Title: On a Theoretical Interpretation of the Period Gap in Binary Millisecond Pulsars
Abstract: 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.