Viscous Elsasser number (and RMS magnetic field) as a function of the ratio of the Brunt-Väisälä frequency to the rotation rate at the outer sphere. Filled and empty markers represent self-sustained and transient dynamos, respectively. The black dashed vertical line and arrow indicate the zone in which the fluid is hydrodynamically unstable. The inset represents a 3D plot of the radial velocity (violet and green isosurfaces are the positive and negative values, respectively) and the radial magnetic field (red and blue isosurfaces are the positive and negative values, respectively) in a run at Pm = 2 and N/Ω_o = 2. The grey arrow points to the run location in the diagram.