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Comment on Bizarre Star Could Host a Neutron Star in Its Core

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Where does fusion occur then? At the surface of the neutron star? Or is the star supported by the kinetic energy of matter falling onto the inner star?

Both. Red giants exhausted supply of hydrogen in the core, so fusion is switched to shell. This causes pressure/temperature of red giant to drop dramatically and radius to balloon. Neutron stars are incredibly dense, so under certain conditions collision of red giant with neutron start could work out.

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