TOV limit

The Tolman–Oppenheimer–Volkoff limit (or TOV limit) (also referred to as the Landau–Oppenheimer–Volkoff limit (or LOV limit)) is an upper bound to the mass of stars composed of neutron-degenerate matter (i.e. neutron stars). The TOV limit is analogous to the Chandrasekhar limit for white dwarf stars. It is approximately 1.5 to 3.0 solar masses, corresponding to an original stellar mass of 15 to 20 solar masses. Observations of GW170817, the first gravitational wave event due to merging neutron stars, suggest that the limit is not greater than ~2.17 solar masses.

The idea that there should be an absolute upper limit for the mass of a cold (as distinct from thermal pressure supported) self-gravitating body dates back to the work of Lev Landau. In 1932, he reasoned based on the Pauli exclusion principle. Pauli's principle shows that the Fermionic particles in sufficiently compressed matter would be forced into energy states so high that their rest mass contribution would become negligible when compared with the relativistic kinetic contribution (RKC). RKC is determined just by the relevant quantum wavelength ${\displaystyle \lambda }$, which would be of the order of the mean inter-particle separation. In terms of Planck units, with the reduced Planck constant ${\displaystyle \hbar }$, the speed of light ${\displaystyle c}$ and Newton's constant ${\displaystyle G}$ all set equal to one, there will be a corresponding pressure given roughly by ${\displaystyle P=1/\lambda ^{4}}$. That pressure must be balanced by the pressure needed to resist gravity. The pressure to resist gravity for a body of mass ${\displaystyle M}$ will be given according to the virial theorem roughly by ${\displaystyle P^{3}=M^{2}\rho ^{4}}$, where ${\displaystyle \rho }$ is the density. This will be given by ${\displaystyle \rho =m/\lambda ^{3}}$, where ${\displaystyle m}$ is the relevant mass per particle. It can be seen that the wavelength cancels out so that one obtains an approximate mass limit formula of the very simple form

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