Radio Ejection and Bump-related Orbital Period Gap of Millisecond Binary Pulsars

The monotonic increase of the radius of low-mass stars during their ascent on the red giant branch halts when they suffer a temporary contraction. This occurs when the hydrogen-burning shell reaches the discontinuity in hydrogen content left from the maximum increase in the convective extension, at the time of the first dredge-up, and produces a well known "bump" in the luminosity function of the red giants of globular clusters. If the giant is the mass-losing component in a binary in which mass transfer occurs on the nuclear evolution timescale, this event produces a temporary stop in the mass transfer, which we call "bump-related" detachment. If the accreting companion is a neutron star, in which the previous mass transfer has spun up the pulsar down to millisecond periods, the subsequent mass transfer phase may be altered by the presence of the energetic pulsar. In fact, the onset of a radio ejection phase produces loss of mass and angular momentum from the system. We show that this sequence of events may be at the basis of the shortage of systems with periods between ~20 and ~60 days in the distribution of binaries containing millisecond pulsars. We predict that systems that would be discovered with periods in this gap should preferentially have magnetic moments either smaller than ~2 × 1026 or larger than ~4 × 1026 G cm3. We further show that this period gap should not be present in Population II.