A gas turbine engine has a core engine including: a compressor, combustion equipment which receives compressed air from the compressor, a circumferential row of nozzle guide vanes, and a turbine. The nozzle guide vanes defines a throat receiving hot working gases from the combustion equipment into the turbine. The gas turbine engine further has an air system which is switchably operable between an on-position which opens a diversion pathway along which a portion of the compressed air exiting the compressor bypasses the combustion equipment to join the hot working gases at re-entry holes located between the nozzle guide vanes and a rotor at the front of the turbine, thereby increasing the semi-dimensional mass flow ω(T30)0.5/(P30) of the core engine at the exit of the compressor, and an off-position which closes the diversion pathway, thereby decreasing the semi-dimensional mass flow of the core engine at the exit of the compressor.