So I know that the formation of a supernova has been observed and that we have taken images of blackholes, however, has the formation of a blackhole ever been observed. How do we observe it?
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1$\begingroup$ FWIW, the neutron star merger that was detected via gravitational waves as well as by various electromagnetic instruments, GW 170817, was originally thought to have resulted in a black hole, but later analysis shows that the remnant is consistent with a large neutron star. "The observed frequencies below 1 kHz indicate a hypermassive magnetar rather than a black hole." $\endgroup$– PM 2RingCommented Feb 12, 2020 at 10:52
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“We think that ‘The Cow’ is the formation of an accreting black hole or neutron star,” said Northwestern’s Raffaella Margutti, who led the research. “We know from theory that black holes and neutron stars form when a star dies, but we’ve never seen them right after they are born. Never.” ... Another team of astronomers, led by Paul Kuin from, an astrophysicist at University College London, came to a different conclusion. They think that the Cow is a star that’s been ripped apart in what’s called a “tidal disruption event.” Information on that here.
There are only 25 Stellar black holes and candidates.
If 'The Cow' was a dwarf star being consumed by a blackhole then the most likely occurrence that has been observed is N6946-BH1. "Candidates outside our galaxy come from gravitational wave detections. The disappearance of N6946-BH1 following a failed supernova in NGC 6946 may have resulted in the formation of a black hole." The list of other ones is here and for information on the disappearance of N6946-BH1 here.
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1$\begingroup$ Reading your references it seems like N6946-BH1 is likely the most relevant answer to this question, since a leading hypothesis is that the observed event involved the formation of a stellar mass black hole. You might want to revise your answer to reflect this. $\endgroup$ Commented Feb 11, 2020 at 15:55
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$\begingroup$ Thank you! That was very interesting, I haven't read the paper on the counter argument for 'The Cow' being a black hole consuming a dwarf star just yet but I will! $\endgroup$ Commented Feb 12, 2020 at 0:40
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Yes, when during the 1980s, scientist observe that there was a massive star that explode into a supernova, releasing large amounts of matter into space. Then they use signals to detect remnants from the explosions but couldn't find any.
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1$\begingroup$ Are you talking about SN 1987A in the Large Magellanic Cloud? It's expected that the remnant from that supernova is a neutron star, but if enough material fell back onto the neutron star it might have turned into a black hole, as the Wikipedia article explains. $\endgroup$– PM 2RingCommented Feb 12, 2020 at 11:53