What conditions would lead to this event around the black hole in the Pictor A galaxy?

This is a clear example of an astrophysical jet, in this case, most likely a relativistic jet. In short, an accretion disk forms around a black hole (supermassive or otherwise). Matter is pulled towards the black hole and further energized, before being accelerated into a jet emanating from the black hole's poles. Two different mechanisms have been proposed for the formation of jets:

• The Blandford-Znajek process requires that a magnetic field forms (from the accretion disk) that is centered around the black hole. Charged particles then move along the field lines, into jets. I recently wrote an answer about the details (see How does an accreting black hole acquire magnetic fields?). For this process to work, you need an accretion disk. It is generally considered the most likely explanation for black hole jets.


• The Penrose process takes rotational kinetic energy from the ergosphere outside the event horizon and gives it to particles moving in jets. Note that this does not rely as heavily on the accretion disk as the Blandford-Znajek process does. For this process to work, you need a rotating black hole surrounded by some matter, likely in a disk.

The hotspot is, to me, much more interesting. It reminds me of structures seen around young stars: bipolar outflows (streams of gas that can form shock waves) and Herbig-Haro objects (the results of shock waves from relativistic jets. Obviously, the mechanisms are different, so no clear analogy can be drawn. But what is interesting about bipolar outflows and Herbig-Haro objects is that the shock waves produced therein result from collisions with the interstellar medium.

If a similar mechanism were to cause the shock waves by the hotspot, then we could conclude that the jets have hit the intergalactic medium. But I don't think this is necessarily the case, in part because of just how long these jets are prior to the formation of the hotspot. One would think that if the hotspot and shock waves are because of collisions with the intergalactic medium, the jets would be much shorter, because they would likely have reached higher density regions of it sooner. So that's why I find it interesting, and why I can't give you a good reason as to why the hotspot formed where it did, or the precise reason for it being there at all.