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This week we have read of evidence of the Super Massive Black Hole in the centre of the Galaxy 'flaring'.

My understanding is that light cannot escape from a black hole.

My question is: How does a Super-Massive Black Hole 'flare'?

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The flare happens just outside the black hole. Matter which aproaches a black hole but not perfectly straight on doesn't fall into it immediately. It gets pulled around the black hole, just as a satellite is pulled around the Earth.

If the object is a single small particle, that's almost the end of the story. Gravitational radiation and the precise effects of GR will cause its orbit to decay until it eventually falls in, but if it's small enough not much of anything is emitted in the process.

If there are lots of objects in the neighbourhood, or if your obect is something relatively large and diffuse (like a gas cloud, or a planet or star) on the other hand, different things happen. As gravity pulls on different parts of it with different strengths (tides) the object gets stretched and then pulled to pieces, and multiple objects collide and interact in all sorts of ways. Magnetic fields also start to play a role. Some of that matter escapes completely, but much of it ends up in a disk (a little like Saturn's rings, but less well organised) around the hole. By this point all the stretching and collisions have made it very hot, so it shines.

Now even within the disk there are collisions and friction, and they have the overall effect of heating the matter in the disk and pushing some of it out of orbit, so that it falls into the hole, getting even hotter in the process.

So finally we come to a flare. There are probably many kinds of flare-up in this basically unstable setup, but the most obvious is when a particularly large object or cloud of gas falls into the accretion disk, or when some instability in the disk causes a large amount of matter to fall out of the disk. Either way, the larger amount of hotter matter shines more, and we see a flare.

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A supermassive black hole usually has an accretion disc composed of gas, dust and other debris attracted into close orbit. These materials gradually fall toward the black hole, becoming heated by compression and friction as they go. When a large mass of this matter is drawn to the inner edge of the accretion disc just before it disappears for ever into the black hole, the result is a flare up or rapid but temporary brightening of the accretion disc. The light doesn't escape from the black hole itself, but from regions just outside the black hole. There are also high energy particle jets accelerated by the black hole's magnetic field in precisely opposite directions by the black hole's magnetic poles, but again they are emitted before they enter the event horizon, not afterwards.

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