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 d) and short orbital periods (< 30 d). Systems with initial periods 1 - 2 d ultimately produce low mass He white dwarfs with short orbital periods (< 1 d). For longer initial periods (> few days), early massive Case B evolution produces CO white dwarfs with orbital periods < 20 d. Common envelope evolution result in short period systems (P < 1 d) from unstable low mass Case B evolution producing He white dwarfs, and from unstable Case C evolution leading to CO white dwarfs. On the other hand, the long orbital period group arises from stable low mass Case B evolution with initial periods > few days producing low mass He white dwarfs and periods > 30 d, and from stable Case C evolution producing CO white dwarfs. The lack of observed systems between 23 and 56 days probably reflects the fact that for comparable initial orbital periods (< 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 d) cannot result from common-envelope evolution.