Tolman-Oppenheimer-Volkoff limit

The Tolman-Oppenheimer-Volkoff (TOV) limit is an upper bound to the mass of stars composed of neutron-degenerate matter (neutron stars). It is analogous to the Chandrasekhar limit for white dwarf 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. This leads to a limiting mass of approximately 0.7 solar masses. [ [http://prola.aps.org/abstract/PR/v55/i4/p364_1 Static Solutions of Einstein's Field Equations for Spheres of Fluid] , Richard C. Tolman, "Physical Review" 55, #374 (February 15, 1939), pp. 364–373.] ^, [ [http://prola.aps.org/abstract/PR/v55/i4/p374_1 On Massive Neutron Cores] , J. R. Oppenheimer and G. M. Volkoff, "Physical Review" 55, #374 (February 15, 1939), pp. 374–381.] Modern estimates range from approximately 1.5 to 3.0 solar masses. [cite journal | last = Bombaci | first = I. | title=The maximum mass of a neutron star | journal=Astronomy and Astrophysics | year=1996 | volume=305 | pages=871–877 | url=http://adsabs.harvard.edu/abs/1996A&A...305..871B ] 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 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, 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 masses. [http://adsabs.harvard.edu/abs/2002RvMP...74.1015W The evolution and explosion of massive stars] , S. E. Woosley, A. Heger, and T. A. Weaver, "Reviews of Modern Physics" 74, #4 (October 2002), pp. 1015–1071.] ^{, 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 masses. [ [http://adsabs.harvard.edu/abs/2003astro.ph..6213M Black Hole Binaries] , Jeffrey E. McClintock and Ronald A. Remillard, arXiv:astro-ph/0306213v4.] [ [http://adsabs.harvard.edu/abs/2006astro.ph.12312C Observational evidence for stellar-mass black holes] , Jorge Casares, arXiv:astro-ph/0612312v1.]

References

ee also

* Tolman-Oppenheimer-Volkoff equation