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When can a supernova leave a black hole instead of a pulsar?

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Whether a supernova leaves behind a pulsar—a rapidly spinning neutron star—or a black hole depends on the mass of the star's remaining core after the explosion.12

During the collapse of a massive star, the core's ability to support itself against gravity fails. If the resulting core mass is less than approximately three solar masses, the collapse is halted by the density of neutrons, forming a neutron star. These objects can be observed as pulsars, which emit radiation at extremely regular intervals.12

However, if the core mass exceeds this threshold of about three solar masses, the gravitational collapse is too intense to be stopped by the formation of a neutron star. In this case, the core continues to compress into an even smaller, denser body known as a black hole, from which not even light can escape.12