How is the halo around the fighter plane caused when it flies at high speed?

A conical cloud produced when an airplane breaks through the sound barrier.

When the speed of an object approaches the speed of sound, the surrounding air is superimposed by sound waves, showing a very high pressure state, so once the object crosses the sound barrier, the surrounding pressure will drop sharply. In humid weather, sometimes the instantaneous low temperature caused by the sudden drop of pressure may make the temperature lower than its dew point temperature, and make the water vapor condense into tiny water droplets, which looks like a cloud to the naked eye. However, because this low pressure zone will return to normal pressure with the increase of the distance between the air and the fuselage, it looks like a cone cloud with the object as the central axis and spreading evenly around.