why do planets
not implode? That is, what keeps them held up in a spherical shape? What keeps you help
up in your shape?
2. Jupiter is a very large planet, if matter were added to Jupiter’s surface what would happen
to its size?
3. What is meant by electron degeneracy pressure here?
2. White dwarfs
The Eskimo Nebula is illuminated by the white dwarf at its center.
Main article: White dwarf
The stars called degenerate dwarfs or, more usually, white dwarfs
are made up mainly of degenerate matter—typically, carbon and
oxygen nuclei in a sea of degenerate electrons. White dwarfs arise
from the cores of main-sequence stars and are therefore very hot
when they are formed. As they cool they will redden and dim until
they eventually become dark black dwarfs. White dwarfs were
observed in the 19th century, but the extremely high densities and
pressures they contain were not explained until the 1920s.
The equation of state for degenerate matter is "soft", meaning that adding more mass will result
in a smaller object. Continuing to add mass to what is now a white dwarf, the object shrinks and
the central density becomes even larger, with higher degenerate-electron energies. The star's
radius has now shrunk to only a few thousand kilometers, and the mass is approaching the
theoretical upper limit of the mass of a white dwarf, the Chandrasekhar limit, about 1.44 times
the mass of the Sun.
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If we were to take matter from the center of our white dwarf and slowly start to compress it, we
would first see electrons forced to combine with nuclei, changing their protons to neutrons by
inverse beta decay. The equilibrium would shift towards heavier, more neutron-rich nuclei which
are not stable at everyday densities. As the density increases, these nuclei become still larger and
less well-bound. At a critical density of about 4·1014 kg/m³, called the neutron drip line, the
atomic nucleus would tend to fall apart into protons and neutrons. Eventually we would reach a
point where the matter is on the order of the density (~2·1017 kg/m³) of an atomic nucleus. At
this point the matter is chiefly free neutrons, with a small amount of protons and electrons.
Questions:
3. Describe the composition of a white dwarf star.
4. If you add matter to the surface of a white dwarf star what will happen to its size and
density?
5. What is the Chandrasekhar limit and what do you think will happen if the mass of a white
dwarf star passes the Chandrasekhar limit?
3. Neutron stars
The Crab Nebula is a supernova remnant containing the Crab Pulsar, a
neutron star.
Main article: Neutron star
In certain binary stars containing a white dwarf, mass is transferred
from the companion star onto the white dwarf, eventually pushing it
over the Chandrasekhar limit. Electrons react with protons to form
neutrons and thus no longer supply the necessary pressure to resist
gravity, causing the star to collapse. If the center of the star is
composed mostly of carbon and oxygen then such a gravitational collapse will ignite runaway
fusion of the carbon and oxygen, resulting in a Type Ia supernova which entirely blows apart the
star before the collapse can become irreversible. If the center is composed mostly of magnesium
or heavier elements, the collapse continues. As the density further increases, the remaining
electrons react with the protons to form more neutrons. The collapse continues until (at higher
density) the neutrons become degenerate. A new equilibrium is possible after the star shrinks by
three orders of magnitude, to a radius between 10 and 20 km. This is a neutron star.
Although the first neutron star was not observed until 1967 when the first radio pulsar was
discovered, neutron stars were proposed by Baade and Zwicky in 1933, only one year after the
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neutron was discovered in 1932. They realized that because neutron stars are so dense, the
collapse of an ordinary star to a neutron star would liberate a large amount of gravitational
potential energy, providing a possible explanation for supernovae. This is the explanation for
supernovae of types Ib, Ic, and II. Such supernovae occur when the iron core of a massive star
exceeds the Chandrasekhar limit and collapses to a neutron star.
Like electrons, neutrons are fermions. They therefore provide neutron degeneracy pressure to
support a neutron star against collapse. In addition, repulsive neutron-neutron interactions
provide additional pressure. Like the Chandrasekhar limit for white dwarfs, there is a limiting
mass for neutron stars: the Tolman-Oppenheimer-Volkoff limit (TOV limit), where these forces
are no longer sufficient to hold up the star. As the forces in dense hadronic matter are not well
understood, this limit is not known exactly but is thought to be between 2 and 3 times the mass
of the Sun. If more mass accretes onto a neutron star, eventually this mass limit will be reached.
What happens next is not completely clear.
Questions:
1. In very massive stars, nuclear fusion in the core can produce Iron. At this point in a stars life,
when the core is composed entirely of iron nuclei, really cool things can happen. Describe
what happens when the star has run out of material to fuse?
2. Just like white dwarfs have an upper limit on mass before it experiences a major change in
matter, what is the upper mass limit for neutron stars? List the name and quantity.
3. Make a prediction before you read further: What do you think will happen to a neutron star
if its mass surpasses the TOV limit?
4. Exotic stars Main article: Exotic star
An exotic star is a compact star composed of something other than electrons, protons, and
neutrons balanced against gravitational collapse by degeneracy pressure or other quantum
properties. These include strange stars (composed of strange matter) and the more speculative
preon stars (composed of preons).
Exotic stars are largely theoretical, but observations released by the Chandra X-Ray Observatory
on April 10, 2002 detected two candidate strange stars, designated RX J1856.5-3754 and 3C58,
which had previously been thought to be neutron stars. Based on the known laws of physics, the
former appeared much smaller and the latter much colder than they should, suggesting that they
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are composed of material denser than neutronium. However, these observations are met with
skepticism by researchers who say the results were not conclusive.
Quark stars and strange stars Main article: Quark star
It is possible that the neutrons will decompose into their component quarks. In this case, the star
will shrink further and become denser, but it may survive in this new state indefinitely if no extra
mass is added. It has become a very large nucleon. A star in this hypothetical state is called a
quark star or strange star. The pulsars RX J1856.5-3754 and 3C58 have been suggested as
possible quark stars.
Preon stars
A preon star is a proposed type of compact star made of preons, a group of hypothetical
subatomic particles. Preon stars would be expected to have huge densities, exceeding 1023
kilogram per cubic meter – intermediate between quark stars and black holes. Preon stars could
originate from supernova explosions or the big bang; however, current observations from particle
accelerators speak against the existence of preons.
Q stars
Q stars are hypothetical compact, heavier neutron stars with an exotic state of matter where
particle numbers are preserved. Q stars are also called "gray holes".
Electroweak stars Main article: Electroweak star
An electroweak star is a theoretical type of exotic star, whereby the gravitational collapse of the
star is prevented by radiation pressure resulting from electroweak burning, that is, the energy
released by conversion of quarks to leptons through the electroweak force. This process occurs in
a volume at the star's core approximately the size of an apple, containing about two Earth
masses.
Question:
1. Although exotic stars are still mostly hypothetical, what must be true about their volume and
density compared to neutron stars and why is this true?
5. Black holes
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A simulated black hole of ten solar masses, at a distance of
600km.
Main article: Stellar black hole
As more mass is accumulated, equilibrium against gravitational
collapse reaches its breaking point. The star's pressure is
insufficient to counterbalance gravity and a catastrophic
gravitational collapse occurs in milliseconds. The escape
velocity at the surface, already at least 1/3 light speed, quickly
reaches the velocity of light. No energy or matter can escape: a black hole has been created. All
light will be trapped within an event horizon, and so a black hole appears truly black, except for
the possibility of Hawking radiation. It is presumed that the collapse will continue.
In the classical theory of general relativity, a gravitational singularity will be created occupying
no more than a point. There may be a new halt of the catastrophic gravitational collapse at a size
comparable to the Planck length, but at these lengths there is no known theory of gravity to
predict what will happen. Adding any extra mass to the black hole will cause the radius of the
event horizon to increase linearly with the mass of the central singularity. This will induce
certain changes in the properties of the black hole, such as reducing the tidal stress near the event
horizon, and reducing the gravitational field strength at the horizon. However, there will not be
any further qualitative changes in the structure associated with any mass increase.
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