Where Have All the Submillisecond Pulsars Gone?

The existence of pulsars with spin period below one millisecond is expected, though they have not been detected up to now. Their formation depends on the quantity of matter accreted from the companion which, in turn, is limited by the mechanism of mass ejection from the binary. Mass ejection must be efficient, at least in some cases, in order to produce the observed population of moderately fast spinning millisecond pulsars. First we demonstrate, in the framework of the widely accepted recycling scenario, using a population synthesis approach, that a significant number of pulsars with spin period below one millisecond is expected. Then we propose that significant variations in the mass-transfer rate may cause, in systems with orbital periods larger than 1 hr, the switch-on of a radio pulsar whose radiation pressure is capable of ejecting out of the system most of the matter transferred by the companion and prevent any further accretion. We show how this mechanism could dramatically alter the binary evolution since the mechanism that drives mass overflow from the inner Lagrangian point is still active while the accretion is inhibited. Moreover we demonstrate that the persistency of this ``radio ejection'' phase depends on the binary orbital period, demonstrating that close systems (orbital periods lower than 1 hr) are the only possible hosts for ultra fast spinning neutron stars. This could explain why submillisecond pulsars have not been detected so far, as current radio surveys are hampered by computational limitations with respect to the detection of very short spin period pulsars in short orbital period binaries.