  Observations show that massive star formation quenches first at centers of
galaxies. To understand quenching mechanisms, we investigate the thermal and
nonthermal energy balance in the central kpc of NGC1097- a prototypical galaxy
undergoing quenching- and present a systematic study of the nuclear star
formation efficiency and its dependencies. This region is dominated by the
nonthermal pressure from the magnetic field, cosmic rays, and turbulence. A
comparison of the mass-to-magnetic flux ratio of the molecular clouds shows
that most of them are magnetically critical or supported against gravitational
collapse needed to form cores of massive stars. Moreover, the star formation
efficiency of the clouds drops with the magnetic field strength. Such an
anti-correlation holds with neither the turbulent nor the thermal pressure.
Hence, a progressive built up of the magnetic field results in high-mass stars
forming inefficiently, and it may be the cause of the low-mass stellar
population in the bulges of galaxies.
