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When black holes forms out of a supernova do they have a very high velocity ?? Or do they remains at the position of parent star ??

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There is no specific answer to this -- anything from "just sits there" to flys away at high speed is possible.

It all depends on the symmetry of the supernova (SN) explosion. Extensive modelling shows that the explosions can be quite asymmetrical, and if they are the gravitational waves created can give the new black hole (BH) quite a kick. If the explosion is relatively symmetric, the new BH can more or less stay right where it was formed.

Note that if the exploding star is a member of a close binary, the SN explosion will usually give the companion star a high velocity. Before the explosion, a close pair may be rotating around their joint center of mass at 1000 kps. When one star goes SN, it blows most of its mass right out of the system and high velocity. This doesn't change the velocity of the companion star which suddenly is no longer bound and has escape velocity from the star system -- so it more-or-less goes flying off in a straight line at its orbital velocity.

Some of the runaway stars discovered by Gaia are probably companion stars to SNs.

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  • $\begingroup$ The fastest moving group of stars locally were studied, and the researcher concluded that all of them originated from a supernova zone, Perhaps 30,000 years ago If I recall correctly, he also said that the stars were perhaps formed by the supernova pressure wave. $\endgroup$ – com.prehensible May 29 '18 at 7:52

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