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2 black holes are about to merge to become a larger black hole. Does this mean it'll become a quasar?

From what I know, quasars are supermassive black holes or a collective amount of them. So, if it merges and becomes a supermassive black hole, does this mean that it is a quasar? If the size is smaller than what would be considered as a supermassive black hole would it not be a quasar?

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Does 2 merging black holes necessarily make a quasar?

Basically no. While the merging of 2 black holes is a very interesting event, a quasar is what you get when 1 very large black hole eats a whole bunch of matter and the light from the quasar comes from the intense heat and interactions from that tightly bound, rapidly spiraling and very excited matter.

Quasar's were probably most common when galaxies are young but there are a few more recent ones (see examples in comments). Quasar

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If the size is smaller than what would be considered as a supermassive black hole would it not be a quasar?

Almost all large galaxies have a super-massive black hole in their center. Source. The sizes vary with the size of the galaxy. Quasars are much more rare, only in a few galaxies.

As for the specific size of black hole that can form a quasar, credit to Rob Jeffries below.

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    $\begingroup$ Some factual errors here. Quasars are young, they predominantly occur at redshifts of 2-3. IC 2497 may be the nearest quasar, though has recently turned off. This is only about 730 million light years away. A more active example is the famous 3C 273 which is at a distance of 2.5 billion light years. A minimum black hole mass for a quasar of a given luminosity could be estimated from the Eddington luminosity, which is sort of the maximum luminosity a quasar could have for a given mass of black hole and equals $3.2\times10^{4} (M/M_{\odot})$ solar luminosities. $\endgroup$ – Rob Jeffries Oct 13 '15 at 15:44
  • $\begingroup$ One question. What size black hole corespondent to 32,000 solar luminosity? Luminosity and size not being consistent. $\endgroup$ – userLTK Oct 13 '15 at 22:55
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    $\begingroup$ Well a 1 solar mass black hole could produce this (small) luminosity. The event horizon would have a radius of 3km, and is directly proportional to the mass. $\endgroup$ – Rob Jeffries Oct 13 '15 at 23:08

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