That actually is water vapor around the fighter.
It is created by the sudden extreme drop in air pressure behind the compressed shockwave. Since the pressure suddenly drops, the air cools instantly, and because cool air can hold less moisture than warm air, the moisture condenses into visible water vapor, but only for an instant.
When the shape of the object travelling through the air is faster than the speed of sound in the air, the compacted air has no time to dispand and the shockwave stays. That front does not break apart as it expands from the object - if it would, there would be no sonic boom.
I hope this explanation is comprehensible..
There is an interesting analogy to
Cherenkov radiation.