It's from the afterburners, and Concorde is exempt from noise regs due to it's tiny fleet.
Along with the noise-abatement procedures on t/o, (15% engine throttle-back and when required, avoiding populated areas-as happens after t/o from JFK).
Also Concorde has limits on the times it can operate out of airports.
Actually the noise abatement procedures are what beat the movement to keep it out of JFK, and other noisey jets around in the late 70's, such as 707's, also adopted a similar procedure.
At first the anti-Concorde lobby said Concorde had 'cheated', but shut up when other noisey aircraft reduced their noise too.