What are the upper and lower limits for the mass of a neutron star? - and why?
A neutron star has a mass between 1.4 and 3 times the mass of the Sun.
When a star uses up its available fusion fuel, its mass can no longer be supported by internal gas pressure. While outer layers are blown away, the resulting collapsed core will result in either of a white dwarf, a neutron star, or a black hole, depending on its final mass.
If the core mass is less than about 1.4 times that of the Sun, the result is a white dwarf. It is supported by "electron degeneracy" pressure, a quantum mechanical concept based on the Pauli exclusion principle which restricts the number of electrons occupying the same energy state.
If the mass is greater than 1.4 times that of the Sun, electron degeneracy is not enough to overcome the force of gravity and a neutron star can result. A neutron star is basically a giant neutron, with all matter compressed to a maximum density allowed for matter. A single teaspoon of neutron matter would weigh billions of tons.
If the mass is greater than about 3 times that of the Sun, even a neutron star cannot resist the force of gravity and a black hole is created. It has an "event horizon", inside of which nothing can escape, but has no physical size of its own and can only be described as a "singularity".
Paul Walorski, B.A., Part-time Physics/Astronomy Instructor
'As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.'