On a theoretical interpretation of the period gap in binary millisecond pulsars

We reexamine evolutionary channels for the formation of binary millisecond pulsars in order to understand their observed orbital period distribution. The available paths provide a natural division into systems characterized by long orbital periods (≳60 days) and short orbital periods (≲30 days). Systems with initial periods of ∼1-2 days, mainly driven by the loss of orbital angular momentum, ultimately produce low-mass helium white dwarfs (≲0.2 M_⊙) with short orbital periods (≲1 day). For longer initial periods (≳ a few days), early massive case B evolution produces CO white dwarfs (≳0.35 M_⊙) with orbital periods of ≲20 days. Common envelope evolutionary channels result in the formation of short-period systems (≲1 day) from unstable low-mass case B evolution producing helium white dwarfs in the range of ∼0.2-0.5 M_⊙ and from unstable case C evolution leading to CO white dwarfs more massive than ∼0.6 M_⊙. On the other hand, the long orbital period group of binary millisecond pulsars arises from stable low-mass case B evolution with initial orbital periods of ≳ a few days producing low- mass helium white dwarfs and orbital periods of ≳30 days and from stable case C evolution producing CO white dwarfs with masses of ≳0.5 M_⊙. The lack of observed systems between 23 and 56 days probably reflects the fact that for comparable initial orbital periods (≳ a few days) low-mass case B and early massive case B evolution lead to very discrepant final periods. We show in particular that the lower limit (∼23 days) cannot result from common envelope evolution. We discuss the importance of a phase of nonconservative evolution where mass and angular momentum can be lost from the system through the ejection of matter from accretion disks around the neutron stars in these systems. This leads to a dependence of pulsar mass on evolutionary history. In particular, most low-mass X-ray binaries with orbital periods of ≳2 days are probably transient; the super-Eddington accretion rates likely during outbursts mean that the neutron stars in such systems gain relatively little mass.