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What is the difference between a neutron star and a white dwarf? I know that both are very dense even if they go through different phases.

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In a neutron star, the force of gravity is strong enough to press the protons and electrons together to form neutrons {1}, White dwarfs are only very compact. With even more mass, you get a black hole.
All three types are outcomes of star death, when the failing fusion in the middle of a star is no longer able to counteract gravity. What a star become when it collapses is depending on its mass.

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  • $\begingroup$ White dwarfs are dense enough to force the electrons out of their shells--you have electrons and bare nuclei, not complete atoms. $\endgroup$ – Loren Pechtel Dec 17 '15 at 1:28
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    $\begingroup$ @LorenPechtel The same can be said about the plasma in the Sun. $\endgroup$ – Hohmanfan Dec 17 '15 at 1:42
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    $\begingroup$ True, but the sun is held up by the pressure from it's heat. A white dwarf isn't. Note that the inside of a star can become basically a white dwarf. $\endgroup$ – Loren Pechtel Dec 17 '15 at 1:48
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A white dwarf is less than 1.44 solar masses, and is held up by electron degeneracy pressure, the rule in quantum mechanics that says electrons strongly resist being squeezed together. They're made of highly compressed but still more or less normal matter, mainly carbon and oxygen. Dispite their mass they're only about as big as Earth, meaning one teaspoon of their material would weigh several tons.

After 1.44 solar masses, electron degeneracy is not strong enough to overcome gravity. At this point, it collapses even further, electrons and protons merge to neutrons, forming a neutron star, only the size of a city, and composed almost entirely of neutrons. One teaspoon of neutron star matter would weigh a billion tons. Neutron stars are held up by neutron degeneracy pressure, which is far, far stronger than for electrons.

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Additionally, others haven't said it, is that a neutron star is also much smaller than a white dwarf:

White dwarfs are Venus- and Earth-sized (e.g. about 7000 mi / 11000 km in diameter) while neutron stars (and stellar black holes) have the size of the Martian satellites Phobos and Deimos (e.g. about 10 mi / 16 km in diameter).

The neutron star (or maybe a quark star) PSR B0943+10 is the smallest known star at all, at 5.2 km (3.2 mi) diameter. It is also one of the least massive known stars. Anyway, it is orbited by two known gas giants.

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Please see this article that describes the Chandrasekhar limit. Any star remnant more massive than the Chandrasekhar limit, 1.4x sun mass, will become neutron star or black hole. Otherwise it will become white dwarf.

This mass limit is the threshold at which gravitational will overcome electron degeneration pressure, causing the electrons to join the nucleus. The protons in the nucleus combine with the electrons to become neutrons. Thus the term neutron star.

When the mass of the neutron star surpasses the level at which the escape velocity for the neutron star exceeds the speed of light, then even light cannot escape its gravitation, thus becoming a black hole.

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  • $\begingroup$ The Chandrasekhar limit is relevant, but white dwarfs that exceed the limit are too small to become neutron stars or black holes. They do go supernova, but they don't become neutron stars or black holes. That requires a larger mass and a different process. $\endgroup$ – userLTK May 27 '17 at 23:36
  • $\begingroup$ My bad , I corrected it to say star remnant. The initial star mass pre-collapse is much larger. $\endgroup$ – Ed Kideys May 27 '17 at 23:56
  • $\begingroup$ It's still incorrect in more than one way. You need a LOT more than 1.4 solar masses to create a neutron star. The "remnant" is a bit confusing, but if you look at the Neutron star as the remnant, then the remnant can be less than 1.4 solar masses and be a neutron star. See here: physics.stackexchange.com/questions/143166/… Your red giant statement is also strange. Most stars above a certain mass go red giant (not 100% sure about the largest ones). $\endgroup$ – userLTK May 28 '17 at 13:47
  • $\begingroup$ Ok, I corrected so we are referring to star remnants; ie what is left of the star core after red giant and planetary nebula or supernova explosion. $\endgroup$ – Ed Kideys May 28 '17 at 16:59

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