Information about Degenerate Matter
Degenerate matter is matter which has sufficiently high density that the dominant contribution to its pressure arises from the Pauli exclusion principle. The pressure maintained by a body of degenerate matter is called the degeneracy pressure, and arises because the Pauli principle forbids the constituent particles to occupy identical quantum states. Any attempt to force them close enough together that they are not clearly separated by position must place them in different energy levels. Therefore, reducing the volume requires forcing many of the particles into higher-energy quantum states. This requires additional compression force, and so is felt as a resisting pressure. The species of fermion are sometimes identified, so that we may speak of electron degeneracy pressure, neutron degeneracy pressure, and so forth.
Imagine that there is a plasma, and it is cooled and compressed repeatedly. Eventually, we will not be able to compress the plasma any further, because the Exclusion Principle states that two particles cannot be in the exact same place at the exact same time. When in this state, since there is no extra space for any particles, we can also say that a particle's location is extremely defined. Therefore, since (according to the Heisenberg Uncertainty Principle) uncertainty in momentum × uncertainty in space = Planck's Constant/4
, then we must say that their momentum is extremely uncertain since the molecules are located in a very confined space. Therefore, even though the plasma is cold, the molecules must be moving very fast on average. This leads to the conclusion that if you want to compress an object into a very small space, you must use tremendous force to control its particles' momentum.
Unlike a classical ideal gas, whose pressure is proportional to its temperature (
, where 
is pressure, 
is the volume, 
is the number of particles (typically atoms or molecules), 
is Boltzmann's constant, and 
is temperature), the pressure exerted by degenerate matter depends only weakly on its temperature. In particular, the pressure remains nonzero even at absolute zero temperature. At relatively low densities, the pressure of a fully degenerate gas is given by 
, where 
depends on the properties of the particles making up the gas. At very high densities, where most of the particles are forced into quantum states with relativistic energies, the pressure is given by 
, where 
again depends on the properties of the particles making up the gas.
Degenerate matter still has normal thermal pressure, but at high densities the degeneracy pressure dominates. Thus, increasing the temperature of degenerate matter has a minor effect on total pressure until the temperature rises so high that thermal pressure again dominates total pressure.
Exotic examples of degenerate matter include neutronium, strange matter, metallic hydrogen and white dwarf matter. Degeneracy pressure contributes to the pressure of conventional solids, but these are not usually considered to be degenerate matter as a significant contribution to their pressure is provided by the interplay between the electrical repulsion of atomic nuclei and the screening of nuclei from each other by electrons allocated among the quantum states determined by the nuclear electrical potentials. In metals it is useful to treat the conduction electrons alone as a degenerate, free electron gas while the majority of the electrons are regarded as occupying bound quantum states. This contrasts with the case of the degenerate matter that forms the body of a white dwarf where all the electrons would be treated as occupying free particle momentum states.
A fermion gas in which all the energy states below a critical value, designated Fermi energy, are filled is called a fully degenerate fermion gas. The electron gas in ordinary metals and in the interior of white dwarf stars constitute two examples of a degenerate electron gas. Most stars are supported against their own gravitation by normal gas pressure. White dwarf stars are supported by the degeneracy pressure of the electron gas in their interior. For white dwarfs the degenerate particles are the electrons while for neutron stars the degenerate particles are neutrons.
At the end of a star's life, gravity has an enormous grip on the star's core, and compresses it to where it can go no further because of degeneracy pressure. However, as the molecules' average speed approaches (within quantum uncertainty) the speed of light to make up for gravity, then degeneracy pressure can do no more, because nothing can move faster than the speed of light. If degeneracy pressure fails in this way, then the atoms crush into atomic nuclei in a degenerate electron gas, and if degeneracy pressure fails again, then the electrons will crush into the nuclei and combine with protons to become neutrons.
Under high densities the matter becomes a degenerate gas when the electrons are all stripped from their parent atoms. In the core of a star once hydrogen burning in nuclear fusion reactions stops, it becomes a collection of positively charged ions, largely helium and carbon nuclei, floating in a sea of electrons which have been stripped from the nuclei. Degenerate gas is an almost perfect conductor of heat and does not obey the ordinary gas laws. White dwarfs are luminous not because they are generating any energy but rather because they have trapped a large amount of heat. Normal gas exerts higher pressure when it is heated and expands, but the pressure in a degenerate gas does not depend on the temperature. When gas become super-compressed, particles position right up against each other to produce degenerate gas that behaves more like a solid. In degenerate gases the kinetic energies of electrons are quite high and the rate of collision between electrons and other particles is quite low, therefore degenerate electrons can travel great distances at velocities that approach the speed of light. Instead of temperature, the pressure in a degenerate gas depends only on the speed of the degenerate particles; however, adding heat does not increase the speed. Pressure is only increased by the mass of the particles which increases the gravitational force pulling the particles closer together. Therefore, the phenomenon is opposite that normally found in matter where if the mass of the matter is increased, the object becomes bigger. In degenerate gas, when the mass is increased, the pressure is increased, and the particles become spaced closer together, so the object becomes smaller. Degenerate gas can be compressed to very high densities, typical values being in the range of 107 grams per cubic centimetre.
There is an upper limit to the mass of an electron-degenerate object, the Chandrasekhar limit, beyond which electron degeneracy pressure cannot support the object against collapse. The limit is approximately 1.44 solar masses for objects with compositions similar to the sun. The mass cutoff changes with the chemical composition of the object, as this affects the ratio of mass to number of electrons present. Celestial objects below this limit are white dwarf stars, formed by the collapse of the cores of stars which run out of fuel. During collapse, an electron-degenerate gas forms in the core, providing sufficient degeneracy pressure as it is compressed to resist further collapse. Above this mass limit, a neutron star (supported by neutron degeneracy pressure) or a black hole may be formed instead.
Neutrons in a degenerate neutron gas are spaced much more closely than electrons in an electron-degenerate gas, because the more massive neutron has a much shorter wavelength at a given energy. In the case of neutron stars and white dwarf stars, this is compounded by the fact that the pressures within neutron stars are much higher than those in white dwarfs. The pressure increase is caused by the fact that the compactness of neutron stars causes gravitational forces to be much higher than in a less compact body with similar mass, resulting in a star on the order of a thousand times smaller than a white dwarf.
There is an upper limit to the mass of a neutron-degenerate object, the Tolman-Oppenheimer-Volkoff limit, which is analogous to the Chandrasekhar limit for electron-degenerate objects. The precise limit is unknown, as it depends on the equations of state of nuclear matter, for which a highly accurate model is not yet available. Above this limit, a neutron star may collapse into a black hole, or into other, denser forms of degenerate matter (such as quark matter) if these forms exist and have suitable properties (mainly related to degree of compressibility, or "stiffness", described by the equations of state).
Quark-degenerate matter may occur in the cores of neutron stars, depending on the equations of state of neutron-degenerate matter. It may also occur in hypothetical quark stars, formed by the collapse of objects above the Tolman-Oppenheimer-Volkoff mass limit for neutron-degenerate objects. Whether quark-degenerate matter forms at all in these situations depends on the equations of state of both neutron-degenerate matter and quark-degenerate matter, both of which are poorly known.
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Imagine that there is a plasma, and it is cooled and compressed repeatedly. Eventually, we will not be able to compress the plasma any further, because the Exclusion Principle states that two particles cannot be in the exact same place at the exact same time. When in this state, since there is no extra space for any particles, we can also say that a particle's location is extremely defined. Therefore, since (according to the Heisenberg Uncertainty Principle) uncertainty in momentum × uncertainty in space = Planck's Constant/4
, then we must say that their momentum is extremely uncertain since the molecules are located in a very confined space. Therefore, even though the plasma is cold, the molecules must be moving very fast on average. This leads to the conclusion that if you want to compress an object into a very small space, you must use tremendous force to control its particles' momentum.
Unlike a classical ideal gas, whose pressure is proportional to its temperature (
, where is pressure, is the volume, is the number of particles (typically atoms or molecules), is Boltzmann's constant, and is temperature), the pressure exerted by degenerate matter depends only weakly on its temperature. In particular, the pressure remains nonzero even at absolute zero temperature. At relatively low densities, the pressure of a fully degenerate gas is given by , where depends on the properties of the particles making up the gas. At very high densities, where most of the particles are forced into quantum states with relativistic energies, the pressure is given by , where again depends on the properties of the particles making up the gas.
Degenerate matter still has normal thermal pressure, but at high densities the degeneracy pressure dominates. Thus, increasing the temperature of degenerate matter has a minor effect on total pressure until the temperature rises so high that thermal pressure again dominates total pressure.
Exotic examples of degenerate matter include neutronium, strange matter, metallic hydrogen and white dwarf matter. Degeneracy pressure contributes to the pressure of conventional solids, but these are not usually considered to be degenerate matter as a significant contribution to their pressure is provided by the interplay between the electrical repulsion of atomic nuclei and the screening of nuclei from each other by electrons allocated among the quantum states determined by the nuclear electrical potentials. In metals it is useful to treat the conduction electrons alone as a degenerate, free electron gas while the majority of the electrons are regarded as occupying bound quantum states. This contrasts with the case of the degenerate matter that forms the body of a white dwarf where all the electrons would be treated as occupying free particle momentum states.
Degenerate gases
Degenerate gases are gases composed of fermions that have a particular configuration which usually forms at high densities. Fermions are subatomic particles with half-integer spin. Their behaviour is regulated by a set of quantum mechanical rules called the Fermi-Dirac statistics. One particular rule is the Pauli exclusion principle that states that there can be only one fermion occupying each quantum state which also applies to electrons that are not bound to a nucleus but merely confined to a fixed volume, such as the deep interior of a star. Such particles as electrons, protons, neutrons, and neutrinos are all fermions and obey Fermi-Dirac statistics.A fermion gas in which all the energy states below a critical value, designated Fermi energy, are filled is called a fully degenerate fermion gas. The electron gas in ordinary metals and in the interior of white dwarf stars constitute two examples of a degenerate electron gas. Most stars are supported against their own gravitation by normal gas pressure. White dwarf stars are supported by the degeneracy pressure of the electron gas in their interior. For white dwarfs the degenerate particles are the electrons while for neutron stars the degenerate particles are neutrons.
At the end of a star's life, gravity has an enormous grip on the star's core, and compresses it to where it can go no further because of degeneracy pressure. However, as the molecules' average speed approaches (within quantum uncertainty) the speed of light to make up for gravity, then degeneracy pressure can do no more, because nothing can move faster than the speed of light. If degeneracy pressure fails in this way, then the atoms crush into atomic nuclei in a degenerate electron gas, and if degeneracy pressure fails again, then the electrons will crush into the nuclei and combine with protons to become neutrons.
Electron degeneracy
In ordinary gas, most of the energy levels called n-spheres if only certain discrete energy states available to electrons are unfilled and the electrons are free to move about. As particle density is increased in a fixed volume, electrons progressively fill the lower energy states and additional electrons are forced to occupy states of higher energy. Therefore, degenerate gases strongly resist further compression because the electrons cannot move to lower energy levels which are already filled due to the Pauli Exclusion Principle. The degenerate electrons are locked into place because all of the lower energy shells are filled up so they no longer move freely as in a normal gas. Even though thermal energy may be extracted from the gas, it still may not cool down, since electrons cannot give up energy by moving to a lower energy state. This increases the pressure of the fermion gas termed degeneracy pressure. In a degenerate gas, the average pressure is high enough to keep material from being compressed by gravity.Under high densities the matter becomes a degenerate gas when the electrons are all stripped from their parent atoms. In the core of a star once hydrogen burning in nuclear fusion reactions stops, it becomes a collection of positively charged ions, largely helium and carbon nuclei, floating in a sea of electrons which have been stripped from the nuclei. Degenerate gas is an almost perfect conductor of heat and does not obey the ordinary gas laws. White dwarfs are luminous not because they are generating any energy but rather because they have trapped a large amount of heat. Normal gas exerts higher pressure when it is heated and expands, but the pressure in a degenerate gas does not depend on the temperature. When gas become super-compressed, particles position right up against each other to produce degenerate gas that behaves more like a solid. In degenerate gases the kinetic energies of electrons are quite high and the rate of collision between electrons and other particles is quite low, therefore degenerate electrons can travel great distances at velocities that approach the speed of light. Instead of temperature, the pressure in a degenerate gas depends only on the speed of the degenerate particles; however, adding heat does not increase the speed. Pressure is only increased by the mass of the particles which increases the gravitational force pulling the particles closer together. Therefore, the phenomenon is opposite that normally found in matter where if the mass of the matter is increased, the object becomes bigger. In degenerate gas, when the mass is increased, the pressure is increased, and the particles become spaced closer together, so the object becomes smaller. Degenerate gas can be compressed to very high densities, typical values being in the range of 107 grams per cubic centimetre.
There is an upper limit to the mass of an electron-degenerate object, the Chandrasekhar limit, beyond which electron degeneracy pressure cannot support the object against collapse. The limit is approximately 1.44 solar masses for objects with compositions similar to the sun. The mass cutoff changes with the chemical composition of the object, as this affects the ratio of mass to number of electrons present. Celestial objects below this limit are white dwarf stars, formed by the collapse of the cores of stars which run out of fuel. During collapse, an electron-degenerate gas forms in the core, providing sufficient degeneracy pressure as it is compressed to resist further collapse. Above this mass limit, a neutron star (supported by neutron degeneracy pressure) or a black hole may be formed instead.
Proton degeneracy
Sufficiently dense matter containing protons experiences proton degeneracy pressure, in a manner similar to the electron degeneracy pressure in electron-degenerate matter: protons confined to a sufficiently small volume have a maximum momentum due to the Heisenberg uncertainty principle. Because protons are much more massive than electrons, the same minimum momentum represents a much smaller velocity for protons than for electrons. As a result, in matter with approximately equal numbers of protons and electrons, proton degeneracy pressure is much smaller than electron degeneracy pressure, and proton degeneracy is usually modelled as a correction to the equations of state of electron-degenerate matter.Neutron degeneracy
Neutron degeneracy is analogous to electron degeneracy and is demonstrated in neutron stars, which are supported by the pressure from a degenerate neutron gas. This happens when a stellar core above 1.44 solar masses (the Chandrasekhar limit) collapses and is not halted by the degenerate electrons. As the star collapses, the Fermi energy of the electrons increases to the point where it is energetically favorable for them to combine with protons to produce neutrons (via inverse beta decay, also termed "neutralization" and electron capture). The result of this collapse is an extremely compact star composed of nuclear matter, which is dominantly a degenerate neutron gas, sometimes called neutronium, with a small admixture of degenerate proton and electron gases.Neutrons in a degenerate neutron gas are spaced much more closely than electrons in an electron-degenerate gas, because the more massive neutron has a much shorter wavelength at a given energy. In the case of neutron stars and white dwarf stars, this is compounded by the fact that the pressures within neutron stars are much higher than those in white dwarfs. The pressure increase is caused by the fact that the compactness of neutron stars causes gravitational forces to be much higher than in a less compact body with similar mass, resulting in a star on the order of a thousand times smaller than a white dwarf.
There is an upper limit to the mass of a neutron-degenerate object, the Tolman-Oppenheimer-Volkoff limit, which is analogous to the Chandrasekhar limit for electron-degenerate objects. The precise limit is unknown, as it depends on the equations of state of nuclear matter, for which a highly accurate model is not yet available. Above this limit, a neutron star may collapse into a black hole, or into other, denser forms of degenerate matter (such as quark matter) if these forms exist and have suitable properties (mainly related to degree of compressibility, or "stiffness", described by the equations of state).
Quark degeneracy
At densities greater than those supported by neutron degeneracy, quark matter is expected to occur. Several variations of this have been proposed that represent quark-degenerate states. Strange matter is a degenerate gas of quarks that is often assumed to contain strange quarks in addition to the usual up and down quarks. Color superconductor materials are degenerate gases of quarks in which quarks pair up in a manner similar to Cooper pairing in electrical superconductors. The equations of state for the various proposed forms of quark-degenerate matter vary widely, and are usually also poorly defined, due to the difficulty modeling strong force interactions.Quark-degenerate matter may occur in the cores of neutron stars, depending on the equations of state of neutron-degenerate matter. It may also occur in hypothetical quark stars, formed by the collapse of objects above the Tolman-Oppenheimer-Volkoff mass limit for neutron-degenerate objects. Whether quark-degenerate matter forms at all in these situations depends on the equations of state of both neutron-degenerate matter and quark-degenerate matter, both of which are poorly known.
Speculative types of degenerate matter
Preon degeneracy
Preons are subatomic particles proposed to be the constituents of quarks, which become composite particles in preon-based models. If preons exist, preon-degenerate matter might occur at densities greater than that which can be supported by quark-degenerate matter. The properties of preon-degenerate matter depend very strongly on the model chosen to describe preons, and the existence of preons is not assumed by the majority of the scientific community, due to conflicts between the preon models originally proposed and experimental data from particle accelerators.See also
- Compact star
- White dwarf
- Neutron star - neutronium
- Quark star - QCD matter
- Preon star - preon
- Pauli exclusion principle
- Uncertainty principle
External links
States of Matter (list) |
|---|
| Solid • Liquid • Gas • Plasma • Supercritical fluid • Superfluid • Supersolid • Degenerate matter • Quark-gluon plasma • Fermionic condensate • Bose–Einstein condensate • Strange matter • Melting point • Boiling point • Triple point • Critical point • Equation of state • Cooling curve |
matter is commonly defined as the substance of which physical objects are composed, not counting the contribution of various energy or force-fields, which are not usually considered to be matter per se (though they may contribute to the mass of objects).
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In physics, density is mass m per unit volume V—how heavy something is compared to its size. A small, heavy object, such as a rock or a lump of lead, is denser than a lighter object of the same size or a larger object of the same weight, such as pieces of
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Pressure (symbol: p) is the force per unit area applied on a surface in a direction perpendicular to that surface.
Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.
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Gauge pressure is the pressure relative to the local atmospheric or ambient pressure.
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The Pauli exclusion principle is a quantum mechanical principle formulated by Wolfgang Pauli in 1925. This principle is significant, because it explains why matter occupies space exclusively for itself and does not allow other material objects to pass through it, while at the same
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In particle physics, fermions are particles with half-integer spin, such as protons and electrons. They are named after Enrico Fermi. In the Standard Model there are two types of elementary fermions: quarks and leptons.
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Electron degeneracy pressure is a force caused by the Pauli exclusion principle, which states that two fermions cannot occupy the same quantum state at the same time. This force often sets a limit to how much matter can be squeezed together.
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Neutron
The quark structure of the neutron.
Composition: one up, two down
Family: Fermion
Group: Quark
Interaction: Gravity, Electromagnetic, Weak, Strong
Antiparticle: Antineutron
Discovered: James Chadwick[1]
Symbol: n
Mass: 1.
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The quark structure of the neutron.
Composition: one up, two down
Family: Fermion
Group: Quark
Interaction: Gravity, Electromagnetic, Weak, Strong
Antiparticle: Antineutron
Discovered: James Chadwick[1]
Symbol: n
Mass: 1.
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plasma is typically an ionized gas. Plasma is considered to be a distinct state of matter, apart from gases, because of its unique properties. "Ionized" refers to presence of one or more free electrons, which are not bound to an atom or molecule.
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Heisenberg uncertainty principle, or HUP, gives a lower bound on the product of the standard deviations of position and momentum for a system, implying that it is impossible to have a particle that has an arbitrarily well-defined position and momentum simultaneously.
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Gas is one of the four major states of matter, consisting of freely moving atoms or molecules without a definite shape. Compared to the solid and liquid states of matter a gas has lower density and a lower viscosity.
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The Boltzmann constant (k or kB) is the physical constant relating temperature to energy.
It is named after the Austrian physicist Ludwig Boltzmann, who made important contributions to the theory of statistical mechanics, in which this
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It is named after the Austrian physicist Ludwig Boltzmann, who made important contributions to the theory of statistical mechanics, in which this
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Neutronium is a term originally used in science fiction and in popular literature to refer to an extremely dense phase of matter composed primarily of neutrons; historically, the word was coined by scientist Andreas von Antropoff in 1926 (scil.
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For the physics concept, see Strange matter.
Strange Matter is a children's book series created by Marty M. Engle and Johnny Ray Barnes Jr. The series takes place in the fictional town of Fairfield.
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Strange Matter is a children's book series created by Marty M. Engle and Johnny Ray Barnes Jr. The series takes place in the fictional town of Fairfield.
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Metallic hydrogen results when hydrogen is sufficiently compressed and undergoes a phase change; it is an example of degenerate matter. It consists of a crystal lattice of atomic nuclei (namely, protons), with a spacing which is significantly smaller than a Bohr radius.
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white dwarf, also called a degenerate dwarf, is a small star composed mostly of electron-degenerate matter. As white dwarfs have mass comparable to the Sun's and their volume is comparable to the Earth's, they are very dense.
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A solid object is in the states of matter characterized by resistance to deformation and changes of volume. At the microscopic scale, a solid has these properties :
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- The atoms or molecules that comprise the solid are packed closely together.
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The nucleus of an atom is the very small dense region of an atom, in its center consisting of nucleons (protons and neutrons). The size (diameter) of the nucleus is in the range of 1.
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Potential energy can be thought of as energy stored within a physical system. This energy can be released or converted into other forms of energy, including kinetic energy.
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The Macro Expansion Template Attribute Language complements TAL, providing macros which allow the reuse of code across template files. Both were created for Zope but are used in other Python projects as well.
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In science and engineering, conductors, such as copper or aluminum, are materials with atoms have loosely held valence electrons. See electrical conduction.
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Conductors in context
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In particle physics, fermions are particles with half-integer spin, such as protons and electrons. They are named after Enrico Fermi. In the Standard Model there are two types of elementary fermions: quarks and leptons.
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In atomic physics, the spin quantum number is a quantum number that parametrizes the intrinsic angular momentum (or spin angular momentum, or simply spin) of a given particle.
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The Pauli exclusion principle is a quantum mechanical principle formulated by Wolfgang Pauli in 1925. This principle is significant, because it explains why matter occupies space exclusively for itself and does not allow other material objects to pass through it, while at the same
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white dwarf, also called a degenerate dwarf, is a small star composed mostly of electron-degenerate matter. As white dwarfs have mass comparable to the Sun's and their volume is comparable to the Earth's, they are very dense.
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The nucleus of an atom is the very small dense region of an atom, in its center consisting of nucleons (protons and neutrons). The size (diameter) of the nucleus is in the range of 1.
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In atomic physics, the principal quantum number symbolized as n is the first of a set of quantum numbers (which includes: the principal quantum number, the azimuthal quantum number, the magnetic quantum number, and the spin quantum number) of an atomic orbital.
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nuclear fusion is the process by which multiple atomic particles join together to form a heavier nucleus. It is accompanied by the release or absorption of energy. Iron and nickel nuclei have the largest binding energies per nucleon of all nuclei and therefore are the most stable.
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ion is an atom or molecule which has lost or gained one or more electrons, making it positively or negatively charged. A negatively charged ion, which has more electrons in its electron shells than it has protons in its nuclei, is known as an anion
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kinetic energy of an object is the extra energy which it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its current velocity.
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