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When the two neutron stars merged in the latest event, large amounts of gamma rays were emitted. Given that their deorbitting is a result of gravitational wave production, where does the energy for the gamma rays come from?

The only sources I can think of are the rotational kinetic energies of the merging stars or the potential energy released by the final collapse into a single spherical mass.

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Not Nuclear fusion;
There is also a huge amount of nuclear fusion that creates heavy elements from all the iron there is in neutron star: they in fact are not only made of neutrons. But as said in comment, building of heavier elements rather consumes energy than it generates some.

Not sure scientists has a clear agreement on how this works.

Gravitational collapse

For example I found this (rather old) abstract which states it could be a result of gravitational collapse, without singularity (since here the result of the merger might not be a black-hole, or the lightest ever: around 2.7 solar masses!)

theoretical developments (string theory, quantum gravity, critical collapse), which suggest that complete gravitational collapse can occur without singularities or event horizons

Thermonuclear event again: fission

From Space.com, they say Kilonova energy could be explained by rapid atomic decay of heavy elements

The mergers of dense cosmic bodies that are thought to cause short gamma-ray bursts can also blast out neutron-rich gas that rapidly generates heavy elements such as gold and platinum, scientists say. These "r-process" elements can undergo radioactive decay and release an enormous amount of energy — 1,000 times or so that given off by stellar explosions such as novas. These powerful events are thus known as "kilonovas"

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    $\begingroup$ My understanding is that fusion of elements heavier than iron absorbs energy rather than emitting it? I would think there would be another mechanism for turning the potential and kinetic energy of the colliding neutron stars into gamma ray emission (really, really hot accretion disk?) $\endgroup$ – antlersoft Oct 17 '17 at 15:10
  • $\begingroup$ I read the article on gravitational collapse you mentioned. It would have been nice to see a mathematical treatment that justifies the posited "red hole" the author describes or at least a citation to such. Without that, it's difficult to see that as a likely scenario. I do like the idea that some of the matter from one or both stars is ejected as that address with the spectral analysis that shows heavier elements in the mix. $\endgroup$ – C Teegarden Oct 18 '17 at 21:49

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