 Quote by mathman
This is the scenario to produce Type Ia supernova, which is an extremely bright standard candle.
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Actually, a Type Ia supernova only comes when a
White Dwarf, not a neutron star, accretes matter from a companion. There are some more specifics required such as the exact carcon/oxygen composition of the WD, etc. but even in accreting white dwarf stars this (Type Ia) is very rare.
 Quote by gonzo
In the GR book I read it says that if a neutron star loses mass (the only way it mentions this can happen is to a binary partner) then it can pass the critical threshhol where the pressure is greater than the gravity and it becomes unstable and explodes.
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I have read a lot of books and papers on stellar evolution and have never heard of neutron stars losing mass to any companion star. At that huge density and surface gravity I can't think of any type of companion star that could pull mass off of a neutron star
other than another neutron star or black hole, where it is possible according to one theory. But, since the surface of a neutron star is a shell of (usually) iron of extreme density, with a neutron "superfluid" inside there is no atmosphere to be lost to even a dense companion.
 Quote by gonzo
It also says that if it is the neutron star that sucks mass from the binary partner, than it will eventually pass the threshhold in the other direction and become a black hole.
It also says the neutron stars are the result of a supernova ... they are what's left after a star explodes (or "bounces" off the neutron star core that forms).
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This part is exactly as described in most sources. If the neutron star passes ~3.2 solar masses by accreting matter it would collapse directly to a black hole.