Wingtip Vortex: Heavy, Clean, Slow - Why?

You get the strongest wingtip vortices when an aircraft is flying heavy,
clean and slow. But why?

Re slow: the airplane stays aloft in effect because its wings are pushing air
down. If it's moving fast, the momentum of the displaced air is spread over a
larger distance, so it's more diffuse. Slower means there's much more energy in
the air.

Not so sure about dirty v clean, but at low speeds clean isn't very effecient
at generating lift. That means larger angles of attack, more air displaced,
maybe a bigger vortex.