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Tolman-Oppenheimer-Volkoff limit
 
 
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The Tolman-Oppenheimer-Volkoff (TOV) limit is an upper bound to the mass of stars composed of neutron-degenerate matter
Degenerate matter

Degenerate matter is matter which has such very high density that the dominant contribution to its pressure rises from the Pauli exclusion principle....
 (neutron star
Neutron star

A neutron star is a type of compact star that can result from the gravitational collapse of a massive star during a Type II supernova, Type Ib and Ic supernovae supernova event....
s). It is analogous to the Chandrasekhar limit
Chandrasekhar limit

The Chandrasekhar limit limits the mass of bodies made from electron-degenerate matter, a dense form of matter which consists of atomic nucleus immersed in a gas of electrons....
 for white dwarf
White dwarf

A white dwarf, also called a degenerate dwarf, is a small star composed mostly of electron-degenerate matter. Because a white dwarf's mass is comparable to that of the Sun and its volume is comparable to that of the Earth, it is very density....
 stars.

The limit was computed by J. Robert Oppenheimer and George Michael Volkoff in 1939, using work of Richard Chace Tolman. Oppenheimer and Volkoff assumed that the neutrons in a neutron star formed a cold, degenerate Fermi gas
Fermi gas

A Fermi gas, or Free electron gas, is a collection of non-interacting fermions. It is the quantum mechanics version of an ideal gas, for the case of fermionic particles....
. This leads to a limiting mass of approximately 0.7 solar mass
Solar mass

The solar mass is a standard way to express mass in astronomy, used to describe the masses of other stars and galaxy. It is equal to the mass of the Sun, about two Names of large numbers kilograms or about 332,950 times the mass of the Earth, or 1,048 times the mass of Jupiter....
es., Modern estimates range from approximately 1.5 to 3.0 solar masses.






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The Tolman-Oppenheimer-Volkoff (TOV) limit is an upper bound to the mass of stars composed of neutron-degenerate matter
Degenerate matter

Degenerate matter is matter which has such very high density that the dominant contribution to its pressure rises from the Pauli exclusion principle....
 (neutron star
Neutron star

A neutron star is a type of compact star that can result from the gravitational collapse of a massive star during a Type II supernova, Type Ib and Ic supernovae supernova event....
s). It is analogous to the Chandrasekhar limit
Chandrasekhar limit

The Chandrasekhar limit limits the mass of bodies made from electron-degenerate matter, a dense form of matter which consists of atomic nucleus immersed in a gas of electrons....
 for white dwarf
White dwarf

A white dwarf, also called a degenerate dwarf, is a small star composed mostly of electron-degenerate matter. Because a white dwarf's mass is comparable to that of the Sun and its volume is comparable to that of the Earth, it is very density....
 stars.

The limit was computed by J. Robert Oppenheimer and George Michael Volkoff in 1939, using work of Richard Chace Tolman. Oppenheimer and Volkoff assumed that the neutrons in a neutron star formed a cold, degenerate Fermi gas
Fermi gas

A Fermi gas, or Free electron gas, is a collection of non-interacting fermions. It is the quantum mechanics version of an ideal gas, for the case of fermionic particles....
. This leads to a limiting mass of approximately 0.7 solar mass
Solar mass

The solar mass is a standard way to express mass in astronomy, used to describe the masses of other stars and galaxy. It is equal to the mass of the Sun, about two Names of large numbers kilograms or about 332,950 times the mass of the Earth, or 1,048 times the mass of Jupiter....
es., Modern estimates range from approximately 1.5 to 3.0 solar masses. The uncertainty in the value reflects the fact that the equations of state for extremely dense matter
QCD matter

Quark matter or QCD matter refers to any of a number of theorized phase of matter whose degrees of freedom include quarks and gluons. These theoretical phases would occur at extremely high temperatures and densities, billions of times higher than can be produced in equilibrium in laboratories....
 are not well-known.

In a neutron star lighter than the limit, the weight of the star is supported by short-range repulsive neutron-neutron interactions mediated by the strong force and also by the quantum degeneracy pressure of neutrons. If a neutron star is heavier than the limit, it will collapse to some denser form. It could form a black hole
Black hole

In general relativity, a black hole is a region of space in which the gravitational field is so powerful that nothing, including electromagnetic radiation , can escape its pull after having fallen past its event horizon....
, or change composition and be supported in some other way (for example, by quark degeneracy pressure
Degenerate matter

Degenerate matter is matter which has such very high density that the dominant contribution to its pressure rises from the Pauli exclusion principle....
 if it becomes a quark star
Quark star

A quark star or strange star is a hypothetical type of exotic star composed of quark matter, or strange matter. These are ultra-dense Phase s of degenerate matter theorized to form inside particularly massive neutron stars....
). Because the properties of hypothetical more exotic forms of degenerate matter
Degenerate matter

Degenerate matter is matter which has such very high density that the dominant contribution to its pressure rises from the Pauli exclusion principle....
 are even more poorly known than those of neutron-degenerate matter, most astrophysicists assume, in the absence of evidence to the contrary, that a neutron star above the limit collapses directly into a black hole.

A black hole formed by the collapse of an individual star
Stellar black hole

A stellar black hole is a black hole formed by the gravitational collapse of a massive star at the end of its lifetime. The process is observed as a supernova explosion or as a gamma ray burst....
 must have mass exceeding the Tolman-Oppenheimer-Volkoff limit. Theory predicts that because of mass loss during stellar evolution
Stellar evolution

Stellar evolution is the process by which a star undergoes a sequence of radical changes during its lifetime. Depending on the mass of the star, this lifetime ranges from only few millions of years to trillions of years , considerably more than the age of the universe....
, a black hole formed from an isolated star of solar metallicity
Metallicity

In astronomy and physical cosmology, the metallicity of an object is the proportion of its matter made up of chemical elements other than hydrogen and helium....
 can have mass no more than approximately 10 solar mass
Solar mass

The solar mass is a standard way to express mass in astronomy, used to describe the masses of other stars and galaxy. It is equal to the mass of the Sun, about two Names of large numbers kilograms or about 332,950 times the mass of the Earth, or 1,048 times the mass of Jupiter....
es., Figure 21. Observationally, because of their large mass, relative faintness, and X-ray spectra, a number of massive objects in X-ray binaries are thought to be stellar black holes. These black hole candidates are estimated to have masses between 3 and 20 solar mass
Solar mass

The solar mass is a standard way to express mass in astronomy, used to describe the masses of other stars and galaxy. It is equal to the mass of the Sun, about two Names of large numbers kilograms or about 332,950 times the mass of the Earth, or 1,048 times the mass of Jupiter....
es.

See also

  • Tolman-Oppenheimer-Volkoff equation
    Tolman-Oppenheimer-Volkoff equation

    In astrophysics, the Tolman-Oppenheimer-Volkoff equation constrains the structure of a spherically symmetric body of isotropic material which is in static gravitational equilibrium, as modelled by general relativity....