Tolman-Oppenheimer-Volkoff limit
Encyclopedia
The Tolman–Oppenheimer–Volkoff limit (or TOV limit) is an upper bound to the mass of stars composed of neutron-degenerate matter (i.e. neutron star
s). The TOV limit is analogous to the Chandrasekhar limit
for white dwarf
stars.
in 1939, using the work of Richard Chace Tolman. Oppenheimer and Volkoff assumed that the neutron
s in a neutron star formed a cold, degenerate
Fermi gas
. This leads to a limiting mass of approximately 0.7 solar mass
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
are not well known.
In a neutron star less massive than the limit, the weight of the star is balanced by short-range repulsive neutron-neutron interactions mediated by the strong force and also by the quantum degeneracy pressure of neutrons, preventing collapse. If its mass is above the limit, the star will collapse to some denser form. It could form a black hole
, or change composition and be supported in some other way (for example, by quark degeneracy pressure if it becomes a quark star
). Because the properties of hypothetical more exotic forms of degenerate matter
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
must have mass exceeding the Tolman–Oppenheimer–Volkoff limit. Theory predicts that because of mass loss during stellar evolution
, a black hole formed from an isolated star of solar metallicity
can have mass no more than approximately 10 solar mass
es.:Fig. 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
es.
Neutron star
A neutron star is a type of stellar remnant that can result from the gravitational collapse of a massive star during a Type II, Type Ib or Type Ic supernova event. Such stars are composed almost entirely of neutrons, which are subatomic particles without electrical charge and with a slightly larger...
s). The TOV limit is analogous to the Chandrasekhar limit
Chandrasekhar limit
When a star starts running out of fuel, it usually cools off and collapses into one of three compact forms, depending on its total mass:* a White Dwarf, a big lump of Carbon and Oxygen atoms, almost like one huge molecule...
for white dwarf
White dwarf
A white dwarf, also called a degenerate dwarf, is a small star 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...
stars.
History
The limit was computed by J. Robert Oppenheimer and George VolkoffGeorge Volkoff
George Michael Volkoff, OC, MBE, FRSC was a Canadian physicist and academic who helped, with J. Robert Oppenheimer, predict the existence of neutron stars before they were discovered.-Early life:...
in 1939, using the work of Richard Chace Tolman. Oppenheimer and Volkoff assumed that the neutron
Neutron
The neutron is a subatomic hadron particle which has the symbol or , no net electric charge and a mass slightly larger than that of a proton. With the exception of hydrogen, nuclei of atoms consist of protons and neutrons, which are therefore collectively referred to as nucleons. The number of...
s in a neutron star formed a cold, degenerate
Degeneracy
Degeneracy may refer to:* DegenerationIn science and mathematics:* Degeneracy , a property of quantum states sharing the same energy levels...
Fermi gas
Fermi gas
A Fermi gas is an ensemble of a large number of fermions. Fermions, named after Enrico Fermi, are particles that obey Fermi–Dirac statistics. These statistics determine the energy distribution of fermions in a Fermi gas in thermal equilibrium, and is characterized by their number density,...
. This leads to a limiting mass of approximately 0.7 solar mass
Solar mass
The solar mass , , is a standard unit of mass in astronomy, used to indicate the masses of other stars and galaxies...
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 phases 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 less massive than the limit, the weight of the star is balanced by short-range repulsive neutron-neutron interactions mediated by the strong force and also by the quantum degeneracy pressure of neutrons, preventing collapse. If its mass is above the limit, the star will collapse to some denser form. It could form a black hole
Black hole
A black hole is a region of spacetime from which nothing, not even light, can escape. The theory of general relativity predicts that a sufficiently compact mass will deform spacetime to form a black hole. Around a black hole there is a mathematically defined surface called an event horizon that...
, or change composition and be supported in some other way (for example, by quark degeneracy pressure 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 phases 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 that has such extraordinarily high density that the dominant contribution to its pressure is attributable to the Pauli exclusion principle. The pressure maintained by a body of degenerate matter is called the degeneracy pressure, and arises because the Pauli 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. They have masses ranging from about 3 to several tens of solar masses...
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 a few million years to trillions of years .Stellar evolution is not studied by observing the life of a single...
, 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 unit of mass in astronomy, used to indicate the masses of other stars and galaxies...
es.:Fig. 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 unit of mass in astronomy, used to indicate the masses of other stars and galaxies...
es.