Where may ultrafast rotating neutron stars be hidden?

The existence of ultrafast rotating neutron stars (spin period P less than or similar to1 ms) is expected on the basis of current models for the secular evolution of interacting binaries, although they have not been detected yet. Their formation depends on the quantity of matter accreted by the neutron star which, in turn, is limited by the mechanism of mass ejection from the binary. An efficient mass ejection can avoid the formation of ultrafast pulsars or their accretion-induced collapse to a black hole. We propose that significant reductions of the mass transfer rate may cause the switch-on of a radio pulsar phase, whose radiation pressure may be capable of ejecting out of the system most of the matter transferred by the companion. This can prevent, for long orbital periods and if a sufficiently fast spin has been reached, any further accretion, even if the original transfer rate is restored, thus limiting the minimum spin period attainable by the neutron star. We show that close systems (orbital periods P-orb similar to 1 hr) are the only possible hosts for ultrafast spinning neutron stars. This could explain why ultrafast radio pulsars have not been detected so far, as the detection of pulsars with very short spin periods in close systems is hampered, in current radio surveys, by strong Doppler modulation and computational limitations.