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Beyond the Chandrasekhar limit, white dwarfs become extremely hot. As a result, previously unfusable carbon can become fusable, causing nuclear reactions. This leads to a thermal runaway and ultimately a type Ia supernova.

However, this doesn't seem to happen in neutron stars. They can keep gaining mass until they become black holes. After a certain point, shouldn't the immense temperatures cause a thermal runaway like in white dwarfs, leading to their explosion?

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In a white dwarf, the dense matter is not in its lowest energy configuration. Energy can still be extracted from the white dwarf material by fusion, provided it can be ignited.

What exothermic nuclear reactions would there be that could take place in a neutron star? The bulk of the material is in the form of neutrons with a small number of protons and electrons. At these densities, that is the most stable equilibrium composition.

If a neutron star gains mass in a gradual way, then the most likely course of events will be that its radius will decrease (that is what happens in objects supported by degenerate matter) until it reaches a General Relativistic instability where its collapse to a black hole is inevitable (when $R$ is somewhere between 1.25 and 2 times the Schwarzschild radius). It is possible that neutrons may transform before that into additional hadronic degrees of freedom or into quark matter, but these are endothermic processes that suck kinetic energy out of the neutron gas and only hasten the collapse.

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  • $\begingroup$ What do you mean by "the dense matter is not at its lowest energy configuration"? Aren't the electrons occupying every energy level between the lowest possible one and the Fermi energy? $\endgroup$ May 3 '16 at 20:20
  • $\begingroup$ @SirCumference Indeed the electrons are. But the energy density of the gas is the sum of the energy density of the nuclei plus the electrons.The energy density of the gas can in principle be lowered by fusing the carbon nuclei. $\endgroup$
    – ProfRob
    May 3 '16 at 20:47
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    $\begingroup$ @SirCumference (i) Because there isn't any carbon; (ii) because fusing all the carbon in a white dwarf yields more energy than the gravitational binding energy of the star. $\endgroup$
    – ProfRob
    May 4 '16 at 5:59
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    $\begingroup$ @SirCumference The collapse of a O/Mg/Ne core is rapid (1 second) and results in a type of core-collapse supernova, leaving a neutron star remnant. Collapse is not a feature of type Ia thermonuclear detonations. $\endgroup$
    – ProfRob
    May 10 '16 at 20:13
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    $\begingroup$ @SirCumference Isn't this straying off your original question? Because C/O WDs ignite before they reach a high enough density to collapse. I have answered this at astronomy.stackexchange.com/questions/14740/… $\endgroup$
    – ProfRob
    May 10 '16 at 20:30

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