Question 36.4: Above what mass will a neutron star become unstable?...

The high gravitational fields and compact nature of neutron stars mean that we really ought to include the effects of general relativity and the strong nuclear interactions. However, ignoring these, we can make an estimate on the basis that the neutron star will become unstable when the neutrons themselves become relativistic. By analogy with eqn 36.19, and taking Z/A = 1, we have the maximum mass{}^{3} as

M\gtrsim \left(\frac{Z}{Am_{p} } \right) ^{2} \frac{3\sqrt{\pi } }{2 } \left(\frac{\hbar c}{G} \right) ^{3/2} ≈ 1.2 M_{\odot } ,           (36.19)

M\gtrsim \frac{3\sqrt{\pi } }{2m^{2} _{p} } \left(\frac{\hbar c}{G} \right) ^{3/2} ≈ 5 M_{\odot } .           (36.22)

{}^{3}Including general relativity reduces the maximum mass to about 0.7 M_{\odot}, but including a more realistic equation of state raises the maximum mass up again, to somewhere around 2–3 M_{\odot}.